This web page was written by Craig L. Zirbel of the Department of Mathematics and Statistics at Bowling Green State University, for graduate students taking Math 5910, Curriculum Analysis and Classroom Behaviors (the class about How to Teach Math). It is posted publicly because the thoughts here may be helpful for others who are teaching first year college mathematics. It is organized in a "just in time" fashion, with the most important things first. It is not organized like a textbook, I do not try to treat each topic comprehensively the first time it is introduced. Opinions expressed here are my own, and I bear responsibility for their correctness or inaccuracy. Suggestions for corrections are welcome!
Later in the semester
Activities that replace lectures collects together things you can print and have your students work on, instead of giving a lecture. Various types of inquiry learning. Separate page for calculus activities.
Introduction to Statistics has some ideas for teaching an introductory statistics course
Teaching specific topics contains some ideas for teaching specific things
Technology for teaching Mathematics tells how to use various computer tools to improve your teaching of mathematics.
Things to learn is a broader collection of things that I have developed over the years
I would like to help your first day of teaching go as smoothly as possible. This section will help you prepare. In a later section, you will find some suggestions for the first day of class.
Here are some generalizations about the first-year students you will be teaching. Please be careful to note that every student is different; some have very good study skills, some have very good algebra skills, etc. Still, these descriptions may help you understand your students as a whole. This is especially true if you are unfamiliar with the American high school system. Also, not all of the students in your class will be freshmen, but some of these comments also apply to sophomores, juniors, and seniors as well.
"Math brain". Many students believe that they are "bad at math". They think that their brain is different from the brains of people who are "good at math". As a result, they have settled for low grades in math and they don't try very hard to do better. It would be much better for students to realize that, if they have been placed into a certain course, they have an adequate background and adequate mental abilities to succeed in the course. What they really need is to work hard, not wish that they had been born with a different brain. They need to come to class every day, they need to do all of the homework, they need to come to their teacher's office hours or visit the tutoring center or hire a tutor. They need to pay attention in class, take good notes, go over their notes after class, and they need to read the textbook.
Math anxiety. Many students suffer from what is called "Math anxiety." Being asked to solve math problems makes them nervous, especially on quizzes and tests. They do not enjoy mathematics. Maybe math makes them feel stupid, and they are very afraid of seeming to be stupid. There are many resources to show you how to help your students deal with math anxiety, just start searching the web.
Weak and strong high schools. Students come from a wide variety of high schools. Some are challenging, strong high schools, but some are weak. Most schools have at least a few poor math teachers, who reduce math to a set of rules that you follow without knowing why, and so have not done very well at getting students to think independently.
No standard high school math curriculum. Unlike in other countries, every state and every city is able to run their schools differently; there is no national curriculum, there is no standard high school curriculum. Besides this, different students take different math courses in high school. Some students have had Algebra I, Geometry, Algebra II. Some have also had Trigonometry in high school, some have had Precalculus, and a few have had Calculus. But that doesn't mean that they know Algebra! In other high schools, the math courses are called Integrated Mathematics I, II, and III. These courses have algebra, geometry, statistics, and more mixed together every year, so that you don't take a whole year off from algebra when you take geometry.
Poor study skills. For many students, high school classes are pretty easy. If the students listen in class and do the worksheets they are given, they'll get B's on their exams and be happy. Many students are not used to reading their textbooks, not used to doing much homework. Many expect to get a good grade on their homework if they scribble down some answers and hand it in, even if the answers are wrong. They do not study consistently; they wait until the night before the exam and study for hours, but it doesn't help much.
Easy high school graduation requirements. Although there is no standard high school curriculum, the state of Ohio requires students to pass the Ohio Graduation Test. The OGT is an exam that students take in the spring of their sophomore year or later, if they don't pass the first time. Their high school graduation, and school funding, is dependent on the results of their OGT scores in the five core subject areas. In mathematics a level of proficient is around 50%. The majority of the questions are at the Algebra I level, with some Geometry. Furthermore, students may be taught straight to the test or "spoon fed", so they are not used to being independent thinkers. After the OGT, there is no other exit exam (at this time), so the material taught after Geometry can vary greatly between school districts and from student to student.
ACT math scores. The ACT (pronounced A-C-T) and SAT (pronounced S-A-T) are standardized nationwide tests that students take in their senior year in high school. Many of the students in Math 99 will have scored below 22 on the ACT, even though 22 is the target that the State of Ohio has set for students to take College Algebra.
Math placement. For most students at BGSU, for algebra and calculus courses, their mathematics placement is determined by their high school GPA and their ACT Mathematics test score. Students with a low ACT Math score are simply placed into Math 99 in the Math Emporium. Students are not allowed to take a higher-level course than where they place. No placement system is completely accurate; some students may not be ready for your course. Some students may be ready for the next higher course. Math 1150, Introduction to Statistics, has essentially no prerequisite or placement requirement. In that course, students' mathematics skills may be very weak. On the other hand, some students in that class have already learned all the material in high school!
First generation in college. About 40% of BGSU have parents who did not go to college. About 60% have parents who did not graduate from college. In some families, students are advised NOT to go to college because it is thought to be a waste of money. These things may help to explain the fact that students think it's no big deal to miss class. But then they get behind and never catch up.
Wrong expectations about grading. Students think that if they miss an exam they can take a makeup exam later. We don't offer makeup exams. Most students think that they can turn homework in late, but most teachers won't accept it late. Most students expect that if they do poorly on their exams or quizzes or homework, there will be an opportunity later in the semester to save their grade by doing extra credit. We do not offer extra work for extra credit, especially not to individual students whose grade is low. Or when we do offer extra credit, it is for the purpose of going above and beyond course expectations; one instructor gave this as extra credit problem: Give an example of two functions (not the identity function) which are not inverses but for which f(g(x)) = g(f(x)). No one solved it. Most students expect that grades will be "curved" so that most students will get an A, B, or C. We do not curve grades, and we have no qualms about giving D's and F's to every student who deserves it, even if that is more than half of the class. Lots of students think that they can just study really hard for the final exam and bring their grade up to passing. In fact, students usually do worse on the final exam than on the mid-term exams.
Reliance on their calculator. Most students have not done much mental or pencil-and-paper arithmetic in high school. They rely on their calculator for arithmetic such as 7*8, 14+19, even 3*(1/3). They are particularly poor at manipulating fractions, not knowing how to add 2/7 and 4/5, and not knowing how to divide 2/7 by 4/5.
Not math majors. First-year graduate students generally teach Math 99, 1150, 1220, 1280, or 1310. Students in MATH 99, 1150, and 1220 are almost never mathematics majors. They are taking the course because their major (education, psychology, business, nursing, etc.) requires them to take a math course. The students generally are not very interested in mathematics. Students in Math 1150 are highly unlikely to become Statistics majors. Some of the students in Math 1280 are mathematics majors, some are future high school and middle school teachers, and others are science majors (biology, computer science, etc.). They take Math 1280 only to prepare for Math 1310/1340.
A course syllabus tells students basic important information about the course. You should post it on Canvas on or before the first day of class. It takes a few hours at least to make a good syllabus. Fortunately, on Thursday before the first day of classes in August, there will be meetings with your course coordinators, who will tell you how to get a template syllabus for the course you are teaching. You can make a few small changes and be ready to go. You will also learn something about the course you are teaching. For most 1000-level mathematics courses at BGSU, you should have access to a Canvas community where various documents from your coordinator are stored.
Require attendance. On your syllabus, I think it is important to have a policy which requires students to attend class, and that penalizes students for missing more than 2 or 3 classes. Otherwise, it is harder to convince students that they need to come to class. There are many ways to do this. It does not need to be a harsh penalty, just subtracting 20 points out of 600 for poor attendance is enough to encourage students to come to class. Unfortunately, it won't be successful with everyone! Avoid making a policy whereby students immediately lose a whole letter grade for missing a smallish number of classes. Those can work out very badly.
Important dates. It is very important to list the dates and times of the common exams if you are teaching Math 1280. It is very important to list the date and time of the final exam. Every semester, there are several students who miss exams and claim that they were never told when they were, and then it's hard to deal with them. This is especially true with the final exam. Make sure they have no excuse for missing an exam.
Missed exam policy. Every course has a different policy on missed exams. In most cases, if a student misses an exam for any reason, they cannot take a makeup exam. You need to know the policy in the course you are teaching, and your students need to know it as well.
Contact information. On the syllabus, tell them how to contact you: your office number, your office telephone number (not your cell phone number), and your email address.
Office hours. If you have already scheduled office hours, tell what days and times they are. You might want to wait to schedule office hours until you know the schedule of seminars in the department. You may want to schedule, say, 3 office hours at set times, and leave yourself some time to schedule meetings with students who need to see you but can't make it to your scheduled office hours. You can ask students what time(s) would work well for them. A good way to do that is to have them write their initials on a time grid: Time grid for office hours.docx That said, it's a good idea to have office hours after class (unless you teach an evening class) so you can remind students every day that office hours are later that day. They are more likely to come then.
Academic honesty policy. You will save yourself a lot of trouble if you make sure that your syllabus contains an "academic honesty policy" of some sort. The university has clear policies about cheating on examinations; we will talk about those in Math 5910. What is not so clear is what is expected of students when they turn in homework. Often, it makes sense to encourage students to work together, and to encourage them to go to the Math and Stat Tutoring Center in the BGSU Learning Commons to work on homework, where they can ask tutors and other students for help.
The trouble is that you will sometimes get two or more students whose homework is so similar that you conclude that one student did the work and the other one simply copied it. You will want to penalize the student who copied, and will probably want to penalize the one who allowed his/her work to be copied. An academic honesty policy allows you to penalize students who work more closely together than you allow.
Here is a policy you could use, or modify as you like:
If you have trouble doing the homework, either come and see me, go to the Learning Commons in Jerome Library, or find someone from the class to work with. You are encouraged to work together to figure out how to do the homework, but once you figure out how to do the problems, you must write your answers on your own, so that they are different from what other students write. Copying homework will be closely monitored and will not be tolerated. Also, in your homework, keep more decimal digits than the answer key in the back of the book.
The last line here is very helpful in preventing people from simply copying down the answer in the back of the book without doing the work. I believe it is also good teaching practice to have students keep a lot of decimal digits, but we'll talk more about that later. You should think about how much you would like students to work together and write an academic honesty policy that you like.
Making paper copies of the syllabus. Syllabi these days tend to be quite long, since they contain many sections about university policies. It is probably best to simply post the syllabus electronically on Canvas. Use the computer projector to show it to the students on the first day of class and mention some of the most important facts, like the number of exams, dates of exams if known, the distribution of points in the class between homework, quizzes, exams, attendance, and any other components.
Make up a syllabus for the course, as described above. Find and follow the generic syllabus that the course coordinator has made up.
Plan out how the first day of class will go. Write down what you want to say, because it is very easy to forget important things when you are talking to a class the first time, and it is easy to repeat things that don't need to be repeated. Consider doing a first-day project, see below.
Relax! The class will go just fine.
Prepare some notes for the first few topics you will teach. The more you can prepare now, the easier your semester will be. On the other hand, it is difficult to prepare before you know what your students' mathematical background is.
Assign some homework on the first day of class, due on the second day of class. There are good reasons to assign a fairly large amount of homework early in the class and plan to collect it and grade at least some of the problems. It gets students working and you get very quick feedback about how well they can do problems. You can assign less homework once you see that they are developing good work habits.
It is a good idea to work through some of the homework problems yourself. This way, you really understand what you are asking them to do, and you will realize some things that need to be mentioned in class.
Consider the idea of requiring all students to visit you in your office in the first week of class. Students are usually not very busy then. Have a sign-up sheet with many short time slots, 10 or 15 minutes each. Have two or three people sign up for the same time slot; you can talk with a small group all at once, and you get through everyone more quickly that way. The point is to make personal contact with them right away, and to make sure that they all know where your office is.
Schedule a quiz for late in the first week of class, or for the third day of class if you meet just twice a week. It's good practice to have quizzes on Fridays, if you teach on Fridays.
The first day of class is usually uncomfortable for the students and the instructor, especially an instructor who has never taught before. It is the best day to set the tone for the class, to start to tell the students what you expect of them. However, instructors often use this day to read the roster (which always results in mis-pronouncing students' names and otherwise boring them) and start with Section 1.1 of the textbook, which is what happens in every class the students attend on that day, and so is pretty dull. Also, one rarely hears students talking on the first day of class, since they don't know anyone in the class yet.
I like to start class in a different way, one which gets students working together, gets them talking, and which communicates my expectations to them immediately. It avoids reading the roster to the whole class and instead lets you talk with students in small groups. The instructor does not need to talk to the class very much, which is very helpful if it is your first time teaching in English.
I begin class by introducing myself and welcoming the students to Math XXXX. I don't spend a lot of time giving an overview of the course. I don't tell my whole life story; I can tell them about myself on the second or third day of class if I want to. I hand out the syllabus and describe the class very briefly to answer the key questions that students have on the first day (for example, that we meet every day of the week, that students need to come to class, that there will be four examinations during the semester on Tuesday evenings, and how much exams, quizzes, homework, and attendance will count toward their grade). I can tell them more on the second day of class.
Then I announce that, instead of reading the roster and starting on Section 1.1, I have a project for them to work on. It is designed to get them thinking about math again after the break, to get the gears in their heads turning. I ask them to get into groups of four students and to turn their desks to face one another. I have them form groups starting from the sides of the room so no one is left isolated on the outside. Students love moving their desks around, generally. Sometimes I need to help them get organized, and move one or two students so the groups have four students in them. You may need a few groups with three students in, that's just fine, but don't make a group with five. That's too many.
While they are getting organized, I hand out a sheet of problems for them to work on together. The first "problem" asks them to write down the names of the other people in their group. They can exchange email addresses or even phone numbers if they want, but don't push them to do this, they might not be comfortable doing that. In this way, every student meets two or three of their fellow students on the first day. (Without doing something like this, it can often take weeks for students to meet each other, and sometimes it never happens!) Also, it gets them more comfortable talking in class. The rest of the sheet has some mathematics problems appropriate to the class. They may be straightforward math problems that most of the are familiar with, or they might be more discussion oriented. Below are some sample first-day projects from Fall 2019.
Math 1150, Introduction to Statistics | 1.1 Statistical versus mathematical questions.docx | Instructions
Math 1230, Mathematics for Architecture and Construction Management | 1.8 Unit conversions activity.docx
Math 1280, Precalculus | Distance Formula, Equation of a Circle, Midpoint Formula
Math 1310, Calculus and Analytic Geometry I | Math 1310 trip to the library.docx
While they work together, I walk around the room, talking with the people in the groups. I ask one member of the group to introduce me to the other members of the group, and I ask for help pronouncing names, like, "Bill, how do you pronounce your last name?" This way, I never mispronounce a name! I look at the names they have written down record them on my roster, so I do not need to read the roster out loud. It is very important to take attendance accurately on the first day, since we need to drop students who do not come to class under the First Day Attendance Policy. I use an Attendance Chart to learn how to put names to faces; it's too hard to do that in class on the first day.
Just as important, by doing an activity, I quickly learn which problems the students already know how to do, and what things we need to work on in class. That way, on the second day, I can cover exactly what they need to learn. This is especially useful if you have never taught a class at this level. It can take quite a while to learn what the skill level of the students is.
It is not important that the students finish all of the problems, or that they get them right!!! The main reason for the first day project is to get the students talking with each other and thinking, and to help them realize that they do or do not remember as much as they should. There is no need for them to turn them in at the end of class, and I would not grade them. But if it would be helpful for you to understand better just how well they did, you can collect the sheets and return them on the second day of class. The sheets have some good problems on them and, more importantly, the names of other students in the class, so students should hold on to these. Some groups will finish all the problems, but some will not. That is OK. Some of the problems will be hard for some students. Point out that you will soon be reviewing material, especially the things that people found difficult on the first day project. It's good that you find out what they know and what they don't know!
This technique has worked for me, but that does not guarantee that it will work for you. Think hard about whether you want to do something like this. You may have better ideas yourself! Make sure you leave at least 30 minutes for this project. Make absolutely sure that you get around to all the students so you know exactly who is there. Work out the solutions yourself ahead of time so you know how to do them, so you can recognize right and wrong answers quickly, and so that you know that the problems can be done. (When I used these problems, the quadratic I asked them to factor did not factor nicely. Big disaster!) Whatever you do, good luck!
One thing that does not work very well on the first day of class is lecturing for 50 minutes. Unless you have taught the class several times already, and even if you have taught it before, you have to guess what the students in your class know and what they don't know. It's hard to know the right level. If you are not a native English speaker, it might be very hard for students to understand your voice right away, so talk less in the beginning of the semester.
Dress nicely. What you wear tells the students about your attitude toward the class. If you wear old or dirty clothes, you are probably being too casual about the class. Be careful about dressing too formally also. For example, don't wear a tie unless you plan to wear one often during the semester.
Print out your class roster shortly before the first class meeting and bring it to class. Enrollments often change, even after the first day of class.
Bring the textbook for the course so the students know what it looks like.
Bring a graphing calculator if one is required, also to show to the students.
Consider using a first-day project, see above.
If you plan to lecture on the first day, choose your topics well. It is fairly difficult to make this go well. Consider a first-day project instead.
Everyone is nervous before the first class of the semester. That includes new instructors, students, and experienced professors.
It is good to arrive one or two minutes before the official starting time. If you arrive earlier than that, you need to have a plan of what to say or do. Chatting with students is a good idea, but if you're not comfortable, arrive one or two minutes early. Don't arrive late!
You might want to write some of the most important things from the syllabus on the board, like exam dates and certain policies. You might need to erase the blackboard first. It's a good idea to do this before class starts.
If you have some time before the official starting time, you might chat with the students a little. You might ask them if they have bought the textbook, and ask how much it cost. Ask them where they are living and how the dorms are. Ask them how the food is. You can ask them how moving in went.
Look at the students and smile! Smiling is evidence that you have a good attitude about the class and that you look forward to working with them.
Begin class by introducing yourself. If you are an international TA, you might enjoy trying this: Write your name on the board and have students guess how to pronounce it. If your name is not a common American name, your students may have trouble being able to say it, and this will make it hard for them to approach you. You might want to make up a nickname ("My name is Jakravlimaskulowala, but you can call me Jack.") Or you might want to write out an Americanized pronunciation of it ( / jack RAHV lee MASK you loh WAH lah / ) that you can write on the board the first day. Say your name slowly, and say it more than once. It's amazing how many students don't know their teacher's name halfway through the semester. Smile!
You might want to tell your students a little bit about where you come from and how long you've been here. Or ask students to guess what continent and what country you're from. If your English is poor, there is no advantage to telling people that you have just arrived. If you have taught before, it can help to tell students that. It is probably not a good idea to say "This is the first class I have ever taught, and boy am I nervous!" It will be obvious enough!
It is good to give a little overview of the course. For example, "In Math 1280 we cover Algebra and Trigonometry, mostly, which may be familiar to you from high school. We will cover chapters 1 through 5 plus some algebra review sections. Please note that this class will go much faster than a high school class, and I will expect you to know things very well, maybe better than you were expected to know them in high school. The first few days may be boring for you, but they are helpful for others. Keep coming to class!" But you don't need to give a complete table of contents for the course. Too much for the first day.
Remember to refer to your notes about what you planned to say. I always forget to look at my notes, and I always end up saying things out of order!
Students want to know what they have to do to get a good grade. (For some students, a C is a good grade, and it's all they want!) Tell them if there will be homework ("Homework will be collected daily, and I will grade a randomly-chosen problem each day"). Tell them if there will be quizzes ("There will be a short quiz every Friday."). Tell them whether the quizzes will be announced ahead of time or not ("There may be pop quizzes on any day of the semester. Be prepared and come to class!"). Tell them about the exams during the semester. If you know what the dates of the exams will be, put them in the syllabus. Some classes, like Math 1280, have common exams in the evening, and students cannot miss the exam, so they should make their schedules so they don't miss an exam.
Take attendance in some way. You can read the names on the roster and make note of who is there, but that is always awkward because you will mispronounce people's names. You can pass around a sign-in sheet; I like to make an attendance chart (see below) so students can write in their name in a location that corresponds to where they are sitting, so you can start to learn their names. Or, best of all, have them do a first day project and make note of the names that way.
Don't worry so much about covering material on the first day. It is most important to set up a good atmosphere, be friendly, be understandable, etc. If you can do this and cover material, that's great. Whatever you do, do not end class after just 10 or 20 minutes. Make it a real class.
Assign some homework for the second day of class, to be handed in on paper. This could be just to finish the first-day project on their own, or it could be to do a few problems very similar to what you discussed in class. The homework does not need to be worth many points. Assigning homework sends students the message that it is time to get to work, and it will give you some feedback from your students about what they know, right from the beginning.
There are sometimes students who want to be in your class but are not on the roster. Sometimes this is because the class was full. Most mathematics classes have an absolute upper limit of 29 students, because the rooms only have 29 seats in them. Some rooms have even fewer seats. But students often change their class schedules during the first week of class, so a place in the class may become open. Make a list of the people who are there but who are not on the roster. Tell them to keep trying to register using the online system. Check with the administrative secretary to see if there is something special that can be done for a particular student.
Erase the blackboard after your class is done. It's polite.
This web page was written for graduate students who are teaching mathematics to first-year college students. Here are some comments for such students at this moment.
Graduate school is hard. The courses are a significant step harder than senior-level undergraduate courses, and between the master’s and Ph.D. level courses there is another jump. Prepare to work harder than ever on your classes. At the same time, many of you are teaching for us in return for a stipend. It is hard to balance your time between the classes you are taking and the classes you are teaching. But teaching undergraduates well is vitally important to the university. We need all of you to do a good job at teaching. Teaching well does not require much more time than teaching poorly, but it does require more mental effort and preparation. Your students will appreciate your effort, you will enjoy teaching more, and your teaching evaluations will do you a lot of good in your future.
Some day you will leave BGSU and you will want the help of the faculty here in getting another job elsewhere. We will write you letters of recommendation. Please give us lots of good material to write about. Teach well. Be responsible. Be on time for class, turn in assignments on time. Work hard to do everything right, even if you don’t always succeed. Work on your English, especially if it is not your native language.
Teaching takes a lot of time, but you can't let it take too much of your time. Ultimately, you have to limit how much time you put into teaching. The trick is to do it as efficiently as you can, so you get the best result with the amount of effort that you can afford. My personal suggestion: Get enough sleep, and do what you can with the rest of the time.
The course is designed to help you improve your teaching. You can all teach better, not because you teach poorly, but because you are smart and can reflect on how successful your teaching is. I do not know the best way for you to teach. It depends very much on you, your personality, and what you prefer. I can only give general guidelines and suggestions and things for you to think about.
If a student misses the first two days of a 3, 4, or 5 day a week class, or the first day of a 2 day a week class, tell our administrative secretary. She will check into it and will drop the student if it is warranted. Some students miss class because they have ROTC (Reserve Officers’ Training Corps), so some care is needed. If a student sends you email or calls you to explain why they missed and that they intend to be in the class, they shouldn't be dropped.
Having a first-day attendance policy helps people sort out what class they will be in more quickly. There are always students moving around in the first week, and people holding onto a spot in a full class that they don’t intend to take makes it harder for everything to get sorted out. This helps us get people off the waiting list and into a class. Also, because of this policy, students who miss the first day of class assume they will be dropped, and are sometimes surprised to learn, at the end of the semester, that they have not been dropped. That is a big problem for them, and also causes some trouble for you. So make sure to have them dropped if they miss class.
On the first day of class or a little later in the semester, a few students may give you a Student Accommodation Form from the Office of Accessibility Services, formerly known as Disability Services. Students may have a documented learning disability that makes it harder for them to learn in class. We are required by law to provide reasonable accommodations. You can read a nice summary here. This does not mean that some students have easier requirements for the course, only that we go about the course differently. The most common accommodation is extra time on exams. Since that is hard to schedule in our busy classrooms, you can arrange for students to take exams in the Office of Accessibility Services. Read about exam proctoring and this page about proctoring for faculty. It can be easiest and fastest to email the exam to Accessibility Services and to have them scan and email back the student's work. Occasionally a student will need someone to take notes for them in class.
On the first day of class or a little later in the semester, a student may give you a form from the Athletics program which identifies them as a student athlete and has a schedule of days that they may miss class due to travel to competitions or games on campus. Please work to accommodate their schedule. If they need to miss an exam, you can give an alternate exam a day or two earlier or a day or two later. Consult with your course coordinator, who may be able to provide an alternate exam so you don't have to write one yourself. It is a good practice to give different exam questions. This makes it harder for students to cheat by getting or giving the exam questions to others, but it also protects them from any suspicion of having done so. Another possibility is to work with the athletic program and their academic advisor to have them proctor the exam while the student is traveling. Here again, consult with your course coordinator to make sure to do things right. Specific suggestions from Student Athlete Services (SAS) in Fall 2018:
Student & instructor can agree on an alternative time to take the exam (office hours, class period before, another section time)
Our full-time SAS staff can proctor the exam here in SAS. We would need specific requirements that the instructor would provide (time allotted, calculator allowed?, scrap paper, method of test delivery and return, etc.)
If students are on the road traveling and the instructor requires the exam to be taken at a specific time (if feasible given game times) we can typically arrange for a staff member (academic coordinator, athletic training staff member) to proctor the exam.
We can also reach out to the academic center for student-athletes at whichever campus our BGSU student is traveling to and try to arrange for one of their academic advisors to proctor the exam.
Take attendance of some sort every day. Make note of who is missing because it will be useful to you later, sometimes to break the tie when the student's grade is on the borderline, or to document when the student stopped participating. Sometimes students say they have come faithfully, when they have not, in fact, come to class, and it is very helpful to you to know the facts. At BGSU, after three weeks of class, you can submit an Early Alert report to let college advisors know which of your students are not attending class or are otherwise doing poorly. This is our one opportunity to get help from outside the department for our wayward students. Tell your students today to come to class. This may be the last time you see them!
The attendance chart is an idea I learned from graduate student Jason Hasbrouck some years ago. You make a master chart of where the seats are and the students sign their name each day, passing it from student to student. This gives you a record of attendance and information on what face goes with what name, which makes it easier to learn which name goes with which face. Emphasize to students that they do not need to sit in the same place each day.
Here are some sample attendance charts, as pdf files you can print and as Excel spreadsheets you can modify as you see fit. You should write the date and the starting time of the class on the attendance chart so you can refer back to them later. When you hand it to the first student, make very clear to them where they should put their name, and which way to pass the sheet.
As long as you are passing this sheet around every day, you can get even more useful information out of it. Ask students to write suggestions for you on the back of the sheet. For instance, "Don't stand in front of what you just wrote!" or "You are mispronouncing the word 'variable'. It's like this /VAR ee a bull/." Every day you can get useful feedback on how you are doing. Not only will this help you improve your teaching, it lets your students know that you are open to feedback and improvement, which will be good for the atmosphere in the classroom.
I also use the attendance chart to arrange papers that I am handing back, so I can walk section by section through the classroom returning papers, rather than having to find them in an alphabetized stack of papers, or zigzag around the room to hand them back in alphabetical order. It helps to alphabetize papers to record the grades, but after grading and before class I put them in different piles according to where they sit in class. Much faster to do that in my office than in the classroom, and then it's much faster and easier to hand them back.
One of the easiest things to do is to stand in front of the room and explain. You give an introduction, you give some examples, more general explanations, etc. You ask students what to do next, and the ones who understand what you're doing will tell you. But students can only follow this for so long before you lose their attention. Another problem is that you can’t be sure that they are learning what you want. What is going on in the brains of the students who are not answering questions? You can’t tell just by looking at them, or by asking them, "Do you understand?" They will often say that they understand when in fact they don't. You need to stop talking and make the students show you that they can do some problems. There are several ways to do that. I'll describe two of them below, and more in later weeks.
Do two problems on the board. Explain them thoroughly, ask students to help by telling what step is next. Then write two problems on the board, one next to the other at the top of the board, for students to work on at their seats. (Make sure that you have solved these problems ahead of time.) Go around the room to see how they are doing, getting right up close to all of the desks, and really check that everyone is working. Answer any questions they have.
This is a good strategy for the first week of class. It keeps you from talking too much. This is absolutely the best way to know if your students can do the problems you want them to be able to do. If you see that a student has solved it correctly, ask him or her to go to the board to write the solution. Students are much more comfortable going to the board when they know they have the right answer. Having a student put a correct solution on the board saves you time, all students get to see several correct solutions, but they are also pushed to do the work themselves, individually. This is a good strategy for the first week of class because, unless you have taught the class many times before, you don't really know how well the students can do each type of problem.
Write five problems on the board, each in a column by itself. Two easy ones, one medium, one medium-hard, and one hard. Explain that to the students. Ask students to work on the problems at their desks. Students who are having a hard time should start with the first problem, students who think they know what they’re doing, start at the middle or the end. Tell them that the easy problems are good for in-class examples, the medium problem is good for homework, the medium-hard problem is good for exams (to set their expectations for the difficulty of problems on exams) and the hard problem is to challenge them. Otherwise, students have a hard time knowing how hard the exams will be. Tell students to raise their hand if they have a question. When they do, go to help them. Otherwise, just go from student to student to see how they are doing. Tell them it's OK if they ask a neighbor, and OK to help each other. If you see that a student has solved the problem correctly, have him or her write the solution on the board in the column under the statement of the problem. By the time you are done, all the solutions will be on the board, and you can move on to the next topic. This saves class time and gets students to work individually.
You may want to hand out background surveys to your students on the second day of class, to get an idea who they are. It may not help much to ask what math classes they had in high school, since different high schools organize and name their math courses differently. It is a great idea to ask students what high school math class went the best for them and why, and what class went the worst for them and why. Also ask what kind of student they are. Often, students will open up and tell you all kinds of interesting things. If you ask personal questions, be sure to let students know that they don't need to answer every question. It's fun to encourage them to write down any questions they have for you, or about you. It makes it easier for students to ask questions this way.
A slightly different way to look at it is that you can ask students to write a little math autobiography. Ask them how they have liked math courses in the past, what specific things they like about math, what they don't like about math, what they liked about their favorite teacher, what they disliked. The great thing is that some students will really open up and write a lot, and then you learn a lot about your students.
You can write questions on the board and have students respond on their own paper, you can hand out index cards or blank sheets of paper, or you can print the questions on paper and have them turn them in. Printing questions has the advantage that you can hand the sheets out at the end of class and have the students fill them out after class is over, not during class. This saves class time.
If you teach two math classes without assigning any homework for them to do outside of class, it seems to me that something is wrong. Students need to do more work than there is time for in class, and it's very important for them to write out solutions on paper and for you to read those solutions. You don't need to commit to reading all of their solutions, and you don't need to grade all of them, but it is important for them to get feedback on their efforts from you.
Students get busy, and then they run out of time to study for their classes. A really good idea is for them to schedule a time and place that they will work on their math homework. At BGSU, an especially good place for them to plan to work is the Learning Commons in Jerome Library. They can plan to sit and work on homework, and if they have questions, there will be tutors nearby to answer their questions. They will likely find other students from the same course (maybe a different section), and they can sit at the same table and work on things together. The Learning Commons is not a place to go only when you know you need help, it's a good place to go every day just to work.
This week or next, arrange to observe someone teach the same course you are teaching. Find someone who is not in Math 5910. If possible, find someone who has been teaching here for a while, perhaps an instructor. Write a brief report to me. Please comment on good teaching practices that you observe and things you learned by watching someone new teach. If you do not have a teaching assignment, choose from Math 1150, 1280, or 1310. If you are studying statistics, choose 1150. If you are in the Math Emporium, maybe choose 1280 or 1310 to see what students will do after they are done in the Emporium.
Until Sunday after the first day of classes, students can use the online registration system to drop and add classes. Expect to have some changes in the roster for your class. Be prepared to hand out additional copies of the syllabus. In the second week of classes, it is possible for students to add or drop using a "Schedule change form," with the instructor's permission. They can get a form in the Math Department office. After the second week of class, students can add or drop, but only with the instructor's and department's permission. It gets harder the later it goes.
Some students may be totally unprepared for your class. You may notice a student getting less than 50% on each quiz you give. As soon as you notice something like this, talk with the student to see if, in fact, the course seems to be inappropriate for him/her. The first week is the best time to get students into the right class, because the student can go online and drop your class and add a lower-level class. The student should work with our secretaries if the sections that fit their schedule are full. Changes can be made in the second week as well. Even after that, it can be done. It is better to try to make this happen than to just hope that the student will do better. It may save their GPA and save them a whole semester of misery.
Most classes deliberately start with some amount of review. Many students have already seen most of what you will teach for at least the first few weeks. Some Math 1220, College Algebra, students may have had calculus in high school! It is a challenge to keep students' attention when you go over familiar things. It is hard to bring them to realize that, even though they have seen things before, they might not be very good at solving problems you give them. This often leads to students not attending class, and often leads to surprisingly low grades on the first exam. Here are some suggestions:
Make sure they understand that you are making sure that everyone is “on the same page” and that it is likely to be familiar to many people. Still, it is necessary, and they need to keep coming to class.
Give students problems to work on at their desks and then put them on the board, as described above. At least they all stay busy, even if they are bored.
Introduce topics in a new way that they haven't seen before.
Don't say, "See, I told you you were too confident! You don't know how to do these!"
The course will go quickly, so keep coming to class.
Use basic terminology so you can use it later. Numerator, denominator, radicand, index, ... Make sure to use this terminology later.
Instead of telling them what a rational number is, ask them for examples of such numbers. Make them do the thinking in class, don't do it all for them.
Instead of walking them through something that seems to be very familiar, give them problems to work on. If you find that they don’t know, THEN talk about it to everyone.
Keep on probing how well they know things by making them do things.
Students in past Math 5910 classes have said they should have given more quizzes early in the semester. It is too easy to get the impression that students know how to do the sorts of problems you are talking about. It is no fun to realize several weeks into the semester that students don't know how to do basic problems! Give an early quiz on some algebra that is important to the class. A first day project will help to assess students right away. And giving them problems to work on every 15 minutes will also help, as long as you go and look at their papers.
This is an activity for the graduate students in Math 5910. Go to the board and solve these problems individually, then we’ll compare the solutions.
Solve 3x + 5 = 9x – 12 for x.
Solve x^2 - 4x = 14 for x.
Graph y = 1 + 3(x-5)^2
Factoring 2x^2 + 7x – 4
Solve 2x-3y=9 and x+y=4
The quadratic formula
Shifting and scaling a function
Compound interest
Explain why statistics is useful in your life
This activity typically goes great. The solutions are so different, and they show natural differences in approaches, but allow us to talk about what students are used to doing and seeing.
Everyone loves the sound of their own name. If you are teaching a class of 40 or under, make it a goal to learn your students' names as quickly as possible. Use them when you call on students. At the very least, learning names will make it faster and easier to hand back homework and examinations (it is also embarrassing to not know students' names by the time you are handing back the first exam). Suggestions:
Have students fill out an attendance chart each day, and study the chart after class to put names with faces
Ideas from Ohio State University at this site
I write detailed notes, in pencil. Writing the notes is how I think through what I will do. By the time they are written, I don’t need to look at them to know what to do in class. Try it. If you get good at it, it will serve you very well. I find that my notes are very helpful the next time I teach the course. I make a point of editing them with pencil and eraser each time I teach; that makes them fresh in my mind and makes them better every semester.
I have posted many of my class notes online. You can see the whole collection under the Course Notes tab, or jump straight to these specific courses:
Math 3320 Linear Algebra (one of my favorites)
Now that I have a lot of experience preparing for classes, it doesn't take that long to write up notes like this. Writing is slow enough that I can think ahead while I write. The act of writing helps me organize my thoughts and remember what I want to say. I would recommend that you try this. It often happens that I prepare more than I need for one class, and so I'm halfway through the next class before I know it. Also, I pretty consistently cover 3 pages of notes per 50-minute class period. That helps me set the pace.
It is very helpful to write some notes for the next class right after you finish teaching. Your mind is ready for the next topic, and once you think about it, you will keep thinking about it as you go about your day. There is more happening in your mind than what you are consciously aware of.
It is so tempting to stand at the board and explain. You understand this material so well, and you figure that you can get the students to understand as well. As you work through a problem, you may ask students what step to take next, and you will usually find that a few students always know the answer. This will give you the impression that all the students understand, but this is very rarely true.
Talk and explain for at most 10-15 minutes. Do a few examples. Then give students problems to work on, and make sure you see whether they can do them or not. There are several ways to do that. I put two of them in week 1, and here is another one.
It is refreshing to have students at the board instead of you. It changes the pace in the classroom, and that is good. But be careful about how you do it. Above, I mentioned the idea of sending a student to the board after you have seen their correct solution. Here, the idea is to send students to the board to work out a solution on the board. Some suggestions:
Put at least three or more problems on the board simultaneously, so that several problems are being solved in parallel. This saves time. Have the students at their desks work on the problems as well. Having three at the board at once makes sure that no one student is the object of everyone's attention. That would be too much pressure for some students.
Send two students to work on each problem. That way, students have a "buddy" at the board with them. It reduces their fear of making a mistake.
Ask for volunteers, but also choose people who don't volunteer to make sure you don't keep getting the same students.
This is a great way to find out how the class is going and to let your students know that you care about what they think. It's good to do around the end of the second week and every few weeks after that. Leave 5-10 minutes for this at the end of class, and say: I want to know what you think about the class so far. Use a half sheet of paper. Don't put your name on it; this is anonymous.
You can type up questions; I type questions that fill half a page, copy the questions to the bottom of the page, print half as many sheets as students in the class, cut them in half and hand them out. Here is a template you could use; of course, you may need to change some of the questions.
Or, you can ask the students to take out a sheet of paper, tear it in half (and save the other half for a few weeks from now or share with a neighbor), and write questions like these on the board:
What is working well, that we should not change?
What is not working well, and how can we change it to make it work better?
Is the pace OK? Too fast or too slow?
Is the level OK?
Any other ideas?
When students hand them in, turn them face down and shuffle them to keep them anonymous. It's nice to do this survey at the end of class; some students like to write a lot, some only a little.
Don't read the surveys until after you leave the classroom. When you read them, have a thick skin; sometimes students say things that hurt. On the other hand, they usually write positive, constructive comments! And you would rather read what they have to say now rather than after the end of the semester. Students will fill out course evaluations in the last few weeks of class, and you can see them after you turn in your grades. I have read comments to the effect of "Don't stand in front of what you have just written!" It's much better to read this comment after week 2!
The next class period, hold up the surveys and thank the class for their feedback. Tell them what changes you will make, and ask them to remind you if you forget. Sometimes students want opposite things; explain that you can't always do what all of the students want, but you'll try to make it work for everyone.
Some students believe that only people who have a “math brain” can do well in math. They conclude that, if they have done poorly in math before, they are doomed to do poorly again. This is simply not true. Math involves some abstract thinking and a whole lot of specific skills that you can get better at if you practice more. Encourage your students to do many, many problems from each section and to keep track of how many problems they’ve done in each section. Write cheerful notes on the homework they turn in when they have done a lot of hard work. Recognize it.
Students need to be made to do a lot of homework, especially before the first exam, which is almost always a big bad surprise for students.
Do they know how to study for an exam? Probably not. I bet that most of them sit in front of a screen and have their book open and vaguely look around in it. Instead, they should open their book, set it to the side, take a pencil and paper, and write down what they are reading in the book. Write down the examples. It is a great way to focus the mind on the topics. Also tell them to sit down and do problems. They should not check answers in the back of the book until they have the problem done and they think they are right. Have them go through their notebooks and fill in missing steps and rewrite solutions, etc. Don’t just look at your notes and the book. It won’t help!
Talk with your students about how to take notes. You could do this before class when you are looking for something to talk about. They should at least write down what the examples are, even if they can't keep up with the solutions. They should be writing most of the time, not just listening, and certainly not tuning out and not paying attention.
Every once in a while, ask them if you can have a look at their notebooks. I guarantee that you will be surprised by what you see, and you will get a better idea why students don't seem to be learning when you lecture. They are generally just not very good at taking notes. I don't know why. Maybe no one ever taught them in high school, maybe their high school classes were so easy they never had to learn how to take notes. Well, now is the time, and you might as well give them some suggestions.
Now that you have had some time to work with your students, we can talk more about how to interact with them.
Nothing sounds as good to a person as the sound of their own name. Learn your students' names and use them whenever possible. It makes for a personal connection. A good way to learn names is to have students sign in using an attendance chart. It's also a quick way to take attendance.
Often, you ask a question and you want an answer from your students. After you ask, wait long enough that their minds can figure out what you asked, think about it for a while, and then give an answer. Give them 15 seconds. If they can't answer the question, it's quite possible that they did not understand the question, or that what you think you just taught them didn't actually make sense. Have some humility. "No one is answering my question. Let me ask again with different words." "I see, still no one has the answer. Let's back up a bit and start again."
Often, the same student or students will answer every question. You can give them a smile to show that you appreciate their offering to answer, while waiting for another student to answer. Or you can say, "And John has already done his work for the day, so I'll be looking for someone else to answer" or "Someone in the back row, please?". Often, a student will give the wrong answer. Look them in the eye, give a little shake of the head and a smile, like it's just between you and them, and go on. No need to make a fuss over every wrong answer.
It is healthy to lead students through a train of thought and then ask them what the next step is or what the conclusion is. This is especially good with conceptual questions. It can be fun to ask, "Who thinks the answer is A? Raise your hands. Who thinks the answer is B? Raise your hands. Who is not sure? Raise your hands."
Instead of asking, "Who thinks the answer is A? Who thinks the answer is B? Who is not sure?" one strategy to get students to answer and to not just watch what everyone else does is to ask them to think for a moment and make up their minds. Then ask, "Who is not ready to commit? OK. The rest of you need to commit. Who thinks the answer is A? Who thinks the answer is B?" I think this will result in fewer students waffling about what their answer is.
Thank the student for the question. At the very least, smile as they ask and after they ask. Asking a question is a very difficult thing to do, especially in a room full of strangers, especially when asking a question may make you look stupid, and especially when you don't really understand what is going on, so you know that you can't phrase the question very well. Encourage your students to ask questions, even if they don't know exactly what they are trying to get at.
Sometimes students are so confused, they aren't able to formulate a clear question. Tell them it's OK if they just ask you to rewind and play back what you said again. Do you ever want your professors to just rewind and say it again? Actually, this is one of the best things about teaching videos. One student said, comparing a video to class in person, "I liked you better when I could pause you."
Wait for the student to finish the whole question; catch yourself so you don't start answering too soon. Make sure you understand the question. If it's a long question, restate it or paraphrase it so that everyone knows what question you are answering. Fairly often, a teacher misunderstands the question and answers a different question. Restating the question can save a lot of wasted time. Once you're done with the answer, let the student know it was a great question. Or at least thank them for the question!
I let students come in late or leave early. I encourage them to come late/leave early rather than miss class entirely. Some students skip lots of classes. Also, students sometimes get sick during class. Let them go! I usually close the door of the classroom at some point during class, but I encourage students to come in even if the door is closed. I hate it when a student say, "I was going to be 10 minutes late, so I didn't come to class." That makes me more upset than a student coming 10 minutes late. If a student makes a habit of being late, talk with them about it.
I let them sleep. They're there. I don’t let it make me feel bad about myself. But you should decide how YOU feel about it. If it bothers you, please tell students this ahead of time and tell them what you are going to do if someone is sleeping. You can talk with the student to see if there is anything you can do about it. Sometimes a student will tell you that they work all night and they would appreciate it if you wake them up. It may seem silly to wake your students up during class, but at least you know how to handle an awkward moment. Don't make fun of them, don't let students make fun of them, don't drop a book near them.
During the second week of classes at BGSU, a student can add or drop a course with no difficulty by filling out a schedule change form. You and the student need to sign it. The student takes it to the Office of Registration and Records. In the third week, you need further approvals on the form, including college approval.
Encourage your students to visit you during your office hours. They get one on one attention to their difficulties and you can help to figure out where they may be confused. You also benefit: you learn quickly what troubles they are having and improve your teaching. I find that some of my best ideas for teaching come from working with confused students in office hours. I realize what I should have said in class, and make a point to say it to the whole class the next time we meet.
If you have not yet scheduled office hours, late in the first week or early in the second week of classes is a good time to ask students what time(s) would work well for them. A good way to do that is to have them write their initials on a time grid, see below. Print the grid, mark out any time slots when you are not available (for example, when you are teaching another class or taking classes), and explain to students that if they think they will come to office hours, they should write their initials in all slots in the time grid when they are available. Then you will choose office hour times that make it possible for the most students to come to office hours.
Some students don't automatically understand what "office hours" are, so you should explain that.
Office hours are a time when you can come to ask me questions about the class or anything else
You can ask me to look at your homework and see if you are doing things right
You can ask me about what class to take next
You want to help them, and wish more students would come to your office hours
I would suggest that every day, just before class, you write on the board what days and times you have office hours and tell where they are.
If you are having trouble getting students to come to your office hours, one idea is to require students visit you in your office for 10-15 minutes, maybe in a group of two or three (so that you can get through all of them). Ask them about the classes they took in high school, what classes went well and why, what classes went poorly and why. Ask them what their favorite math class or teacher was, what their least favorite teacher was. Make a sign-up sheet and hand it around the room. This can be a good thing to do in the first or second week.
Some courses, like Introduction to Statistics, have PowerPoint slides provided by the textbook publisher. They look very nice and cover all of the important points in each section of each chapter. However, students really find it hard to pay attention to those slides for more than, say, 30 seconds. Reading slide after slide to students simply does not amount to teaching.
What seems to work much better is to use the PowerPoint slides only for presenting things that are hard to quickly reproduce on the board, like problem statements, datasets, graphs of data, and some definitions. Also, content on a PowerPoint slide is quickly gone; some things need more permanence. As much as possible, use the board for things like:
Definitions or diagrams that need to be visible for several minutes or the whole class period
Working through problems step by step
Drawing diagrams that need to be done step by step, for example, drawing histograms
In short, try to use the board as much as possible, because it's easier to engage students that way.
Avoid these. Arrange for someone who can substitute for you at short notice. Even if they just help students while they work on problems, it's better than canceling class. When you end class early, you send the wrong message to the students: "Relax, take it easy, this is so easy we're already done." Give them five problems and make sure they get them right. Always have some extra material that you can cover if class ends early. Or just open the textbook and start doing problems on the board with them.
Walk over to the Learning Commons and have a look around. See what is going on. Then you can say to your students: I've been there, it's nice! Encourage your students to go there regularly, well before the exam. Encourage your students to go there to do their homework. Take your students there after class to show them where it is! Students need to develop good habits - you can help! You could hold office hours there - they love that!
This is especially relevant for international TAs. First, let me say that it is an absolutely amazing thing to study another language in school and then move to a foreign country where they speak another language and then teach in that foreign language. Good for you! But it's really hard. Fortunately, your students can help you get better. The most important thing here is your attitude. If you are open to being corrected and open to improving your English, things will go very well. Let your students know that you are interested in improving your English. Give them easy ways to give you pointers, like writing a short note and handing it to you at the end of class, or writing on the back of an attendance chart when you hand that around.
Some are more appropriate for some parts of the semester than another.
Come to class even if the material is familiar. We are still reviewing now, trying to get everyone on the same page so we can start moving through new material. Be patient. It is really, really important that you keep coming to class. Students who stop coming to class, even for a few days, very often end up failing the class. You will probably miss something new and important when you miss class. The new material builds on the old. And it’s amazing how often students have trouble doing problems that they think should be easy to do.
Come to class even if the material is easy. The content of many mathematics and statistics classes starts out easy, but builds and builds until it gets much harder. If you are not solid on the earlier material, you may find that you are not able to fully understand the more complicated material that comes later in the semester, and by then it may be too late to catch up.
Class time is not enough. There is not enough time in class for you to learn everything that you need to know and to practice it enough. As the teacher, I choose carefully how to spend class time. Outside of class, you need to re-read your notes and fill in things that you didn’t have time to write down, or fill in steps in problems. Do this shortly after class. You need to do homework problems. You need to read the textbook to improve your understanding of the material. You need to plan to review for at least a week before the first exam. Just because I don’t collect something doesn’t mean it isn’t important. College is a good opportunity to start depending on yourself rather than solely on your teachers.
Spend time working outside of class. A good rule of thumb is to spend two hours outside of class for each hour you spend in class. And that is not time watching videos or chatting on social media with your math book open, that is time actually working! Any time you can concentrate on math is a good time, it doesn’t have to be all at once. When you study regularly, you don’t need to spend as much time to prepare for exams. A very good plan is to go to the Learning Commons after class to review your notes and start working on your homework. There are people right there who can answer questions for you.
How to read a math book. Here is one good way to read a math book. Open the book and set it to the side. Take a pencil and some paper, and start writing down the things you read in the book. Write down the key points for sure. You are likely to learn best when you are writing. You learn how to do problems by practicing and repetition.
Hard work pays off. Everyone who was placed into this course has the basic ability required to succeed in the course. What is needed now is hard work. Come to class every day, pay attention, and take notes. Do your homework and do it well. Do extra problems before quizzes and exams. You don’t do well in math class just because you’re smart or have a “math brain”. You do well by working hard. Ray Heitger, a former mathematics instructor at BGSU, says "Attitude, not aptitude".
You can succeed in math class. You might have struggled with math in the past. You might have some degree of math anxiety. Regardless of that, you can do better and better by working hard at the right things. Pay attention in class. Ask if you have questions. Come to see me in my office hours. Go to the Learning Commons. Get together with other students to make a study group. Hire a tutor if you think that will help - $10 an hour could be a bargain compared to having to take this class again!
No extra credit. There is no extra credit for extra work in this course, but there are many opportunities to improve your grade, by doing homework, by preparing for quizzes, and by studying ahead to do well on exams.
Prepare early for exams. Do not wait until the night before the first exam to start studying. Students usually do much worse on the first exam than they expect to. Start preparing now.
Grades are not curved. Grades are not curved at the end of the semester. This makes grading and the effort you need to put in more predictable. You have many opportunities throughout the semester to see what your current grade is, so pay attention and take action if your grade is lower than you would like.
You and I each have jobs to do. As the instructor, I have certain jobs here. I structure class time the best I can, I explain the best I can, I give useful examples, I give assignments that help you master skills and deepen your understanding, I grade them and give you feedback on how you’re doing, and I meet with you individually outside of class. You also have responsibilities, to come to class, to pay attention, to think hard during class to figure things out and fix any misunderstandings that are holding you back, to do homework problems, to review your notes and do additional problems to prepare for exams. I cannot do the learning for you. You do your part, I’ll do mine!
I am here to help you. My job is to help you learn math. I do that by teaching, by giving you feedback on homework, quizzes, and exams, by setting up the course to push you to learn to do well on exams and other graded things. I want you to succeed.
I know you can do better. (Appropriate for after a classwide poor result on a quiz/homework/exam.) Your performance was overall not as good as we want. I know you can do better than that. High school students do better than that. You need to work harder. There is only so much that I can do, you need to do the rest yourself. I will explain what I can and guide you toward the work you need to do, but you need to do the work.
Your grade is in trouble, but you can improve it. Your grade right now reflects, say, 40% of the points available in the course. That means that you can move your grade 60% of the way toward 100% (or 60% of the way toward 0%). I can’t promise you that much improvement in your grade, you have to earn it. But remember that your grade can move a lot still, depending on how hard your work and how well you prepare for exams.
Think of your life after college. Some day, you are going to need to get a job. Who do you think is going to get hired in this economy? College dropouts? College graduates with low grades? No. Hard-working people who succeed at what they set out to do. Being a college graduate is a demonstration to an employer that you are trainable, that you can learn new skills and that you have an interest in learning new things. You’ve enrolled in this class. Now get down to work at succeeding in it. Come to class. Pay attention. Do your homework and do it well.
The bigger picture. You are a university student. A university degree is the hallmark of a broadly trained and intelligent person, and confers prestige on its recipient. Some of that may require that you learn and master skills or domains of knowledge that you don't personally find all that interesting, but that other intelligent and accomplished people find indispensable. Don't doubt their collective wisdom. Saying "I don't care about that" is a loser attitude!
Compare to athletics. Our class is like a sports team. You are the players, and I am the coach. We all want to do the best we can do. I am not your adversary, I want the best for you and for the team. So I am going to push you hard. I am going to design practices (classes) to prepare you the best I can for the games (exams). As a coach, I can see how you are performing, I can tell where you need to get better. As a player, you should listen to your coach and work harder on what you need to improve.
These have been edited and improved by past Math 5910 students. Please read these and reflect on them. Choose two of them to write about, and hand that in at the beginning of the next class.
Good practices when lecturing.pdf | Good practices when lecturing.docx
You may also be interested in reading Chickering and Gamson's seven principles:
Seven principles for good practice in undergraduate education
Previous Math 5910 students say, “Before the first exam, prepare instructors to face the likelihood that ALL of them will have a class average in the 50's.”
The first exam is often the worst, then students spend the rest of the semester struggling to bring their grade back up. Let's see if we can make the first exam go better than usual for your students.
Students often wait too long to start studying for an exam. That might be overconfidence, but just as likely, they don't know exactly what to do to start getting prepared. You might be able to pick out some book exercises that you have not yet assigned that they could do for additional practice. If you have never taught before, start planning your exam early and, if possible, have a look at exams that other people have given in the past, to get some idea what types of questions will be on the exam.
When giving examples or sample problems in class in the weeks that you are covering new material, note which problems would make good exam problems. Often, we give first examples which are easier than what we intend to put on an exam, and students might think that those problems are typical exam problems. Then on the exam they are surprised that they are not ready.
Students like to have a study guide, or a set of review questions. This is good, because students will work on it. But it can also be bad, because students don't work on anything besides the study guide, and they might not study something that ends up on the test, and then they get upset that you tested them on something you didn't warn them about. But this might prompt you to make a study guide that is too long. It is hard to get the right balance.
If you spend time reviewing in class, I suggest that you focus mostly on giving students problems to work on individually or in groups and you answer questions, rather than doing problems on the board at the pace of the strongest student. One good compromise is to put a question on the board and ask them to start working on it on their own. Give them 30 seconds to get started, go an answer any questions anyone has, and then return to the board and silently write out an answer. Maybe write the first part of the answer and then check for student questions, then the second part, etc. Students will generally stay focused on their own work, but they will be able to confirm that they are making good progress by looking at your solution on the board. Eventually, the students have all worked on the problem, plus there is a correct solution on the board. Much better than you solving the problem and them not really being able to do it themselves.
Before the exam, be encouraging and optimistic with your students. Try to put them at ease before the exam. Point out that their grade in the course is based on many pieces of information, many individual grades, and this is just one of them. Of course, it will help them if they do well on it!
These handouts about math anxiety and test anxiety may be a bit out of date, but are probably still useful.
Read about math anxiety here, so that you understand a little bit of how it might affect students:
Refer to the Text Anxiety Assessment. It will give you some idea how students may look at tests. Certain students might find it useful to complete:
Some students might benefit from a concrete list of tips for doing homework. See here:
They might also benefit from a concrete list of things to do to prepare for tests:
Finally, here are some general tips for doing well in math and stat classes:
Top Tips for College Math or Stats Course Success.pdf
Math anxiety and test anxiety may be a symptom of a learning disability; contact Accessibility Services.
There is a well written section in a previous textbook (Krantz, How to Teach Mathematics, pages 100-101).
Ask your course coordinator for previous exams that you can use to match the right level, type of question, and number of questions.
For freshman-level classes, write straightforward questions. Don't get fancy. Try to use questions that have the same wording and the same expectations as homework questions. This avoids a situation in which a student is confused by how a question was asked, but could have done the question if it was asked in the usual way. It also avoids students blaming you for making the test too hard.
Many instructors put a large number of questions on each exam. This has the advantage that no one problem counts for all that many points, but the disadvantage that students need to work really fast and cannot go over every problem twice. Personally, I prefer exams with fewer questions.
Be aware that making a question just a little bit harder can make it go from reasonable to impossible for many students.
I highly recommend printing out the exam for yourself and sitting down and solving all the problems. This will help you spot any typos or more serious problems with exam questions. It will give you a better idea just how long it will take students to physically write down correct solutions. And you will have an answer key. My students always appreciate being able to look at the answer key after they turn in their exam. You need to make sure they don't walk off with the answer key, though!
Make a few extra copies of the exam in case you need to ask a student to finish their work on a new copy; see below.
Let the students know that you really want them to do well, and wish them good luck. If you can chat a little and put them at ease, it helps.
Personally, I like to announce ahead of time that I'll hand out the exams 5 minutes before class starts, so that everyone has all the time they need to take the exam. They appreciate this. Some students can't arrive 5 minutes early, but it is rare that any of those students actually need extra time, and if they do, they can probably take an extra 5 minutes at the end.
During the exam, be very reluctant to change any of the problems. If you realize that a problem is mis-stated, simply ask them to skip it. Some students get really thrown off by changes during an exam. I spoke with one student who spent a great deal of time on one problem, but then was told it was stated wrong and so was changed, and she simply couldn't do it over again, nor could she do any of the rest of the exam. It's really amazing how stressful examinations can be for students.
Reduce the opportunities for cheating before the exam begins. Tell your students that for good form, they should do these things:
have them put away all papers, books, etc. and close their book bags and put them under their seats
put cell phones away. It's reasonable to have a strict policy with no cell phones out for any reason.
turn their baseball caps around so the visor is in the back
avoid allowing calculators because they type things in them (in coordinated courses you have no control over this)
an extra step you could take is to have them sit somewhere different than usual
It is much better to do this ahead of time rather than singling someone out during the exam. If everyone follows good form, it protects them, because there is less for you to be suspicious or mistaken about. It also protects you, because you are less likely to
Students will occasionally cheat, or attempt to cheat, on an exam. It's not very common, but still it is your responsibility to be aware of what your students are doing during an exam or quiz. Generally, you can sit in the room and look around and give students encouraging smiles when they look up at you. Look for students who are trying to ask you a question, because sometimes they are confused by a problem. This gives you the opportunity to be aware of what else students might be doing. The most likely thing is that they look at someone else's paper to try to get an idea how to answer a question. Less common is that they try to use some notes that they brought to the exam, but which are not allowed. Watch for paper in the covers of calculators; students can hide notes there. Some students might get out their cell phones to look something up. Or they might absentmindedly just look at their cell phone when it buzzes; it might be an innocent mistake.
Don't get too busy with your own work while they are taking an exam. On the other hand, don't prowl around the room like you know there is a cheater in the room and you are going to catch them and throw them in jail. That is not the right way to look at it! Also, it's really easy to make your students nervous, even more nervous than they already are during an exam. If you stand up once in a while and walk side to side and look around, that is plenty.
It is your responsibility as an instructor to keep your eye out for cheating and to confront it. It is very difficult to get up the courage to confront someone who is cheating, so make a plan ahead of time and be ready to carry it out.
If you suspect but can't confirm that a student is cheating, begin by staring the person down during an exam. They'll squirm, but may stop whatever they are doing that makes you suspicious. That will probably be enough.
If not, say something general like "Please keep your eyes on your own papers." rather than singling someone out, and don't look at the person you have in mind when you say it.
If you really think someone is cheating, take action. The simplest and least disruptive thing to do during an exam is to approach the person and give them a fresh copy of the exam and ask them to hand you the copy they have been already working on. That way, they can't go back and fix anything they copied. You could also move them to a new location if they are copying from someone else. Moving someone is disruptive and will embarrass them, since it is pretty much the same as accusing them of cheating. So I would be reluctant to do that.
For example, if someone has a cell phone out, have them put the cell phone away, take the copy of the exam they have already been writing on, and give them a new copy. This way you can grade the two parts of the exam separately.
If possible, get independent verification (in common exams, large rooms).
Immediately start writing notes about what you saw, what the student said, what time it was, where the student was sitting, who was sitting next to them, etc. This information will be useful, and it's easy to forget.
This is a draft of a set of common policies across the 1000-level mathematics courses at BGSU.
Procedures for common exams.doc
Academic honesty is critical to universities. The degrees we give are certifications that students have achieved certain levels of mastery of material, and if they cheat, they don't deserve the degree.
If you suspect that someone has cheated, DO NOT EVER return the original copy of the exam or homework. Keep the original, return a photocopy.
Grading exams is time consuming and difficult. In my experience, the hardest part is assigning a number to each problem, and doing that consistently across all students. Here are some suggestions for how to do that.
I personally don't try to make up a rubric ahead of time, to say how many points I'll give or take off for certain types of solutions. Instead, for the first problem on the exam, I read the first four or five solutions and mark things that I notice, but I don't assign a grade until I am sure what grade to assign. Then I work through the rest of the papers, write comments and assign grades, and then go back and put a grade on the first four or five at the end. Meanwhile, the ones that are graded, I sort from best to worst. This makes it easy to compare new solutions to previous ones and keep the grading consistent on that first problem. Sometimes it's really hard to assign the first grades, so I just sort the papers from strongest to weakest, and then assign grades to all papers once I've read them all.
In addition, I make notes on a separate piece of paper, usually a second copy of the exam, about how many points I am taking off for different types of mistakes. Essentially, I am creating the rubric as I read the papers. Usually there are not all that many different types of mistakes. This record of what I took off points for can be helpful later when a student asks me to give more points for their solution; I may have missed something that they did right, and I can modify the score but still be consistent with how I graded other exams.
When I grade the second problem, I start with the students who did the best on the first problem, since they usually do well on the second problem as well, and usually I can see that their solution is correct or has just a few points off, and that makes it faster to grade the second question. By the time I get to the weaker students, where more and stranger answers appear, I have a pretty good idea how many points the solution should get. It's easier to build the rubric from the strongest solutions to the weakest ones.
Write encouraging words like "great!" or "super!" whenever possible on exams you are grading. If someone makes a dumb mistake write "oops" or "ouch" but don't criticize. If a student does badly, write a note to encourage them to come and see you in your office, soon. Follow up with them if they don't.
I am told that students prefer seeing how many points their earn, rather than how many points are taken off. So it might be better to write "18/20" instead of "-2". On the other hand, students have told me that they want to know exactly what part was wrong and how many points they lost there. Overall, I tend to go with the second opinion here, and write "-2" exactly where the problem occurred.
You are not their adversary, you are their teacher, and at times like these, the grader. Their grade is not a matter of your opinion, it is simply a mechanical reaction to what they wrote. This way, you are not the bad guy if their grade is low.
Consider requiring students to pick up their first exam in your office during your office hours. (You may need to add extra office hours that week.) That forces them to visit your office at least once, and you can discuss any concerns you have. This might be a good way to get the weaker students to start coming to your office.
To prevent cheating on exams: When a student does not write an answer, use pen to somehow indicate that there was no answer, so that the student cannot write in an answer after you hand back the exam and claim that they had the right answer all along. One way is to draw a red line through the blank space on the page. Be on the lookout for this cheat: after you hand back exams, a student comes to you with their exam and says you missed a page, didn't grade it, and so the grade is so much lower than it should be. Sometimes students will write in new solutions or correct solutions, and pretend that the answer was there. It is possible that the student has photocopied the page with the first solution masked out, and written a correct solution. If this happens, keep what the student hands you and explain that you need to grade it later, not on the spot. Then ask other people in the department to look at it and see if it seems to be valid.
Sometimes, when you are grading an exam, you will realize that two students have such similar answers that one must have copied from the other. It helps if you can remember if they were sitting near each other in the exam. If you suspect that someone has cheated, DO NOT EVER return the original copy of the exam or homework. Keep the original, return a photocopy.
When handing exams back, do not openly congratulate or chastise students so that others can hear. Your written comments will be enough. FERPA is a federal law that limits us from telling anyone but the student their grades. For this reason, it's helpful to write the grade on the exam on an inside page, not the top page. Or at least write it small.
Some students will stop coming to class once they get their first exam back. They might decide to stop coming after the exam itself, even before they get their grade. The sooner you try to contact these students the better.
You could indicate on the board how many students scored between 90 and 100, 80 and 90, 70 and 80, 60 to 70, and below 60. Don't tell how many students got a 40! If there is just one student below 60, don't mention how many got less than 60.
It can be helpful to remind students that, if their exam grade counts for 20% of their overall grade, then after the exam is graded, they can still move their grade 80% of the way toward 100% (or 80% of the way toward 0%!). Usually this is encouraging to them, to see that they can still really improve their grade if they want to.
Often, the scores will not be as good as students wanted or expected. Emphasize that there is a lot of time left to improve grades. In some classes, Exam 1 counts for 1/5 of the grade, so you can move your grade 4/5 of the way toward 100 (or 4/5 of the way toward 0).
You can say:
it seems that many of you may have overestimated how well you understand.
I have heard that going to the math lab can help. I have been there.
Try doing ALL the problems in each section. Spend your time practicing!
If the results were poor, say so, but don't be angry. Don't tell the students they're stupid, or even suggest it.
Suggest that they can work harder, prepare better.
Tell them that you are determined to keep working with them, to design classes and requirements for their benefit. This may mean giving more homework, more quizzes, or otherwise changing the structure of the class.
Emphasize that you WANT them to do well. You are, in some ways, their coach, and they are athletes.
They need to be encouraged, pushed, pulled.
A former department chair told me about complaints he got from students. #1 complaint: The instructor said I would get, or be able to get, a C, but I got an F.
Too many easy assignments (extra credit, projects) may give students the impression that they are doing well, but the exams count so heavily that they cannot pass
Saundra Y. McGuire is a chemistry professor and director of the Center for Academic Success at Louisiana State University. She wrote the book "Teach Students How to Learn," published in 2015 and spoke at BGSU in March, 2018. She has had great success with a 50-minute talk (which she calls an intervention) after the first exam in chemistry classes and in many other non-chemistry classes. In her talk, she talks about study strategies and about metacognition, which means "thinking about how you think."
She has a 45-minute talk available online. You can watch Dr. McGuire's talk to chemistry students at this link. I highly recommend getting your students to watch the video. It would probably be worth spending a class period on that. Don't announce it in advance or students might just skip class.
Key points from her talk and her book are:
Several students she has personally worked with got low grades on their first exam, then changed their approach and got grades above 90% or even 95% for the rest of the semester. Students who attended one of her talks improved their grades, on average, much more than students who did not attend.
Her number one recommendation: The best way to approach homework is:
Start the homework the day it is assigned
Do each problem on your own, do not flip back in the book to see example problems
Don't give up too soon; spend at least 15 minutes before you give up.
Don't work on any one problem too long, no more than 30 minutes
You can change how you approach a course and learn to study smarter, not necessarily harder
What would require harder work?
Getting an A on a test
Teaching the material to the class
Her recommendation: Focus on learning the material, as you would if you were teaching the material to the class
That covers the ideas in the first 12 of 44 slides from her presentation. The remaining slides introduce Bloom's taxonomy and get students to think about the difference between knowing/remembering, then understanding, then applying, analyzing, synthesizing, and evaluating at the highest level. High school classes might have only required knowing/remembering, but college classes require higher level thinking skills. There is a slide about The Study Cycle, telling students how they should study in more detail than the list above. There is a slide about metacognitive strategies, how students should consciously direct their learning. Metacognition is the ability to: 1. think about your thinking, 2. be consciously aware of yourself as a problem solver, 3. monitor and control your mental processing, 4. accurately judge your level of learning. Finally, there is a helpful list contrasting what students who scored poorly did before an exam compared to students who did well on the exam.
Talk with your class about what happened on the exam. Use this sheet, or modify it as you see fit:
Looking back at the exam.pdf Looking back at the exam.doc
You may be able to get your students to really think about what happened on the exam. If they turn it in to you, you’ll learn something about what they need more of. One benefit of this is that it emphasizes that the responsibility for preparing for exams lies with them, not with you, the instructor.
My suggestion is that you take some time in class for students to write down answers to these questions, put their names on them, hand them in, you read them, make encouraging comments, and hand them back. You may learn a lot from doing this!
At the end of the semester, your students will fill out a course evaluation.
[insert current BGSU student evaluation questions here]
You should read through these questions now so that you know, in some sense, how you will be evaluated at the end of the semester. For instance, question 10 asks the students whether you, the instructor, always seemed well prepared for class.
Students overestimate how much time they spend studying for your class. One reason is that they "study" while they watch videos or sports. Consider challenging them this way. Ask them to open their notebook to the back, or inside front cover, and ask them to start keeping track of when they really work on your class in a place with no distractions. Have them write down to the minute when they start, when they end, and calculate how many hours and minutes they spend each week. Encourage them to try for, say, 2 hours this week, then 3 hours next week, etc. In order to have an effect on how much time your students actually work, remember to keep asking them about it. Ask how many people documented more than 2 hours, more than 3 hours, etc.
As I will write elsewhere, I consider this to be part of developing our students into successful college students. You may complain that we shouldn't baby our students this way, but I found this to be extremely helpful when I was a graduate student, and I find it appropriate to challenge our graduate students this way.
I'm still teaching material that isn't extraordinarily difficult to students who admit, freely, that the material isn't extraordinarily difficult and yet I still have students who are bombing every single assignment just because they put in practically zero effort. Even though it's been happening for 8 weeks now, it's still pretty flummoxing overall: I'm not sure if I'll ever be "desensitized" enough for it NOT to be, though. I guess it would probably be helpful if I give some sort of example.
Personally, I give out a lot of turn-in homeworks. Not book homeworks, though, because to me, I have more freedom to "customize" my students' assignments based on what I've taught if I personally create assignments to give them. So, long story short: I usually give out "1.5 turn-in homeworks" per week (one on Monday that's due Wednesday and one on Wednesday that's due Monday). In the 150 points I'm allotted to bestow, I have 50 points allotted to homeworks (which, subsequently has to be split-up between turn-in homework AND Mathzone) and 100 points allotted for quizzes; for whatever reason, I haven't given many quizzes this semester and the majority of my assignments have been into the first, 50 point category. Well, even though my students come across as terrible math students, they were clever enough to realize that the turn-in homework points were being "saturated," so a lot of my strong-B students will turn in 20-and-30 percent complete assignments because they don't really "matter" at this point.
So, I decided to change that. I started giving mini-quizzes almost every day during the Matrix supplement lessons AND I gave a big "take home quiz" that counted as two full quiz grades and that covered the pre-Matrix stuff (optimization, absolute max/min, exponential/log functions and their derivatives). Given the small number of quizzes they've had up to this point, it ended up counting about 6.5% of their grade and so I was careful to emphasize REPEATEDLY that good time-management skills were necessary. My goal was two-fold: I wanted to encourage "good students" to be "good students" (i.e. NOT to turn in an assignment that's practically blank) and I wanted, of course, to make sure they kept all of the stuff fresh in their minds during the Matrix supplement. For exam purposes, that part was key. I even threw in some "cool" bonuses (cool to me, probably not to them) and I gave them a full SEVEN DAYS to complete this thing and turn it in. The results to me were staggering.
I had a few students who had been very average (at best) turn in some staggeringly good work. I also had several of the good students CONTINUE the habit of turning in subpar assignments. One guy was borderline A after the second exam (88% range, if I'm not mistaken) and turned in yet ANOTHER almost blank assignment (it's his fourth-or-so in a row); needless to say, his average is down to like 82%.
So, long story short: All of my predictions turned out to be incorrect. I don't know what to do, really.
See this link Advisors and students around campus have found these maps to be very helpful in understanding how the 1000-level math courses fit together. You might want to carry a copy with you in case a student asks about another course.
Attend the mandatory meetings. Follow procedures! Don’t hand out old tests. Don’t give makeup tests unless the coordinator says it’s OK.
As the semester goes on, students might start missing classes or skipping classes. They get tired, they want a break. They might be extra busy in their other classes. They might have all kinds of personal difficulties. In the end, they are adults, they get to decide whether to come to class or not, and there is only so much you can do or should do. Still, here are some things you can do
Take attendance every so often and keep any notes that students give you. It can be helpful at the end of the semester to know when a student last attended class.
You can write emails or handwritten notes to students who miss class to let them know that it's important that they come to class. This also signals to them that you are keeping track and that you care.
If attendance counts toward their grade, you can let them know that missing class is starting to hurt their grade.
You can schedule quizzes on Fridays, or whatever the last day of the week is in your class.
It's good to ask them to let you know ahead of time when they will have to miss class. They will usually tell you why even if you don't ask, and I think it's best not to get too nosy about it. If they miss class without letting you know, you can write to them to let them know that you expected them in class and that they really need to come to class and that you want them to do well in the class. You can say that you are concerned about them. But in the end, you cannot really force them to let you know that they will miss class.
Probably the most effective way to get students to come to class is to make class useful to them. Keep thinking about how to make class more obviously useful, and how to get students doing more during class. If they are working on problems during class that are like the ones that will be on their homework or on exams, and getting feedback and help from you, then they know that class is useful. If they are getting insight from your short lectures on various topics, then they know that class is useful.
You can give a half sheet survey at the end of class with the usual questions, what is going well that we should not change, what should we change, and add a question that says, "I notice that students are starting to miss more classes. What can we do differently so that everyone comes to class?" That lets students know that you are concerned about it.
It doesn't really work to force students to come to class by taking away more and more points. If attendance counts a small amount toward their grade, that helps to encourage students who don't really have much of a problem. But students who miss a lot of classes have bigger issues in their lives. Keep encouraging them. hope for the best.
After you do a few examples, write another problem on the board, ask them to start working on it on their own, wait a minute or two checking on a few of them at their seats, then write the solution on the board yourself silently. Students should be working on their own, ahead of you. They can check their work as you catch up to them. At the end, they have their solutions, and you have a correct solution on the board, almost as quickly as if you did it with them on the board, but they have each done the work themselves. This breaks the reliance on the few students who already know how to solve the problem.
(These comments are inspired by notes from September 2005 from international students at this time in the semester)
Very early in the semester, international TA's (and some American ones too) need a lot of help learning the right level at which to teach. In some classes, when you solve a linear equation like 7x-3=18, you should write things like 3 = 3 and add equations. In others, you should take time to add fractions. In every class, you should start with concrete examples and then give a definition. For example, don't give a general definition of a polynomial, then examples. Give some examples, look at their graphs maybe, and then describe this whole class of functions with a definition, and make note of some of the properties of polynomials generally. So that, whenever the definition is met, there are certain things they can count on. Now they have a REASON for using the definition; it is not for its own sake, but rather so you can be sure of some things about the function you're seeing.
For all students, a good approach is to give a specific example, say, 3(x-2)^2 + 5, make the graph by plotting points, then look again at the graph. The most interesting point is x = 2; when you plug that in, you are getting 0 squared. Draw their attention to this. Around that you see symmetry. The 3 has a meaning. The 5 has its effect. By considering an example, you now have the means to think about a(x-h)^2 + k. This is how to go from the specific to the general.
It's great that you recognize this difficulty and try to do something about it as soon as you can. It is a real problem. I have seen international TAs (and TAs from the US as well!) answer a different question than what is being answered, and it is frustrating to students, both the one who asked the question and the others in the class. Also, at the end of the semester, students often write on their evaluation forms things like "communication was a problem" and "she didn't understand our questions." What can you do?
Always be aware that you might not understand what the student is asking about. Students ask questions when they are confused, and they might not know the right words to say. They might not be able to identify exactly what they are confused about, but it's good that they stop the class and try to figure it out.
Once the student asks a question, restate the question to the whole class, and ask if that is the right question. If there is confusion, say "Someone help me here" and someone else may be able to re-phrase the question so that you understand. Or someone can re-state the question slower, if that is the problem.
Always be clear with the students that you are trying hard to understand English and that you really want to understand and help them. Also that you are trying to improve your English. They will be sympathetic. Laugh at yourself. Remember that you are doing something very difficult, coming to another country and trying to teach in a language that you didn't grow up speaking. But also remember that you are a solid mathematician. You know this material. You are competent to teach the course.
Be aware that misunderstanding just one word can make a big difference. For your part, pay attention to how mathematical words are pronounced in English, so that when you say them, your students will have less difficulty understanding them. Ask your students to help you learn the American pronunciation, and smile and thank them when they correct you. It will improve the atmosphere in the class.
When you are solving a problem out of the book, like Exercise #12 in Section 2.3, ask a student by name to read the problem for the class, "Bill, would you please read #12 in Section 2.3?". This wakes Bill up, the students will understand what he says, and you get a few seconds to collect your thoughts.
I believe that students benefit in a number of ways from being taught by instructors who did not go to high school in the US. Certainly this difference makes it harder to connect with them, but it also increases the level of formality in the classroom, which you can use to your advantage. You can more easily set high expectations. Just the way you speak about homework and exams will be different enough that it will make students look at them differently.
This is always a problem. We need to cover a certain amount of material in each course, both to prepare for the next course, and to make the course able to be transferred to another school. But the students have a hard time learning as fast as we might want them to. Fortunately, the coordinators have been covering this material for many semesters, and we have worked out reasonably well how much can be covered and at what pace. Here are some suggestions.
Be prepared for class so that you can use your time efficiently. Plan out what needs to be said and try hard not to say any more than that. Don't repeat what you already said unless it really needs to be repeated.
Arrive to class a few minutes early to hand back homework or answer students' questions. Write general announcements on the board and tell students to read them, but don't spend your time reading them out loud. Your students will learn to pay attention to them.
Pump some energy into the class. Be energetic, push students to respond a little faster. Call on them by name, so everyone has to be attentive at all times. In sports, you often wait for the play standing on your tiptoes, and it helps you react more quickly. Keep your students on their toes.
Change the pace during each class period. You know that I encourage you to put problems on the board and have students work on them, but don't do that all class long. It takes too much time. Work through some examples with the students helping you along. Work through some examples deliberately but without waiting for students to tell you what to do. Put up some problems, give them a 45 second head start, then solve the problem on the board silently while they work.
Have high expectations for your students. Expect them to be on time for your class. Start right on time, and make sure that people feel a bit behind when they arrive late. Call on people by name. Ask them to read a problem out loud before you solve it.
Know what the coordinator REALLY wants you to cover in each section. Math 1120 and 1220 each have a Master Plan which tries to outline, section by section, what is important to cover and what can be omitted.
Don't hammer away at a subject until every student understands. Spend your time wisely. Give a reasonable number of examples and give students an opportunity to attempt the problems, then send them home with specific homework problems to do and the expectation that they will work on them. They have responsibilities in your class just as much as you do. You are working together.
As you know, I am a big proponent of posting problems for students to solve and circulating among them to see how they are doing and interacting with them one on one to help them with problems. Unfortunately, this takes a lot of time. Here are some ideas for getting this sort of feedback more quickly.
Work through a problem on the board. Here and there, stop and ask the class what to do next. The pace tends to be driven by students who understand very well what you are doing, and so does not give much information about the class a a whole. Instead, call on specific students to see if they can supply the next step. Be gentle, they might not be following. Here is good idea that Mary Paler uses when no one answers. Pick a row of the class and ask the students in that row when you need to call on someone. That can make it easier to remember who to call on, and it gets them prepared to answer the next question.
Write a problem on the board and let the students work on it for one minute. During this time, walk around and look at a few papers. Then go to the board and solve the problem silently, telling students to check their answer when they are done. Once you've written your solution, spend another minute to check on students who seem to be having trouble.
In the middle of class, have students take a half-sheet of paper to write down any specific questions they have and any general areas they are confused about. They are not necessarily good at self-diagnosis, but then again they rarely engage in it.
In the last few minutes of class, ask the students to take a half-sheet of paper to write down what they thought the main lesson of the day had been and how well they think they learned it. I'm sure this will give surprising results!
At the beginning of class, post one problem on the board as a "do now" problem. Choose a problem that was covered in the previous class. Give them 3 minutes to do it (or whatever is appropriate, but make it short to push them). You can look through them very quickly and get an idea how they're doing. Plus, it gets their brains going and forces THEM to remember what they learned the previous class.
Placement into a first mathematics course is not an exact science. At BGSU, we use high school GPA, ACT Math score, and the score on the online placement test that we give. Sometimes students use their calculator or get help when they take the placement test, and so place into a higher level class than they really belong in. On the other hand, some students choose to take a lower-level course than what they place into because the lower-level course will satisfy their degree requirements and they think it will be easier for them. (This is true unless they get so bored that they start skipping class and quizzes and exams.) Here are some ideas for dealing with weak students.
You may have a few students who do very poorly on everything - first day project, first quizzes, first homework assignments, etc. Talk with these students individually to suggest that they consider dropping this course and taking the prerequisite course instead. There is no need to accuse a student of cheating on the placement test. Sometimes students can't drop the current course, especially so if they have already received a C or higher in the prerequisite course. Such students may benefit from spending more time in your office hours, in the Math and Stat Tutoring Center, or they may wish to hire a private tutor.
Often, students have not taken a math course for many months or years. This is a reason to begin the course by asking them to do some relatively simple problems. It is also the reason to spend a week or so on "review". Review helps to get everyone together with a common set of recently-practiced skills.
Despite the truth of the first two points, teachers perennially complain that their students' math skills are weak. There is probably some truth in this. In 1000-level math courses, there is probably some selection bias: the students who are in these classes are exactly the students who had a hard time learning math in high school, students who had poor high school teachers, and students who were not very motivated in high school.
Besides this, many of the students we teach are first-semester freshmen. Many of them are not quite yet settled in and have lots of changes going on in their lives outside of class. Many of them are enjoying their freedom to stay up late and go to parties and haven't balanced themselves out yet. People who teach freshmen do the rest of the university a favor by working with these students, getting them focused on their academic subjects, teaching them organizational skills (or at least demanding them). This is different from seeing your role as a teacher as "weeding out" students who are not ready for college. The US (and other countries) can really benefit from having more students do what it takes to graduate from college. We should try to help these students develop into successful college students rather than seek to "weed them out." Even so, some of them will get poor grades in their first semester and won't be allowed to return to school. That's also appropriate.
Having read all that, you have the students you have. What are you going to do with them? Here are some suggestions.
Set high expectations. This is college after all. Identify the level of difficulty of the examples you do, so they don't get complacent. Keep the pace in class moving relatively quickly.
Praise good performance. Make note of anything and everything that students do well. If someone's homework is written neatly or nicely organized, make note of that. If they show improvement, tell them that you see it.
Encourage them to work hard. The folks who work in our Math Lab found that having students do literally every problem in every section of the book turned students into B students for the first time in their lives. Hard work is much more important to success in 1000-level math courses than having a "math brain." Many, many students just like them have figured out how to succeed in courses like this.
Motivate, don't threaten. Surprisingly, the final course grade does not seem to be a big motivator for students. So don't rely on that to get students working. Tell them, in general terms, what benefit comes to people who master the material you are covering in class. Let them know that employers are always looking for people with good quantitative skills. Many students like math because they like solving problems, they don't need any more justification than that. Others enjoy that what they are doing will have some benefit to them later on.
Compare math to sports. Many students play sports, and they don't seem to mind spending lots of time practicing. Working on math is something like going to the gym to lift weights. It's hard work, very concentrated. It may or may not directly correspond to something you'll do when you leave the gym (lifting weights may help you play tennis, but you don't do the same motions in each case), but you know it's good for you. Math is not unique in the whole university this way, but it is a specific form of mental exercise that makes people better thinkers.
Encourage them to figure out what works for them. Some students benefit from taking careful notes in class. Some read the section ahead of time. Some need to do their homework right after class. Some really find that doing their homework in the Math and Stat Tutoring Center works well, even if they don't talk to a tutor.
Challenge them to really spend time on the class. As I mention above, students often don't have an accurate idea of how much time they really spend on a class. Once they start to keep track, they may have a better understanding of why they do poorly.
Understand the concept well yourself. In many cases, explaining is a good way to improve your own understanding.
Think about what your audience already knows, and what background knowledge they need but may lack.
Orient your audience, perhaps by giving a motivating example of the need for a new concept or by reminding them of something they already know, which they need to keep in mind as they start to hear about the new idea. It’s nice to have a short story or illustration that helps people remember. Something historical can go well, something from the real world. It helps to have something vivid. Of course, the details depend on the concept you want to explain.
State the concept – a clear statement is the right place to start, without using the word itself in the definition / statement
Elaborate on the concept – restate it, put it into different words
Give examples of the concept. Choose appropriate examples.
Contrast with non-examples.
Illustrate – draw a picture, a diagram, show something in action
Use analogies: start with a familiar concept or situation and explain how the new concept is similar but different
When explaining a concept to a non-technical audience: Speak English, not Math.
A person is on trial for murder. You are on the jury, listening to the evidence from both sides. Soon, you need to decide whether to send the person to prison or set them free. The trouble is, it's hard to be sure if they are innocent or if they committed the murder. The table below shows four possibilities, according to what really happened, and according to what you decide.
| set free | send to jail |
innocent | | |
committed murder | | |
(The wording in the example is carefully chosen. Please avoid using the word "guilty" because it is ambiguous, "guilty" means that the person committed the murder, but it is also the decision that is made by the jury. The same word is used for the reality of the situation and for the decision that needs to be made, and that is confusing.)
There are four empty cells in the table. In two cases, you make the right decision:
| set free | send to jail |
innocent | OK | |
committed murder | | OK |
However, if you send an innocent person to jail, or set free a person who committed murder, that's bad.
| set free | send to jail |
innocent | OK | bad #1 |
committed murder | bad #2 | OK |
In the United States, a person on trial is presumed innocent until proven guilty. In other words, the system is set up to be very careful about making the mistake marked "bad #1". That provides protection against a problem where the police are careless in arresting the wrong person, or the government is trying to target a person with a murder charge to get them in trouble. Of course, setting free a murderer is also bad. It's good that we have new tools like genetic testing that can help to improve our accuracy.
In the United States, to convict a person, the jury needs to decide that there is evidence "beyond a reasonable doubt" that the person committed the murder. That is not the same as "absolutely certain" but it's still a strong standard. When the jury decides to set a person free, we say that the person is acquitted, not that the jury found the person to be innocent. That is an important difference! The members of the jury may all strongly suspect that the person committed the murder, but the evidence might not be strong enough to send them to jail.
We can rephrase the jury decision in the language that will be used for hypothesis testing. The null hypothesis is that the person is innocent. Type 1 error is called bad #1 above, and is the more serious kind of error. Type 2 error is called bad #2 above, and it's also bad. When we say that we "reject the null hypothesis" it's like deciding that the person is not actually innocent, and needs to be sent to prison. When we "fail to reject the null hypothesis" is not's the same as deciding that the null hypothesis is true, that person is innocent. The null hypothesis may be true, and it may not, we don't have enough evidence to say.
[apologies for the poor display of a table; new google sites does not have a good way to insert a table without inserting a lot of extra white space above and below]
Today I'm going to show you how to juggle:
One ball, throw it back and forth
Two balls, throw one, then the other at the right time
Three balls, just keep it going
Ask a volunteer to come to the front and show us
What would I have done differently if I had set out to TEACH you how to juggle?
I would have motivated you to learn:
How many of you know how to juggle?
Juggling is a sport, like many sports, but usually more individual
Like many things, it's not impossibly hard, but you need to practice
Many people find juggling to be fun, they can amaze their friends, and the practical outcome is that you get better at catching things before they hit the floor, like soap, pens, keys
I would have broken it down step by step, as I did when showing you
I would have brought enough balls so you could try right now
I would have gone around the room to work with each one of you individually
I would have asked you to go home and practice this on your own and it would have been obvious to you that you would need to practice
Consider joining the MAA.
Help students notice the difference between
[Sorry ... images are missing since I moved from a wiki to google sites. Hopefully I can restore them.]
and
Ask them to tell you what the difference is.
This is similar to something valid,
Here is a suggestion. Ask the students to look at
and compare it to
Have them describe the difference to you. Ask them what you can do to simplify or rewrite each one. Follow this up, maybe the next day with these:
and compare it to
Ask them to work with all four of them to see how they can be rewritten and simplified. Then, the next day, make up another example, give them all four combinations of multiplication and addition but in a different order, and ask them to take a few minutes to rewrite them. Repeat this lesson as many times as it takes. Also repeat it a few weeks later. Don't spend much time on it each time. Spaced practice helps.
How to explain
to a student who doesn't understand?
Academic honesty cases: What is the appropriate sanction?
Think of the class you are teaching. (If you are not teaching, think of Algebra.) Explain in about 45 seconds what your class is about, what it covers, what the goals are.
How do you try to incorporate good practices into your teaching? What are you trying to remember to do in class?
If you could change one thing about your students, what would you change?
Next time you teach, how can you start at the beginning of the semester to change the students in the way you identified?
Make sure to address two of the "Good practices when lecturing". Do you agree or not agree with the suggestion?
Do you know your students' names? Keep trying to say their names each time they ask a question, each time you call on them, each time you return a paper to them.
A major reason that students drop out of college (as measured by follow up interviews with students who have left college) is that they never developed any personal relationships with anyone at the school. There is a benefit to the institution to you getting to know your students as more than just faces in the room, and more as individuals.
Observe an instructor who is teaching the same course as you are; if no time works to observe an instructor, observe a graduate student not in Math 5910 and write a report. Your notes in the class can be the report itself. Pay attention to the following in particular:
How the teacher interacts with students, before class, during class, after class, including answering questions, asking questions, eye contact.
How the teacher "teaches". What is the strategy for teaching? How does the teacher try to promote understanding?
How the teacher motivates the material.
If there is not much to say about these things, write about what is most interesting to you. Tell me what you learned by observing.
Also, of course, keep yourself up to date on weekly reflections, do your previous classroom observation, colloquium notes, etc.
Every student is different. Their motivation level changes over time. The messages they will respond to change over time. A reasonable strategy is to use a variety of means to try to get them motivated. Be enthusiastic in class - this has been recommended to me as the most important thing you can do to motivate students. Pump energy into the room. Pay individual attention to your students, to the extent that you can. Write to or call students who miss class. Talk with students who are struggling. Write notes to get them to visit you in your office hours. Keep sending them messages designed to get them to work on doing well in the course. Keep hammering away at these basic messages:
Hard work pays off. Everyone who was placed into this course has the basic ability required to succeed in the course. What is needed now is hard work. Come to class every day, pay attention, and take notes. Do your homework and do it well. Do extra problems before quizzes and exams. You don’t do well in math class just because you’re smart or have a “math brain”. You do well by working hard. Ray Heitger says "Attitude, not aptitude".
You can succeed in math class. You might have struggled with math in the past. You might have some degree of math anxiety. Regardless of that, you can do better and better by working hard at the right things. Pay attention in class. Ask if you have questions. Come to see me in my office hours. Hire a tutor if you think that will help - $10 an hour could be a bargain compared to having to take this class again!
You and I each have jobs to do. As the instructor, I have certain jobs here. I structure class time the best I can, I explain the best I can, I give useful examples, I give assignments that help you master skills and deepen your understanding, I grade them and give you feedback on how you’re doing, and I meet with you individually outside of class. You also have responsibilities, to come to class, to pay attention, to think hard during class to figure things out and fix any misunderstandings that are holding you back, to do homework problems, to review your notes and do additional problems to prepare for exams. You do your part, I’ll do mine!
I am here to help you. My job is to help you learn math. I do that by teaching, by giving you feedback on homework, quizzes, and exams, by setting up the course to push you to learn to do well on exams and other graded things. I want you to succeed.
I know you can do better. Your performance on the last exam/quiz/homework was, overall, pathetic. I know you can do better than that. High school students do better than that. You need to work harder. There is only so much that I can do, you need to do the rest yourself.
Your grade is in trouble, but you can improve it. Often, students don’t seem to be very motivated by grades. It is your main power over them. But be their ally, and let them know you can work together to make their grade get better.
The economy is a mess. You are going to need a job. Who do you think is going to get hired in this economy? College dropouts? College graduates with low grades? No. Hard-working people who succeed at what they set out to do. Being a college graduate is a demonstration to an employer that you are trainable, that you can learn new skills and that you have an interest in learning new things. You’ve enrolled in this class. Now get down to work at succeeding in it. Come to class. Pay attention. Do your homework and do it well.
The bigger picture. You are a university student. A university degree is the hallmark of a broadly trained and intelligent person, and confers prestige on its recipient. Some of that may require that you learn and master skills or domains of knowledge that you don't personally find all that interesting, but that other intelligent and accomplished people find indispensable. Don't doubt their collective wisdom. Saying "I don't care about that" is a loser attitude!
What would a sports coach do to motivate his or her team? You have probably seen movies about sports coaches, or maybe you have been an athlete on a competitive team. What do coaches do? Does it work? One great thing about a coach is that he/she is not your adversary. The coach is your partner, someone who knows better than you what you should be doing to get better. Coaches use all kinds of devices to motivate their players. Sometimes they yell, and I don't recommend that you do that, but sometimes they inspire, they always challenge, etc. What is great about the coach metaphor is that students are generally aware of what it takes to be a solid member of a team on a great team, either from personal experience or from watching movies. They know that they have to work hard, that they have to push themselves.
Read this site: (google “motivating students” It should be the first link.)
http://honolulu.hawaii.edu/intranet/committees/FacDevCom/guidebk/teachtip/motiv.htm
How do we motivate un-motivated students? I once asked this question of my Math 591 students.
Keith Richards writes:
I have one student, for example, who received 32 out of 75 on the exam, yet he never came to my office hours, even though we discussed and agreed it would be extremely beneficial. In addition, he did not complete either of the two homework assignments due this week, he scored 3 out of 10 on a quiz we took, and he even fell asleep in both classes I taught. …. I have many students whose situation is similar to this one student I described, and most of them do not seem to care about their poor grades. Some will laugh or smirk when I realize they have not done the homework, as if it is funny that they are not doing well in my class. I have some students who openly admit they are just lazy students, and for me not to take it personally.
Kai Di writes:
Last week I gave all the students the 1st exam's results, they seemed to be upset. However, after class only the top students came to me to argue about the grading. Others, whom I encouraged to talk to me, did not show interest in adjusting their learning methods. Now, I am really confused. How can I help them?
In my conversation with the top students, I asked them why they did not go to my office to ask questions. They told me they understood everything. Maybe this is the main problem here. They think they are fully prepared, but in fact, none of them get enough practice. They must take more efforts. I can't always stand behind them, push them. They have to take their own responsibility.
Here are some words of advice from Grace Ngunkeng's 1220, College Algebra, students to future Math 1220 students:
Start studying right away
Definitely start studying at least a week or two before exam. Don't cram on the last 2 days before exam.
Work on problems that you don't know first and get help if you need it.
Just go to class and do all the work!
Make use of the Math and Stat Tutoring center
Don't give up
What to do with students who don't turn in homework even though it counts for a big part of their grade?
How do you get across to them that we, as instructors, want them to succeed and aren't grading harshly because we want them to fail, but because we want them to do better?
What do we do when we run into a student in a social situation over the weekend, like at a bar?
By giving special treatment to students with "learning disabilities" (presumably those of the "test anxiety" sort rather than more physical disabilities) are we really preparing students for real life?
How would you show students that you cannot cancel addition through division?
Cognitive psychology finds that people learn things better when they work on them for a while, then come back to them again, and then again, rather than spending the same amount of time all at once. The advice for math teachers is to keep going back to previous problem types and ask students to work on them, a week and a month after you cover them for the first time.
Students need to remember that hard work is the way to succeed in math. Not just "being smart".
Imagine the difference between telling a child "good job, you're working hard" versus "good job, you're really smart". Which one helps to develop the right work habits?
Look up and watch videos by Carol Dweck.
At BGSU, undergraduate students need to be registered for 12 credit hours in order to be considered full-time students. This prevents some of them from withdrawing from a class, even though they have little chance of passing the course. There are two main reasons. First, students are concerned that they may lose their financial aid; this may or may not be true; they should talk to the Office of Student Financial Aid to see about getting their aid "repackaged". Second, students may have health insurance through their parents' insurance, which will generally require that they be full-time college students. If they go below 12 hours, they may lose their health insurance. Keep these things in mind when talking with a student about withdrawing from your course.
Cognitive psychology finds that people learn things better when they work on them for a while, then come back to them again, and then again, rather than spending the same amount of time all at once. The advice for math teachers is to keep going back to previous problem types and ask students to work on them, a week and a month after you cover them for the first time.
Example: Draw a parabola on the board, then ask students to identify the signs of a, b, c in the standard representation f(x) = ax^2+bx+c of the parabola. This is an exercise in reverse. It is an example of promoting deep learning as opposed to surface learning. The difference: surface learning is what you get when you present the same problem from the same angle every time, and then ask students to do exercises that are exactly the same. They never have to confront their misconceptions or lack of understanding in a serious way. But when you ask a question that requires a deeper level of understanding or insight, you force students to work harder, and as a result they will learn more. A question such as this one is one that they have all the tools to answer, but may have never been asked before. Even you may never have had to answer such a question before!
Simpler example: with grade school children, one often practices "math facts" using flash cards. Card after card with things like 2+7=?, 5+4=?, 9+0=?. These ask the question in one way. Another way to ask the question is: what do I need to add to 7 to get 15? That's not exactly subtraction, and it's not exactly addition. It gets at the math facts in a different way.
Teach something just as you plan to do in the class you are teaching.
Focus on a lesson in which you deliberately try to deepen your students' understanding, their intuition, rather than simply building up a skill or teaching a process.
Please limit yourself to 5-7 minutes. Plan your time well.
You should be able to say a lot in 5 minutes.
Don't erase what you write, so we can look at it, comment on it
Afterward, 5-7 minutes of commentary on good practices that we see, the commentary and comparison with other possible approaches to the material
There are a number of types of problems in which students need to decide what to do. For example, integration by substitution requires that students identify an appropriate substitution. Often they are stymied because it seems like there are so many possible things that they could try. A very good suggestion is that you have them make a list of 5 possible things to do, 5 things they could conceivably do. Do this will them on a few problems. Don't reject any of the suggestions, just list them. Then, have them look through the 5 possibilities and choose one that they want to try first. Usually the right thing to do will be among the five, and they will often be able to identify it. This will help students build independence, which is mentioned below.
For example, when teaching integration by parts, there are often several conceivable ways to break apart the integrand. List five of them, and then choose one to try.
How do we teach the students that we have?
How are they different from what you were like as undergraduate math students?
What are they interested in?
What motivates them?
How can we make them better students?
Can we make them better students?
Can we really change their skill level at all?
Do we make them more likely to pass the next course?
Have them read the section ahead of time and write down what is in all of the "boxes". Have them write the definitions of terms ahead of time. This saves you time in class. It can be especially useful when you are behind the schedule set by the coordinator. You should explain to the students that, in order to catch up, you need them to do more work outside of class. This is in their best interest, as it allows more time during class for the things that are most important and most difficult.
Shihai Liu, from his experience in the tutoring center, recommends that we focus on building up our students' confidence in themselves, which can lead to them working more independently, which will help them push through problems that appear at first to be difficult, but which they can actually do. First, about confidence. Many of our students lack confidence. They have not been successful with math in the past, and if they don't build some confidence in their abilities early in the semester, they may resort to hanging on for dear life and trying any crazy method to memorize the steps needed to solve problems. I have seen this myself when tutoring students who are studying calculus. They stop trying to understand, they just try to memorize. We need to build confidence before students get to this stage. We do this by having them do problems that they are ready for and get them right, then move on to slightly harder problems and so on.
This website and this organization have interesting ideas about where education is going in the long term.
This article in Scientific American suggests that it is helpful to have students try to answer a question before you teach them the answer or how to find it. The act of thinking about it helps to focus their attention on what they will subsequently learn.
Educators may legally use some copyrighted material in the classroom for educational purposes. Read more here.
There is another page about teaching. Here is the link: Teaching part 2
Help students start to prepare for the final exam. Students are often overwhelmed in the last week of class and final exam week. I think it is a good idea to get them started in the second to last week of class with very concrete things that they can just sit down and do. You can make a set of review questions that they can work through. Much better to give them specific things that will not take forever, than to say "review the whole semester" or even "review chapters 5 and 6".
Ask your current students to write some advice to students who will take the same class with you in the future. Your future students will respond well to advice from real students just like them. You can use the form below, and cut the page in half to make a half-sheet survey.
Advice for future students.docx
I would suggest that you scan the half-page comments you get; make sure to darken the scan so it picks up pencil well and ends up being legible. Use the comments selectively at different points in the next semester. You can copy and paste some comments into your syllabus, or an assignment or a review sheet. You can use the scanned original if it's easy enough to read or retype it. You should certainly screen the comments in case someone misunderstands the request or deliberately writes something that is not helpful.
Prepare them and yourself for the final exam
Keep encouraging them to prepare for the final exam with concrete things they can do.
Students can’t do as well as usual during final exam week, don’t hope for miracles
Students believe they will get extra credit, or curved grades, or will ace the final exam. Now is a good time to tell them about reality.
Remind them of the final exam day, time, and location, every day of the last week or two. It is really awkward if people miss the final exam!
Students may miss the final. Tell them:
Notify me as soon as possible if you have to miss the final.
Do not skip the final because you are going to be late. Come late to the final. It's easier to have them start late and finish a few minutes after everyone else. You don't have to worry that they are getting the answers from other people who already took the exam.
If your school has students do online course evaluations outside of class, encourage your students to fill out the evaluation, because you need feedback on your teaching, to make your teaching better. Ask them to add written comments, because those are the most informative for you and for people writing you letters of recommendation.
If your school has you hand out paper course evaluations at the end of a class period, I suggest that you not do this on the last day of class. Before you hand out the evaluations, encourage students to take put some time and effort into filling them out, because you need the information.
Usually a day for review. It is good to allow students to ask you to go back over some topic, or ask you to do specific problems or problem types. I suggest that you also bring relevant review questions instead of thinking that the students will ask all of the right questions to review.
The last day of class, not the final exam, is the right time to thank the students for working hard during the semester, to let them know that you enjoyed working with them, to wish them good luck on all of their exams, and to wish them the best in future semesters or after college. It is awkward to follow this up with handing out course evaluations, and besides, if you hand out course evaluations, you should leave the room, and then it is hard for students to find you and ask you questions.
Make sure it’s not too long
Don’t get fancy. Concrete, familiar questions work better, and they are easier to grade.
It's quite OK to put some easy questions on the final. It's nice to have those first on the exam.
I don't know why people think that the final exam should be worth more points than midterm exams, except that you usually have more time allocated for it. Students are usually tired, sick, and stressed during final exam week, and so they usually do not impress me with how much they have learned over the semester. So I would suggest you lower your expectations for the final exam. With that said, it would be very nice for students to prepare well and be able to demonstrate mastery of what you taught the whole semester. That could happen for some students, but it won't happen for all students.
Follow the usual procedures for reducing academic honesty violations.
Be encouraging before the exam and wish students good luck.
Each instructor/TA should meet with their coordinator during final exam week to go over their grade sheets and decide on final grades together. This will be a big help for students who are on the borderline between two grades.
When you read teaching evaluations, be prepared for the likelihood that some students will say that they disliked certain things about you or about the class. Comments like that hurt, maybe more than you would expect, but fortunately, the pain goes away over time. It's a really good idea to make note of any ways that you can make your teaching go better the next time.