9/4 due 9/10    1.4 part 2            bigideasmath.com

Study “6th 1.4 Prime Factorizations,” "6th 1.4 Divisibility Tests," and text section 1.4

9/3 due 9/9    1.4 part 1         bigideasmath.com

Study "6th 1.4 Divisibility Tests" and text section 1.4

9/2 due 9/5    1.3 part 2         bigideasmath.com & Classkick

Study "6th 1.3 Order of Operations" and text section 1.3

8/29 due 9/4    1.3 part 1         bigideasmath.com

Study "6th 1.3 Order of Operations" and text section 1.3

8/28 due 9/3    1.2         bigideasmath.com

Study "6th 1.2 Powers and Exponents" and text section 1.2

Please follow the directions below under "Class Logins and Links" to add yourself to our Google Classroom. When you have done that, I'll be able to add you to our class for Classkick and Desmos for many of our in-class activities. 

Please follow the directions below under "Class Logins and Links" to add yourself to our Big Ideas Math class (you won't be able to do that until Monday, August 25th).

If you were in my class last year then your work on Classkick will be archived under the Google Classroom "Class of 2028 Math”.

Sixth through Eighth Grade Math: Policies and Procedures

Materials that you will need to have with you every day:

·  Charged iPad

That's it!! We're going (mostly) paperless this year in math for grades six through eight, but you must have your charged iPad with you. 

I will supply styluses for you to use during class (they are shared so they can't go with you) 

Pencils and erasers will be supplied during class when needed. 

Grading Policy:

60% Assessments

30% Student Work

10% Participation/Engagement (class participation, tardiness, conduct, effort during class, focus and attention on work, focus and attention during instruction, cooperation, and preparedness for class). This is your best indicator of upcoming “Behavioral Expectations” scores on report cards.

Homework:

Please see the separate document titled “The Homework Process for Students in Grades 6 through 8.”

Homework is an essential component of learning and applying mathematical concepts and skills. This is a guide for how to complete and use your homework as the learning opportunity that it is.

1. Obtain the assignment by going to the school website. Click on the drop-down menu above titled “Assessments and Assignments Drop-Down Menu,” and read the assignment description. Here you will also find resources that you should use and study in conjunction with completing the assignment.

2.   Assemble your resources. Before beginning the homework, it is important to review your work and notes from class and have them handy for reference while working. 

3. Open up your textbook. You should be using the textbook for reference as you work and reading the problems in their original form to make sure you aren’t missing any parts.

There are four ways that you can access the textbook:

a. Your hardcover textbook that should be at home.

b. Login at bigideasmath.com and find it under the “Resources” tab. Here you will be able to make and see your own highlighting and notes in the digital text.

c. The iPad app contains the full digital text with all the interactive features and functions without internet access. You will be able to view any notes and highlighting up to the last time it synched with the online version.

d. If you have internet access but have forgotten your login information, then you can go to the login page for bigideasmath.com, click on “Easy Access Materials” at the bottom of the page. Click on “Looking for the Free Easy Access Home Edition?” choose “California” as your program, click “Go”, and click on the picture of the textbook. The textbook will not include any of the interactive features and will not include your notes or highlighting, but you will be able to view every page of the textbook.

4.     Open up the assignment in the “Assignments” tab on your dashboard on bigideasmath.com, read any notes or messages that I may have included, and do the assignment. The assignments are designed so that they should not take longer than thirty minutes for a typical student who is following directions and instructions from class and has grade level computation skills and a mastery of basic math facts. Some assignments are assigned over the course of more than one day with no additional homework, so they may take longer (such as the chapter reviews). If homework is consistently taking an excessive amount of time, come and see me so we can figure out why and develop a strategy to help.

• • • Your homework will take longer if you are, for instance, doing long division to find the answer to 19,825.4/1,000 instead of just moving the decimal point three spaces to the left.

    • Your homework will take longer if you are, for instance, multiplying fractions without first factoring out common factors.

    • Your homework will take longer if it takes more than two seconds to come up with  the product for basic multiplication fact.

    • Your homework will take longer if you are choosing to use a less efficient technique than what I have presented in class that should be in your notes for reference.

I appreciate and celebrate that there are multiple methods of solving problems, however, I mean, for instance, performing a computation such as 15 and 1/13 + 32 and 12/13 by writing the mixed numbers as improper fractions, adding the numerators, and converting the sum to a mixed number by dividing by 13, instead of just adding the whole parts, adding the fractional parts, and mentally obtaining 48 in a matter of seconds.

5.     Complete any portion of the assignment that you must complete on Classkick. Make sure to follow the directions. Your process should also include computation unless I explicitly state that you may use a calculator. The answers may still be checked online. After the due date and after your score appears in my gradebook, you should return to Classkick to see if I provided you with any feedback on your work.

6.     Check the answers as you work and attempt to diagnose and correct your errors within reason. Your best references are your notes from class and the textbook. If you find that you are spending more than a few minutes on a particular problem (though some problems may take longer, in which case, I will have assigned fewer problems or the assignment will be over the course of more than one day) enter your best answer, click on “save,” and move on. As long as you have not submitted the assignment and the due date has not passed, you can see me for help in the Math Room. Any time that my door is open, and I am there, then you may come in and see me. This is the reason that the due date is not the next day (not so that you will procrastinate about doing your homework). Don’t let the work pile up as it is best to at least attempt every assignment on the first day that it is assigned.

In the digital text, you may click on the yellow number that appears to the left of some sets of problems that will take you back in the text to similar examples (the number in the yellow circle is the number of the example in the text). Similarly, you can click on the red arrow buttons to watch instructional videos. For some problems, instructional videos will pop up for you to click on for help, and for some problems, if you have watched a video or tried to correct your error, a button will pop up offering the help of a free, live tutor from a bank of graduate students at Penn State University who have been thoroughly vetted and trained to help you. This will happen in the form of a “chat” so they will not be able to see you, and you will not be able to see them.

Please keep in mind that I still consider homework scores to be a reflection of your effort, so the scores are not dependent on your answers being correct or not. Do not submit items with blank answers or skipped items, since this will cause a loss of points. I always view all incorrect responses online and can generally determine effort from your incorrect answers so you should not assume that simply filling in the blank spaces will ensure full credit. For instance, if you scroll through the assignment entering a “2” for every answer, you will not receive credit even though you technically did not leave the items blank. If you are asked for a regular price on an item that is on sale for $160 and was 20% off and you say “$1” you will not receive credit. If you are asked for the equation of a line in slope-intercept form and you type in “idk” you will not receive credit.

7.     Save and submit the homework online. The due date for homework is generally three days after it was assigned, though it is best for your learning to try to complete your assignments on a daily basis since math is cumulative (the lessons build on each other daily). I post the “due date” and time on bigideasmath.com, and the date on the learning site, and on Rediker/PlusPortals, so assignments will be automatically force submitted if not submitted by you in time. If for some reason you have an extension of the due date (such as an excused absence) the assignment will still be accessible on bigideasmath.com.

8.     After you have submitted your homework, which may include some incorrect answers, click on the “Reports” tab to view the assignment. You will be able to see the correct answers along with your own and may be able to diagnose any errors from there. If not, stop in and see me in the Math Room, and we will likely be able to clear it up in a matter of seconds. Be very careful not to submit assignments that you don’t intend to submit because I will not unsubmit them upon request.

I realize that this may look complicated at first, but consider that it is replacing this old process: 

1. Get the assignment from your assignment notebook and hope that you remembered to write it down and have done so correctly.

2. Open the (big, heavy) textbook, which you hopefully remembered to bring home and that is hopefully not too damaged from past years so that you can read it.

3. Do your assignment on paper.

4. Check your answers in the back of the book if they were odd-numbered or with a calculator if possible. Otherwise, you’ll have to wait for the next day in class, at the earliest, to find out from me if you are correct or not as we correct it in class (which is boring, a terrible use of time in class, and a complete waste of class time for most students and most problems).

5. Turn your homework in the next day and hope it doesn’t get lost or left at home between now and then.

6. Wait for it to be returned to you to find out if your work and answers are validated or invalided by me instead of getting the immediate feedback from the website.

Please read the document posted here titled “How to Help Your Child Succeed in Math,” which is written to parents, but it may be helpful to you as well since a lot of it is about how you can help yourself be successful at math.

How to Help Your Child Succeed in Math

Regardless of your understanding of mathematics, you can help your child succeed in their math class by encouraging them to have scholarly habits, to keep a positive attitude about the class and their own mathematical abilities, and to support a growth mindset. Consistent effort and perseverance is key for success in any challenge, and we should expect nothing less when learning mathematics.

When your child is doing their math homework:

·            Do they take out the in-class work, notes, and relevant workbook/textbook sections for reference before beginning the homework? Is the work from class neat, complete, and easy to read so that it is meaningful and useful to your child? Reviewing this work before beginning will help to refresh their memory and underscores the value of maintaining in-class work.  

·            Are they checking the homework and trying to learn from their mistakes? Mistakes are valuable learning experiences and make your brain grow since when we make mistakes in math there is activity in the brain that is absent when people get work correct.

·            What does your child do when they are incorrect? Do they try to diagnose their error and correct their work or do they simply correct the answer? If they are in the Sixth through Eighth Grade, do they watch the tutorial videos embedded in the eText?

·            If they get stuck do they check the book or in-class work or notes for related content or attempt to use a problem-solving technique such as drawing a picture or diagram, or restating the problem in their own words? Not every problem will fit into an algorithm or mirror exactly a problem solved in class, but similar techniques may have been used. Please resist rescuing them from productive struggle or helping in a way that reduces the cognitive demand. If you lead them step by step or simply tell them what computation to do after reading the problem yourself, for instance, you are inadvertently doing their homework for them no matter how well-intentioned I know you are.

·            Are they doing their work in an organized manner and showing their process? It is difficult for them to diagnose errors and learn from mistakes if the work is absent or hard to follow, and difficult for me to give constructive feedback if I can’t see their process.

·            Are they noting questions that occur to them as they work? Students should be completing as much of the homework as they can on their own on the first day that it is assigned, but if questions arise, they may want to jot them down since mental notes can be easily forgotten. The three-day deadline does not exist to teach procrastination, rather it is to give them time to really learn from the homework process which includes seeking help (but there must be a deadline so that they will keep up with the class material!).

·            Is your child getting distracted while doing homework? Television, other people, and music with lyrics can be distracting*. Students should put away cell phones and close all non-relevant Apps on the iPad during math homework. Also, students should not be doing homework in a central, family location such as the kitchen table. Rather it should be completed in their own private space to help define homework as their responsibility and to help parents resist the temptation to hover (this may not apply to students with learning or attention challenges who may need a parent to keep them focused and on-task)

*See the brain research of Ann Anzalone about the often-misinterpreted research about playing music while you work, and the work of John Medina about attention and “multi-tasking.”

When your child is studying for a math assessment:

·            Does your child know what concepts will be on the assessment?

·            Are they studying the notes, cumulative review homework, and corrections and notes they may have made on or about the Reality Check?

·            Are they reviewing any previous homework assignments paying particular attention to items where mistakes were made?

·            In the sixth through eighth grades, are they attempting the practice quizzes?  These are generally optional, but they are still valuable.

Ask your child about the math they are learning in class. If they cannot explain it after reviewing their resources, then encourage them to seek help from me by seeing me in the Math Room in the morning, during a break, during an independent work time in class, or by sending me an email (with the understanding that I may not be glued to my inbox, even on a school night).

Encourage your child to take responsibility for their learning:

·            Encourage your child to contact me directly.

·            Reinforce the fact that consistent hard work and recognizing errors are key to success in mathematics, and that attitude and an honest effort are key to success everywhere.

·            Encourage your child to be positive about learning math and not to give up on difficult problems. Let them know that it’s okay to be confused because everyone struggles with math concepts from time to time; struggle is a necessary part of the learning process. The motto in the Math Room is, “No Struggle, No Growth.”

We live in an increasingly complex world, and your children’s generation will be faced with very difficult problems that will need perseverance and insights to solve. Developing a positive approach to learning and working through the challenges they experience in class will not only help them retain the concepts they are learning, but it will help them to develop 21st century learning skills.

Finally, if you decide to hire a tutor for your child after giving these suggestions an opportunity to work, I ask that you inform me and work to keep the lines of communication open between your child and myself. If you choose to hire a tutor, please keep in mind the following:

·           A good tutor will support and supplement the math program, not rival it

·           A good tutor will give relevant practice problems to your child, rather than do the homework with or for your child

·           A good tutor will recognize and address gaps in your child’s understanding of concepts or skills from previous grades that may not be in the scope and sequence of their current class

·           A good tutor will insist that your child always attempt their homework to the best of their ability on their own first

·           A good tutor’s objective is always the student’s self-sufficiency

This document was adapted with permission from Marin Catholic High School though I have supplemented throughout by paraphrasing from the work of Jo Boaler and John Rosemond. Please see Jo Boaler’s excellent books “What’s Math Got to Do With It?”and “Mathematical Mindsets,” as well as her website youcubed.org (I have a link on the website), and John Rosemond’s book, “Ending the Homework Hassle ” (some of his ideas may need some updating, especially with regard to learning differences and retention, but his big ideas are good in my opinion).

Program

Big Ideas Math California Course 1, by Ron Larson and Laurie Boswell

Big Ideas Learning LLC 2015

Focus

The Big Ideas Math program is based on the Common Core State Standards and Standards for Mathematical Practice. There are significantly fewer standards than in the past, allowing for extended instructional time on each. The program’s balanced approach, blending discovery with direct instruction, helps students move from concrete to representative understanding and then to abstract representation and the ability to apply the concepts in real life.

Coherence

Learning mathematics is cumulative. In the Big Ideas Math program, each grade level builds on the concepts students learned in earlier grades, without repetition. This learning creates a fabric of knowledge that is woven tighter and tighter throughout students’ schooling.

Rigor

The Big Ideas Math program meets the three aspects of rigor defined by the Criteria for Evaluating Mathematics Instructional Material: 1. Conceptual understanding; 2. Procedural skill and fluency; and 3. Applications through a balanced approach to instruction.

Applications

The Mathematical Practices are embedded throughout the Big Ideas Math program. Robust real-life applications in the lessons and exercise sets provide students the opportunity to use the practices and to develop an appreciation for mathematics as it applies to their lives. Big Ideas Math offers a true balanced approach through student-directed activities to develop conceptual understanding and direct instruction lessons that offer processes and procedures for fluency and real-life applications throughout.

The Common Core State Standards require students to do more than memorize how to solve problems. The standards define skills and knowledge that young people need to succeed academically in credit-bearing, college entry courses and in workforce training programs. Mastering the skills reflected in the Common Core State Standards prepares students for college and career. Research shows that students benefit from a program that includes equal exposure to discovery and direct instruction. By beginning each lesson with an inquiry-based activity, Big Ideas Math allows students to explore, question, explain, and persevere as they seek to answer Essential Questions that encourage abstract thought. These student-directed activities are followed by direct instruction lessons, allowing for procedural fluency, modeling, and the opportunity to use clear, precise mathematical language.

Course Content

First Trimester

Chapter One

Solve problems where all four operations with whole numbers are reviewed. Simplify expressions with exponents, recognize square numbers, and review the order of operations. Review divisibility tests and apply them to find the prime factorization of a number and determine if a number is prime or composite. Extend divisibility tests to include those for 7, 11, and possibly 13 (optional). Use the prime factorization of a number to find all of its factors. Use the prime factorizations of a pair of numbers to determine their common factors, greatest common factor (GCF), and least common multiple (LCM). Use common factors and common multiples to solve problems. Time permitting, apply and practice with these number theory concepts and skills to determine if a number is deficient, abundant, or perfect. 

Chapter Two (and Chapter 1.6 Extension)

Add, subtract, multiply, and divide with fractions, mixed numbers, and decimals. Employ mental math and estimation techniques throughout to build number sense and reflect on reasonableness of answers. Review multiplying and dividing by powers of ten that are greater than or smaller than one. Find reciprocals of a given number to use the definition of division. Using “number and word” notation as examples of multiplying by powers of ten and to reinforce the concept of place value. Possible introduction to converting fractions into equivalent repeating or terminating decimals to reinforce fraction bar as division symbol.

Chapter Three

Write and evaluate algebraic expressions. Generalize patterns with one or several variables, and recognize properties of addition, multiplication, one, and zero by name (see list below). Simplify expressions by applying the distributive property and combining like terms, and recognize equivalent expressions.  Use a variable to articulate a pattern or “rule” in a function table.

During this chapter, students will begin a packet titled “Properties” which they will maintain throughout their Sixth, Seventh, and Eighth Grade years. It will be saved at the end of each year in students’ files at school.

Properties added to “Properties” list in this Chapter:

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

Additive Identity Property of Zero

Multiplication Property of Zero

Multiplicative Identity Property of One

Definition of Reciprocals (Multiplicative Inverse Property) (possibly saved for Chapter 7)

Distributive Property

Second Trimester

Chapter Four

Discover (using deductive reasoning and area conservation) and apply the area formulas for parallelograms, triangles, and trapezoids. Determine the area of a composite figure and a figure given in a coordinate plane from its coordinates. Review the meaning of and calculate perimeter.

Chapter Five Part One 

(This year, 5.1 - 5.4, focus on ratio and rate reasoning)

Use ratios, rates, unit rates, ratio and rate tables, and limited proportions to solve problems and compare rates. Introduction to converting fractions into equivalent repeating or terminating decimals to reinforce fraction bar as division symbol (and since this is useful in comparing rates and finding unit rates). 

Chapter Five Part Two

(This year, 5.5 & 5.6, focus on percents)

Understand percent to mean a ratio of a number to one-hundred, convert among a percent, a decimal, and a fraction. Solve problems involving percents. Use various methods to find a percent of a number and to find a whole when the part is known, including mental techniques. 

Chapter Six

Compare positive and negative rational numbers and integers, and locate them on a number line. Understand, apply, and determine the absolute value of a number and the definition of opposites. Understand and use coordinate geometry with all four quadrants of the Cartesian Coordinate System. Find distances between points in a coordinate system (when one coordinate is the same) as an informal introduction to subtracting integers.

Properties added to “Properties” list in this Chapter:

Definition of Opposites (Additive Inverse Property) (possibly saved for Chapter 7)

Chapter Seven

Understand the concept of an open sentence and the solution set of an equation or inequality as a set of values that makes the sentence true. Translate information into equations and inequalities to solve problems. Use inverse operations, with positive numbers, to solve equations and inequalities and graph their solution sets on a number line.  Use pan balances to model equations and inequalities, and the process of solving them.

Properties added to “Properties” list in this Chapter:

Addition Property of Equality

Subtraction Property of Equality

Definition of Opposites (Additive Inverse Property) (if not included in Chapter 3)

Multiplication Property of Equality

Division Property of Equality

Definition of Reciprocals (Multiplicative Inverse Property) (if not included in Chapter 3)

Addition Property of Inequality

Subtraction Property of Inequality

Multiplication Property of Inequality

Division Property of Inequality

Third Trimester

Rates 

5.7, part of 5.4, and 7.4. 

Equations with two variables with one being the independent variable and the other being the dependent variable, and an introduction to linear equations (solutions for which are represented by points on a line). Review articulating a pattern or “rule” in a function table, and extend it to writing the associated equation and graphing the function. Using conversion rates (conversion factors) to convert measurements within the standard and metric systems, and between systems. Comparing ratios and rates by using graphs, and recognizing a line as a representation of constant rate. 

Chapter Eight

Recognize aspects of a polyhedron in a two-dimensional drawing, and be able to recognize and draw various views. Understand the faces, edges, and vertices of a polyhedron as two, one, and zero-dimensional features. Recognize a prism and a pyramid and its defining features, such as the base(s) versus the lateral faces. Understand and calculate the surface area of a rectangular prism or pyramid with or without drawing a net. Understand and calculate the volume of a rectangular prism.

Chapter Nine and Ten

Understand the statistical process and the meaning of a statistical question. Calculate and interpret measures of central tendency - mean, median, and mode – and choose the best representative for the data. Calculate and interpret measures of variation (also called dispersion or spread) - range, interquartile range, and mean absolute deviation – and choose the best representative for the data. Understand and calculate the first, second (median), and third quartiles of data. Create and use line plots and stem-and-leaf plots to sort and display data, and to calculate statistical landmarks. Create and use histograms and box-and-whisker-plots to display data. Interpret the shapes of the distributions as symmetric, skewed left, or skewed right, and understand the associated effects on the measures of center and variability. Calculate outliers, and predict and verify the effects of outliers on statistical landmarks and the shape of the distribution. Time permitting, Saint Hilary Census and/or Mystery Graphs project (Census project during census years).

Other Statistical Displays “Chapter Eleven”

Create and interpret other statistical displays such as line graphs, step graphs, pictographs, and circle graphs, and recognize when it is appropriate to use which display.

Probability

Introduction to basic probability concepts including some forms of compound probability.

Trying on homework means…

·     Attempting all of the exercises independently on the first day they’re assigned.

·     Reflecting on your answers to make sure they seem reasonable.

·     Checking your answers after each exercise when possible.

·     Diagnosing any errors in exercises that turned out to be wrong or that seem unreasonable.

·     Correcting any errors in your work and not just the answer.

·     Referring to your multiple resources for help if necessary.

·     Contacting and/or stopping in to see Mrs. De Biasio for help if necessary any time the Math Room door is open (virtually any break time).

Remember:

Every mistake you make

is an opportunity to learn,

and your brain grows

when you make mistakes.

However,

A mistake you don’t discover by checking, 

and then try to learn from,

is just a waste of time.

Adapted from “Ending the Homework Hassle” by John Rosemond

RESPONSIBILITY: the ability to own what belongs to you, to be accountable for your own actions/mistakes. Homework belongs to the child. When parents get too involved or do the work for the child, it changes the nature of the activity. Work may get done, but the child isn’t learning from it.

AUTONOMY: the idea of being self-sufficient and self-governing. Classwork/schoolwork are the first occasions when the child is asked to perform tasks by someone other than his/her parents on a regular basis. This means that the child is now accountable for his/her own actions outside the governance of the parents.

PERSEVERANCE: the idea of completing what you set out to do, the ability to confront difficulties and overcome them. It also includes the idea of pressing one’s own limits to advance to a higher level. It’s a sad fact that many parents shield their child from frustration in the misguided notion that allowing the child to struggle is neglectful, abusive, or will lead to a child feeling unloved. The fact is that parents are putting off the inevitable until a later time when the process will be harder and immeasurably more painful for the child.

TIME MANAGEMENT: the ability to organize materials, thoughts, and performance so as to meet a schedule or deadline. Homework time should not become protracted. In not learning how to manage time, the child learns how to waste it.

INITIATIVE: the idea of taking responsible action on something that needs to be done that falls within the child’s range of capability. If children are never given the chance to experience this, they may never develop the strength to try to start things on their own.

SELF-RELIANCE: the idea that you trust and believe in your abilities. The child who does his/her own work increases his/her sense of independent and confidence, while the child who asks for and receives help feels doubtful and actually feels less able to perform.

RESOURCEFULNESS: the ability to figure out or invent a method to problem-solve. This is a skill that breeds self-confidence and self-esteem. Children who develop this skill will show a willingness to participate fully in classroom activities and discussions.

My approach in a nutshell:

Increased emphasis on teaching for understanding, which: Decreased emphasis on teaching rules and procedures, which:

Emphasizes understanding Emphasizes recall

Encourages students to make their own generalizations Teaches many rules, algorithms, and "tricks" 

 based on their experience and observation without a conceptual foundation   

Develops conceptual schemas Develops fixed or specific processes or skills or interrelated concepts

Identifies global relationships Identifies sequential steps

Is adaptable to new tasks or situations (broad applications) Is used for specific tasks or situations (limited context)

Takes longer to learn but is retained more easily Is learned more quickly but is quickly forgotten

Is difficult to teach Is easy to teach

Is difficult to test Is easy to test

I believe in the value of productive struggle and that all students deserve access to challenging content. Differentiation in a productive struggle classroom takes the form of teachers intervening when necessary by appropriately scaffolding material through their guidance and questioning without reducing the cognitive demand (without “dumbing it down”). Students may need extra help or remediation may be necessary, but this should happen in addition to class instruction and activities and not instead of it. For this reason, you will find a class motto of sorts boldly proclaimed on the front wall of the Math Room, “No Struggle, No Growth.”

I believe in balancing inquiry and problem-based instruction with direct instruction. Students need to be doing math during math class by engaging collaboratively with their peers as they discover the new material and develop their critical thinking, problem-solving, and communication skills. Students are not passive vessels waiting to be filled, and school is not where young people go to watch old people work, but I do recognize the necessity of direct instruction, which generally occurs concurrently with conducting class discussions. I have to make sure that students are making accurate and useful generalizations when we share and summarize our findings following investigations and activities.

I believe that math must be experienced in order to be learned. This is the reason another credo is boldly proclaimed on the front wall of the Math Room, “Math is not a spectator sport.” This is the flip-side of the old Chinese proverb, “Tell me, and I’ll forget; show me, and I’ll remember; involve me, and I’ll understand” as it requires students to actively engage in class in order to understand and not simply regard themselves as passive vessels waiting to be filled. My role is that of a facilitator and not a “sage on the stage.” As Kahlil Gibran wrote, “No man can reveal to you aught but that which already lies half asleep in the dawning of your knowledge. The teacher who walks in the shadow of the temple, among his followers, gives not of his wisdom but rather of his faith and his lovingness. If he is indeed wise he does not bid you enter the house of his wisdom, but rather leads you to the threshold of your own mind.”

I believe that attendance and attitude are crucial components to students’ learning. I can prepare a brilliant lesson for a given topic, but your child needs to come to class and do so with a cooperative and positive attitude and a willingness and ability to stay on-task. Students actively engaging with mathematics along with their peers as they discover new concepts and skills, and participating in a whole class discussion are experiences that are very difficult – and sometimes impossible – to replicate following a student’s absence.

I believe that self-esteem does not come from empty praise, rather it comes from being given challenging tasks and overcoming them. If students are to become resilient, gritty, tenacious, and confident problem solvers, then they need to practice working through challenges. Students need to practice perseverance, and they need to be willing and able to work with constructive feedback. Similarly, students know when they are doing “busy work,” and I don’t believe that completing that type of work yields much satisfaction so praise for completing that type of work is empty.

I believe in the value of internalizing a growth mindset. “I can’t do it” is not allowed unless you are going to follow it with the word “yet.” Also, I have to ask you to do myself and your child a favor by not consoling them when they struggle by telling them about your struggles in math or making comments about not having the “math gene”. I know that your intentions are good, but when parents do this, not only does it not help your child, but student performance actually declines, especially in girls. Before you come after me with torches and pitchforks, please visit Jo Boaler’s website youcubed.org to read her research about the damaging effects of hearing these messages. Jo Boaler is a Professor of Mathematics Education at the Stanford Graduate School of Education and the growth mindset guru when it comes to mathematics.

FAQ

Q.     Why can’t homework be turned in for credit after three days?

A.     The effectiveness of homework as part of the learning process diminishes with every hour that passes between the initial exposure to and the practice with new skills and concepts. Therefore, homework should be at least attempted on the first day that it is assigned to at least limit the delay. The three-day due date effectively means that students may submit homework up to two days later than the day after it is assigned without any penalty. By not accepting work for credit later than that I am trying to discourage a habit that is detrimental to student learning.

Math homework is different from most other subjects in that the content within a given unit or chapter is generally cumulative. This means that if students have not had sufficient experience with skills and concepts by keeping up with their homework, then it will be difficult if not impossible to build on that experience in subsequent lessons.

One may be able to find a lot of debate about homework in general, however it is the consensus of research regarding math homework that the most effective homework is distributed practice and not massed practice (and, by the way, is a mixture of material that is based on same-day instruction, review of past content, and prepares for future lessons). In other words, it is best for homework to be more frequent as opposed to letting it accumulate. By not accepting homework for credit after the three-day deadline I am not enabling students to let homework accumulate. Rather I am requiring them to pace themselves, to keep up with the lessons and material in class, and to have had sufficient practice and feedback before the conclusion of a unit or chapter.

Q.     Why is it important for students to check and review their homework as part of the homework process?

A.     Part of the value and process of doing homework is checking the answers, diagnosing any errors, and attempting to correct any errors to learn from them. By providing students with the resources to check themselves, I am giving them the power of self-validation and the immediate feedback they need before moving on. In other words, it enables the short feedback loop that is essential for the cumulative nature of the material being covered (as does the three-day deadline) and for homework to have the positive impact that research shows it is has especially in mathematics.

On a scale ranking influences on student learning from -0.9 to 1.6, homework overall ranks at 0.29 placing it in the “positive impact” range. As students progress from middle school to high school, this ranking increases from 0.31 to 0.64. When this is disaggregated by subject, it ranks higher in math than in other subjects (foreign language is second, by the way). Feedback ranks at 0.74, therefore, for homework to have the greatest positive impact on learning, it must be coupled with timely feedback. If students have to wait for a teacher to correct it, file it, and send it home in a folder of some kind, then they are waiting too long for the feedback to positively impact their learning. This does, however, require students to choose to access the feedback in the form of reviewing assignments once submitted on bigideasmath.com for sixth through eighth graders, viewing posted solutions for fifth graders, and viewing feedback that I provide on submitted work in Classkick.

Q.     If homework is so important, then why can’t time in class be spent on going over homework?

A.     Of all the activities that students may engage in during a math class, research has shown that there is a strong negative correlation between the time spent going over homework in class and student learning. In other words, the more class time that a teacher devotes to going over homework, the greater the negative impact on student learning. The reason for this is not known, but I suspect that if time in class is devoted to going over homework, then it is being taken away from activities that better promote learning. For my classes, students can check themselves and review the answers once submitted. I always view every incorrect or partially correct answer online and adjust my instruction accordingly without using precious class time to go over homework. If students have trouble diagnosing errors, they can generally find me in the Math Room from 7:30 to 8:00 or at any recess or lunch break (unless my door is closed). Furthermore, students will sometimes send me screenshots of their work asking me to diagnose their errors, which I will do. When I scan my email in my inbox I generally prioritize emails sent from students since they are generally more urgent than other emails.

Q.     Why won’t you “unsubmit” homework upon request in bigideasmath.com?

A.     With every assignment I have the choice of releasing the answers for review by my own action (such as after they are due) or immediately upon student submission. I opt to have the solutions viewable to students immediately upon submission so that they may have that immediate feedback that is so crucial to learning. The downside is that once the answers are viewable by having submitted it, I won’t unsubmit an assignment by request for them to complete for credit because they have already been able to see all the answers.

Also, when students hit the submit button, there is a secondary prompt from bigideasmath.com asking “Are you sure?” and the assignment will only be submitted if the student then clicks, “yes” as well. In the world we live in, it is important to be careful about these redundant digital prompts. One day, they may be buying stock online, transferring money between accounts, or submitting their tax returns, and being mindful of the “Are you sure?” prompt is probably a lesson better learned earlier rather than later.

Q.     What’s a Reality Check?

A.     A reality check is really a summative unit assessment, but it is not graded. In the past I have devoted class periods for it to be taken like a test, corrected as a test, and then gone over. I have discovered recently that it seems to be more effective and a better use of class time to allow students to have it early to work on independently or collaboratively with other students, and then I go over it in class so that students may use as a study guide for the test. It also provides an opportunity to clear up any misunderstandings about directions.

Students and parents may keep the reality checks because they do not count for any part of students’ grades and they collectively provide a summary of the content for the year, which can be used to review before the following year and for eighth graders, to study before high school placement tests.

Some students like getting a score on a reality check because they see it as predictive of their test score, but scores alone do not promote student learning so I prefer not to put a scores on reality checks.  

In fact, studies have been conducted that demonstrate that students learn more from work that is returned when there is no grade on it. When the work has (a) comments and corrections only, (b) a grade only, or (c) comments, corrections, and a grade, that it is the students in group (a) whose learning is most positively affected after they get the work back.

Q.     Why can’t the tests be sent home?

A.     The main reason is to preserve the integrity of the tests. Assessments comprise 60% of students’ grades so if they have no integrity then neither do the grades.

There have been times in the past when it was very clear that students had been provided copies of tests and parents had reported that other parents had been “archiving” tests – and not just in math – to share with younger siblings giving them an unfair advantage and compromising the value of the test. 

Adopting new math programs and standards provided an opportunity to maintain the integrity of my new assessments by not sending them home (or letting students have to distribute as they chose via pictures). This is also a practice that you may have to get used to for some high schools and colleges.

You may ask why I can’t just make up new tests every year, but I have to tell you, writing and curating a collection of problems to create an assessment tool that covers all of the required content and skills for a unit in a balanced way that can be comfortably completed by most students within a class period takes a lot of time and effort, and it is not simply a matter of changing the numbers. If the only thing that mattered were computation and therefore the only thing being assessed, then changing the numbers would be sufficient, but there is more to math than computation. Also, changing a single digit can make a computation out-of-reach or can make an equation unsolvable.

I realize that you want to know why your student performed as they did and what they can do to improve. For this reason, I would direct you to the “Math Unit Reflection” and the “Reality Check.” Students can easily identify corresponding problems on reality checks and tests, and I encourage them to use the reality check for reference when tests are returned in class for students to view.

Sometimes I have students make corrections on some items on tests to learn from their mistakes. If tests don’t leave my room, I can monitor the corrections as they happen in class and reinforce the purpose of the corrections. When tests leave the room and corrections don’t happen under my supervision, students can be tempted to copy answers from others or they find someone else to make their corrections for them (I have seen corrections in a student’s handwriting that the student didn’t seem to understand or was unable to explain only for them to declare to me that they didn’t understand what they had written because they “did it with their tutor”).

Furthermore, in every test in every grade when I used to send them home I invariably would get at least one email from a parent who would ask that their child be excused from making corrections because they accidentally threw it out, or it was otherwise lost. This hardly seems fair to those who didn’t lose their tests and misses the point of making corrections, as does the request that sometimes follows that I provide a blank copy of the test so that we can start all over again. If I keep them in my room, then they don’t get lost, and it is important to me that they don’t get lost. Often, it is the student who most needs to revisit their test who loses it and can’t share with their parents anyway. The test is a tool that I use to inform my teaching, which is part of what makes it a blessing to have the same teacher for four years in a row. With the tests and the notes that I take from them, I can anticipate who will struggle more or less with similar topics in later units and years. If I let the test out of my room and it is lost, then so is the valuable information.

Q.     Why do students have to use pencils?

A.     There are two big reasons. The first has to do with students not being afraid to make mistakes. Your brain grows when you make mistakes so you can’t be afraid to make them. If you have a pencil in your hand you are much more willing to lean in to the struggle and possibly make a mistake than if you are holding a pen, because your eraser can make it go away, and I don’t believe that the same is true for erasable ink because I believe it is psychological, though I confess I have no data to back that up; it is purely from my own observation of students when they work with a pencil versus pen on paper. The second reason is that pens make a bigger mess on the desks. Whether it’s a student writing on the desk, taking a pen apart during class, or a leaky ball-point pen, scrubbing ink stains off of the desks is not the best use of anyone’s time (and it can’t be cleaned off of some surfaces in my room).

Q.     Why can’t you send me a personal email informing me of my progress or letting me know if I fall behind?

A.     The best part of having an open gradebook is that parents and students have this information at their fingertips, twenty-four hours a day, without relying on me or anyone else to inform you. Also, we may have a different threshold for what warrants concern and contact. You may want to know if your grade slips from an A to an A-; others may only be concerned if the grade drops by a full letter grade, while some may not care about grades at all. Some consider a B on a math test a bad grade, while I do not, especially if you studied and did your best. I promise to be vigilant about keeping my gradebook up-to-date and expect that you, in turn, are taking a moment each week to view what I have posted. I suggest that if you choose to do this weekly that it be done on Monday since I may use the weekend for any necessary catch-up in the gradebook.

Q.     What can I do about my grade?

A.     Please see the most recent Math Reflection that I had you complete since it is essentially a list of things you can do to improve your learning; the grade will follow. In short, your grade is in your hands by making sure that you make the best of every precious class that we have, take your assignments seriously, and study the material throughout the unit so that you will understand the material and therefore do well on assessments.

Q.     Can I do some extra credit to improve my grade?

A.     Extra credit does not serve the same purpose for your learning that all of the learning skills listed on the math reflection do, so it is not something that I want you to rely on moving forward, and it does nothing to help identify or correct any issues. Extra credit is not something I want to encourage your reliance on as a substitute for developing better learning skills. 

Finally, extra credit for the sole purpose of raising one’s grade is the very definition of grade inflation, since anything that serves to raise one’s grade without improving learning, is grade inflation, in my opinion.

Q.     What is the best way to get in touch with you?

A.     The best way is via email however, we encourage students to contact teachers directly if they have questions or need help so if the issue or question is something that it is appropriate for your child to contact me about, then please encourage them to do so. I would also appreciate your looking for the answer to your question on the learning site first.

Understand the Problem

(Form a Hypothesis)

Don’t expect to be able to just jump in and solve the problem. 

Any problem worth solving won’t be that simple! Make sure you understand it first:

¨    Read the whole problem carefully

¨    Decide what information is relevant and what additional information you need

¨    Restate the problem in your own words

Solve the Problem

(Do an Experiment)

Ask yourself what makes the problem difficult

and then choose techniques that will help make it easier:

¨    Break the problem into smaller parts or list the things that must be done to solve the problem

¨    Draw a picture or diagram to model the problem

¨    Try to relate it to a simpler version of the problem

¨    Make a table, chart or organized list

¨    Guess and check/eliminate possibilities

¨    Look for patterns

¨    Use logical reasoning

¨    Work backwards if possible

¨    Use Algebra if appropriate

State and Reflect on your Solution

(Come to a Conclusion)

Ask yourself if your answer makes sense  

¨    Decide if your solution makes sense by comparing it to your estimate or prediction

¨    Reread the problem to make sure you’ve really answered the question being asked

¨    Write your solution in a complete sentence and/or include units to help you reflect on whether or not it makes sense

¨    Check your computations

¨    Make sure you used all of the relevant information or be able to explain why you decided to disregard it