Reflective Statements
This page contains reflective statements on my teaching experiences. Some of these reflective statements relate to teaching materials provided in the Teaching Materials page while others are included to complement the teaching materials in this eportfolio. I include an email (reproduced verbatim) written to Dr. Suanne Au in response to her asking a colleague and I for suggestions on how to improve the teaching of MAT 221 Elementary Probability and Statistics I. I include this email as it is essentially a reflective statement on how to improve a particular class. I then include reflective statements on delivering lectures, grading, office hours and student emails. I plan to update these statements over time. I also plan on adding comments or reflections on other aspects of teaching in the future.
On Improving MAT 221 Elementary Probability and Statistics I
Hi Prof. Au,
Colleague name and I met briefly to discuss how we can improve the teaching of the course. I think we can discuss this more while we grade together next week or just via email.
Although it's difficult to come up with anything conclusive, here are some prelim. suggestions:
I think a mini math bootcamp would be helpful for students at the beginning of the semester. The more important topics we could possibly cover include: sigma notation, algebraic symbol manipulation, solving algebraic eqns., eqns. of lines, etc. Although students should be coming into college with this background (SAT math & high school algebra), not all of them remember it and many lack this algebraic facility. This will hopefully bring the students who need it up to speed and serve as a review for those who are already capable.
(i) We can spend a half a lecture and or recitation reviewing the necessary math skills needed for the course. A HW assignment on the material from the math bootcamp could help. I think this is doable since the material in the first two weeks is pretty easy.
(ii) If not (i), then we can write a pdf of the mini math bootcamp with practice problems like we do for MAT 295 (Precalculus bootcamp).Prof. Au has already discussed this in our pre-semester meetings, namely, we should stress good study habits. The material in the first two weeks of the semester is a lot easier than the rest of the course and so many students get a false impression for the difficulty of the course. They think they can just glide through the class without doing any work until they get reality checked by the first exam. We should stress that it will get harder and that they shouldn't neglect this course.
(i) At the beginning of the semester we could make a list of something like "Tips to succeed in MAT 221 (succeed = A)"
(a) Review lecture notes after each class;
(b) Read sections in book corresponding to lecture before class;
(c) Do and understand ALL WebWork problems; start early so you can ask questions.
(d) blah blah blah etc.
(ii) Keep them informed throughout the semester of math clinic, free tutoring, office hours, and other resources they have at their disposal.I am not sure how to phrase this correctly: stress correct/good and consistent use of math notation? (translating words into algebra (this can be a topic covered in (1))
For example, some students write z = 1.96 = .97500. Instead, we can stress writing down what the problem is asking for, e.g., P(X > c) = ?, writing down all givens from the problem statement, writing the formula for the z score, and then plugging in numbers for the symbols and so on.Stress conceptual understanding, not just plug and chug.
I will include more later.
Nick
On Delivering In-Person Lectures
As a math graduate student/TA, I have had the pleasure of sitting in on math lectures that were completely handwritten live and math lectures delivered with only the use of pre-written lecture slides or notes on paper.* With the experience gained in delivering lectures, I have observed that lectures are most effective when there is a "good" combination of both prewritten slides/notes and live handwritten explanations. Before elaborating on this, I first discuss some pros and cons of each form of delivery.
Delivering math lectures handwritten live allows students to see exactly how mathematical arguments are written out step by step. Although one can demonstrate the same step by step processes via lecture slides (next slide = next step) or pre-written notes (all steps present at once), I believe students get more out of seeing the process written out on the board or projector as they themselves are required to write out these steps on assignments and exams (especially at the undergraduate level). Another advantage to writing out math live is that it generally takes more time and so affords students the time needed to digest what has been presented. Lectures being delivered only via slides (or pre-written notes) tend to progress much faster than lectures written out live. This is often due to lecturers giving mostly oral explanations of the content on their slides (or pre-written notes). I personally find it difficult to follow lecturers who “talk math at me” and prefer lecturers who deliver both oral and written explanations. In my teaching, I do my best to write down verbatim most of the explanations I deliver orally. As pointed out by Prof. Grzegrzolka, in addition to stating class session objectives verbally, I should also write them down. From this point forward I will be consistent in writing down class objectives for every lecture.
On the other hand, a clear advantage of prepared material is that one can cover not only a lot of course material, but also supplementary material like geometric figures, images, graphs, data tables, etc., on slides. More importantly, one can save the time needed to handwrite/draw certain course contents and instead spend that time presenting the content via lecture slides or pre-written notes on a projector. Another advantage to pre-written lecture slides or notes is that they are often organized and legible whereas writing on the board can sometimes be disorganized and illegible. (This is not as much of an issue after one obtains good board writing and lecture prepping habits through experience.)
So, by “a good combination of both forms of delivery”, I mean that lectures are most effective when pre-written material is properly incorporated in handwritten live lectures. More concretely, for in-person classes the overall structure of the lecture is handwritten live on the board. Items like definitions, concepts, theorems, and examples are written out thoroughly as the lecture progresses. Pre-written material, including lists of remarks, lists of formulas, long word problems, data tables, etc.., are presented throughout the course of the lecture as needed. I elaborate on these materials both orally and in writing. For in-person classes, I use the projector to show the pre-written material and elaborate on it by writing on an available part of the board. (Some smaller classrooms may not allow for this set up as the projector screen can take up most of the board space when in use.)
Finding a good combination of both forms of lecture delivery allow my lectures to flow more seamlessly. In prepping lectures this way, the material requiring a long time to handwrite/draw have already been prepared and can readily be examined. Moreover, the pacing of the lecture is such that enough material is covered as less time is spent writing. At the same time students are not swamped with constantly writing down all the pre-written material as I have made these materials available before and after lecture for them to reference. I have delivered lectures as described since the Summer 2020 and I have adapted this method of delivery to live class sessions online. I personally think it has been very effective in students’ learning and I will continue to deliver lectures in person this way.
Remark 1: I usually have prepared examples and long word problems written out on slides or notes to present in my lectures. I urge students not to copy them down and to instead focus on examining the problem. There is often lag time in students' note-taking and having examples readily available prevents the situation in which a student is still copying down a problem while the lecturer has moved on to explain the approach. Moreover, I recently adopted the habit of making my prepared material, specifically “pre-lecture notes”, available to students on Blackboard a day or two before lecture so that they can print it out and bring it to class to reference during lecture.
Remark 2: With the help of technology (notability etc.), lecturers who prefer using slides can now use marker/pointer functions to circle or box formulas; underline or highlight definitions; add comments; draw arrows pointing to things; draw geometric objects and graphs etc. directly on their lecture slides or e-notes. This is particularly useful when one needs to give a conference talk and can also be useful for delivering lectures online. More recently, I have found that having more items pre-written can be advantageous when pre-recording video lectures (e.g., see video recordings in Other Materials section). I still however prefer writing most things out for in-person classes.
On Pace of Lectures
It is important to note that when delivering lectures, one can go through both oral and written explanations too quickly. When I first started giving lectures, I had a habit of speaking and writing fast, largely because I wanted to get through the material I had planned for the day. I also did not want to lose the attention of students if I went too slow. Here are a few comments regarding my pacing of lectures from student evaluations earlier in my TA career:
Nick obviously knows what he's talking about, but he teaches like a professor in a lecture hall. Discussion is supposed to be a time to clear things up for us; instead, it's a weekly ritual of jamming in as much material as possible and squeezing in a quiz on the new material we've just learned.
The instructor was hardly prepared for our recitations, he wasn't sure what we were learning in the lecture and his explanations of material were often really confusing. He spoke really fast and sometimes didn't leave enough time for us to finish our quizzes.
Aside: Unfavorable comments like these are very few and are not representative of what students generally thought of my teaching or pacing of lectures (see Teaching Evaluations section for a representative sample). They are offset by comments like:
the TA was extremely knowledgeable and always willing to help students. He always came to class with a plan and written out notes for the class period. the quizzes were fair and never on topics we hadn't covered in lecture/recitation. the TA was extremely helpful.
the instructor was always going above and beyond and making sure that he was giving us accurate information. he was always trying to provide helpful information and make sure that we understood what we were learning.
Over the years I have learned to speak clearer and slower. I have been mindful to not speed through material to stick to a schedule. I have also come to the realization that my concern about losing students’ attention or boring them was based on my level of understanding of course material; that it may be too dry or slow for me if I were a student in the audience. I now keep in mind that most students are encountering the material for first time and so delivering lecture at a slower pace allows them to digest the material better. Moreover, delivering lecture at a slower pace aids in better penmanship and overall board organization, which can benefit students’ note-taking. (My handwritten notes in classes where professors have excellent penmanship and organization have always been much cleaner and clearer than notes where professors were sloppy and disorganized on the board.) Along with better pacing, I have learned to not shy from repeating or over explaining things in lecture as repetition is an integral part of learning.
On Grading
For math courses, it is generally expected that problems from quizzes and exams are graded based on proper justification and correctness of written mathematics. My grading policy inherited from past teachers is “no work = 0 points”. That is, a correct final solution will receive zero credit if no proper justification or mathematical line of argument arriving at that final solution is provided. (This policy is dependent on the problem in question as there are some which may not require much justification.) I often remind students it is their responsibility to show the grader they understand how to approach the problem in their solutions; it is not the grader’s responsibility to guess what they are trying to do.
When authoring quizzes and exams, I inherited from my professors the practice of including the number of points each problem is worth next to the problem number. This allows students to gauge the amount of work they should show in their solutions. In most cases, the more points a problem is worth, the more work is required to be shown. Doing this also aids the grading process; the grader can readily see how many points each problem is worth and grade accordingly. Since Spring 2020, I adopted the habit of writing full solutions to quizzes and exams and making them available on Blackboard so that students can learn from them as well as have an idea of what a model solution receiving full credit looks like. Having detailed solutions can be extremely helpful in determining how many points to deduct when grading.
Over the semesters I have learned to express to students exactly what I look for in a good solution, i.e., a solution that receives full credit. For example, if the constant of integration is missing when finding an indefinite integral, - 1 point; if the conclusion in context is missing from a hypothesis testing question, - 2 points. I used to be strict in my grading. For example, if a student did not write the exact value in their solution for a computational problem or did not include units e.g. m/s, lbs., etc. in their final answer for a problem that involved units, I would take one point off. I have recently become more lenient, i.e., I grade based on correctness of a student’s overall solution. If they have the main components of the solution written, I will give full credit and simply circle any minor computational mistakes without taking points off.
My pace in grading used to be rather slow as I initially wrote very detailed comments and feedback to students. Making full solutions for quizzes and exams available to students have sped up the grading process. Rather than write out detailed comments next to student mistakes, I instead began to circle, underline, or point to their mistakes and write shorter comments. If a mistake seemed like it would take a lot of writing to explain, I would circle it and either give them a hint as to what they did wrong or write next to it “see solutions”. Doing so gives students the opportunity to think about where they went wrong. If they cannot figure it out, they can read my solutions and learn from them. If they still cannot get it after that, I encourage them to contact me either via email or office hours to talk about it.
Moving forward I would like to figure out how to grade quizzes and exams administered online more efficiently. When I first started grading quizzes and exams online (mid-Spring 2020 after SU transitioned online), I typed out detailed feedback in the feedback box on Blackboard. Although I inform students of feedback available on Blackboard, they may not always check it. Furthermore, typed math expressions are not as easy to read as handwritten math expressions (e.g. 2\sqrt(e^{2x})/5 can be difficult to read). I also have tried markup tools for grading on Blackboard. These tools were often spazzy or nonresponsive. To deal with these issues, I began to download individual PDF files of exams from Blackboard, import each one on OneNote, grade it, export as PDF, then upload the PDF in the student feedback box on Blackboard. I recently started to download all exam files first, compile and import them on OneNote, and then after grading, export and split. Doing this is still laborious and time consuming. I plan on exploring other platforms specifically for creating and administering math quizzes and exams that have grading markup tools and gradebook features readily available.
On Office Hours and Student Emails
In my office hours I usually help students with homework problems, review or elaborate on lecture materials, or go through extra practice problems. In more recent semesters I have held office hours online via ZOOM. There are some advantages to holding office hours online. One is that I have access to tablet functions to help explain things. Another is that I can document and export as PDF file what I have written in meetings with students. I usually email the PDF file (file name: “OH Donald Duck 02-09”) of the meeting to students for them to reference.
An evident disadvantage to ZOOM office hours is that only one person can screenshare at a time. Also, if a student has handwritten work they want me to see, they need to either send an image of it beforehand, hold it up to the camera, or try to explain in words what they have written. I have effectively dealt with this issue by anticipating certain questions and by being prepared to write down accurately what students express verbally. This is not as easy to do for more advanced topics.
As for student emails, my exchanges with students are generally about homework problems. I usually first type or write out hints to help students get started on the problem. If necessary, I will give thorough explanations or detailed solutions if a student showed evidence of solid attempts.
Students often ask the same or similar questions in office hours and in emails. I include here some thoughts on how I can use my interactions with students during office hours and in email to benefit other students in the class.
Share my typed or handwritten explanations/solutions from student email exchanges on Blackboard
Remark: If the solution is typed, no permission is needed from the student as I would only be sharing the body text of the email.
Ask student for permission to record office hours meeting and post it on Blackboard along with corresponding notes from the meeting
Remark: “Office Hours Videos/Notes” content section should be made available on Blackboard. If office hours are in person, I can record the session via laptop.
Post PDF of scratch work from office hours on Blackboard
Remark: PDF file should be named differently to respect students who want to remain anonymous, e.g., “OH Donald Duck 02-09” would be renamed “WebWork Ch4Sec2 Problem 3”.
In the future, I plan on exploring how to set up discussion boards on platforms like Piazza where students can interact with each another. I believe that setting this up for future courses can benefit students by allowing them to discuss course material more easily with one another. It may be that some students are shy to approach an instructor and feel more comfortable interacting with their peers. Having a discussion board available to students gives them an extra resource to learn from one another.