For each homework assignment you turn in, you should include in a separate top page, 3-4 items, each of which being either

• "Among the main things I have learned this week"
  or
• "Among the things I am confused (or have questions) about this week"

Be sure to label clearly which of your items are in which category.

If possible, try to give items in each of these two categories. The check/check-plus/check-minus/zero system of grading this part will not be affected by which category you put your items in. Be specific and use full sentences. Don't just say "I learned about X"; explain X, and give examples.

Include (1) at least several worked-out examples, definitions, illustrations, etc, in your "What I've learned this week" summary. (2) Please print (do not use cursive/script) (3) Include page number of cited HW problems.

Why are we including these questions and impressions with our homework?. You may not have realized that you have a certain question or confusion during class, but only realized it upon working on the homework. Although seeking out help (e.g., my office hours, at the Math Lab, etc) is your responsibility, the information you provide will help me in preparing future classes.

Often, it is not easy for an instructor to tell which of two student questions asked in class represent concerns of only a few students, and which represents points that most of the class needs re-emphasized. The collection of everyone's responses gives me a snapshot of which areas are the most common topics students are struggling with.

Similarly, your summaries of what were "the main things [you the student] learned this week are" help me compare and check whether your impressions of what the main and most important topics covered match what I intended to convey in the class presentations, activities, and other learning experiences.

Sample item in first category:

I learned that if a and b are two numbers on the number line, then |a-b|, the absolute value of the difference between a and b, is how far apart these two numbers are. If we think of a and b as two places on the x-axis,then |a-b| is the distance (along the x-axis) between a and b.

A particularly good entry might finish by also pointing out:

The order of a and b is not important here (and it shouldn't be, since distance between two points doesn't depend on their "order") since |a-b| equals |b-a|. This is because |x| equals |-x| for any number x (for example |5| equals |-5|, and they are both equal to 5), and "a-b" is the negative of "b-a" since if we multiply the quantity (a-b) by -1, and use the distributive property, we get (-1)(a)+(-1)(-b), and since (-1)(-b) equals b, this is -a+b, which is b-a.

Sample item for second category:

I understand the basic idea of 'completing the square' but I don't understand how one starts. In particular, how does one choose the value of the number to add to both sides of the equation, which makes one side a 'perfect square'?

In addition to items from the above two categories, if possible, include also:

• Questions you have about the textbook readings, e.g.:

  Does the method of page 131 example 2 work for all functions? For quadratics only? For quadratic and other polynomials but not for other functions? Why or why not?"

  and

• Questions which you didn't get a chance to ask me in class, e.g.

  If a formula for a function f(x) models a real world situation for us, why do we need to also graph f(x) (a visual model?) in addition to the first model?

Note: My aim here is not to add a lot of work to each week's assignments, but to get you thinking in a way which will help you do well in the course.

In addition to the reasons stated above for this assignment, I think you will also benefit from this somewhat structured way to help you sort out and summarize what you've learned, and which areas and topics you're unclear about. It is my hope and belief -- based on past semesters' experience -- that you will gain more out of this course (and perhaps earn a better grade) in the process.

Another way to think about it: your exposition should be written as if you were authoring a (short part of) a section of a textbook. Another way to think about it: if you gave a bundle of the last 5 weeks' of cover sheets to a classmate, they would have an excellent study guide for the next test. Not exhaustive, but a comprehensive overview.