The inspiration for a portfolio comes from Professor Kazemi of the College of Education. She teaches the courses in the CoE on teaching math in elementary school. In discussion of the content of Math 170, she said it would be useful in her courses for students to have a portfolio of examples they had studied in Math 170.
The portfolio is optional. It will count as 5% of the final exam. You will be able to pass the final with 80% of the points, so the portfolio should not be needed to pass if you are doing well with the material.
Periodically during the course I will identify a problem or example for you to write up for your portfolio. I'll mention it in class, and also list it here. A portfolio writeup should be a thorough enough explanation that you will be able to read it several years from now, and understand it easily. You may also include other any other work for the course that you think you would find useful to look back on, to recall things you learned in this course.
I will collect your portfolios on November 18 to look them over and advise you if you need to improve any of your entries. This midquarter check will be required if you want credit for the portfolio. At this time, you don't have to have completed all the entries I've listed to date or a table of contents. Do include all the work you've done on the portfolio so far, fasten the pages together with a clip or folder, and be sure your name is on the front. (If you don't have it ready on the 18th, email me for an appointment to turn it in later in the week.)
The due date for your finished portfolio is Monday, December 6 (so I can return them at the last class on 12/8 and you can use them to study for the final). It should be fastened together with a cover and a table of contents.
Chapter 1 Entry: Problem solving examples. Pick two problems (from homework or classwork) and solve each one in several different ways. Use systematic guess and check for at least one of the problems, showing a table of guesses and related numbers and explaining how you use the table to pick your next guess. For at least one of the problems, include a solution by diagram and an algebraic solution, and discuss how the proof by diagram is related to and prepares a student to understand the algebraic solution. (For instance, explain how the algebraic equations are represented in the proof by diagram.) You do not have to make an explicit list of quantities and values, but you should be very clear about what the quantities are, as you use them. Be sure they are quantities (e.g., the number of mittons not just mittons, and whose mittons they are in a problem about two different people's mittons), and that you say what your varaiables stand for in an algebraic solution. The goal of this item in the portfolio is to provide yourself with models of problem solving that you might not have thought of using, or might not thought of as being related, before taking Math 170.
This item should be similar to the examples worked out in §15.3, but you should not use the problems discussed there, and you may make use a different selection of problem solving techniques than the ones used there. In fact, if your chosen problems do not involve time-varying quantities, some of the techniques used in §15.3 may not apply very well.
Chapters 2 and 4 entries on place value and algorithms:
To remember the struggle. Record
your thoughts and frustrations with trying to understand a new place value
system. What do you want to remember from your own work and class discussions
in this part of the course, years from now when you are helping
a child who is struggling with our base ten system?
What helped you do and understand the work when you didn't know
all your number facts?
Algorithm examples. Do an addition problem and a subtraction problem in another base in three ways: with blocks, in the expanded algorithm, and in the standard algorithm. Be sure your work in the algorithms is all in the other base, not in base ten. Discuss briefly how the same steps can be seen in each algorithm, so that understanding one way can be used to learn another way. Also do a lattice multiplication problem in another base, and explain briefly, in terms of that problem, why the method works.
Chapter 3 entries on the arithmetic operations.
Give one or two examples of each type of problem for each
of the four operations.
(For instance, for subtraction, give examples of story problems for each of the
following types: take-away, comparison, missing addend, missing subtrahend.
One example may be used as an example of than one type, but in this case
you probably want to have more than one example of these types.)
Also draw a good diagram for each problem. The point of this entry
is to have examples that will help you remember the distinctions between
the different types of problem.
Addition: Choose examples from the first page of
the worksheet on division, Dec. 1, of questions asking for
each of the five types of answers from a division calculation that
doesn't come out even. State the problem, and say what type of answer
is being asked for. (You don't have to do the problem.)
Chapter 5 and Number Sense Entry. Give some examples of "number talks." For each computation, give two or three ways of doing the computation mentally. Choose examples that will help you remember different techniques. Also give some examples of methods of estimating. Here are some suggestions of problems in the text from which you might choose examples: §5.1, Activity 1 & Exer. 2 & 3; §5.2, Exer. 6 & 8; §6.2, Exer. 6 (with reasoning); §6.4, Act. 10 and Exer. 12 & 17; §7.1, Exer. 15.
Chapters 6 & 7 entry on Fractions. To remember how to convert decimal to fraction form, §6.3, Exer. 2dgi, with explanation of reasoning. Your choice of problems from §§7.1-2; pick problems that taught you something you want to remember. For §7.3, make drawings for Activity 3, b & d, and Activity 4, abc. Explain where in the drawing the dividend, divisor, integral part of the quotient, remainder, and fractional part of the quotient appear, and be sure if is clear what the referent unit is for each of these.
Optional Entry: Vocabulary List. Even though our text has a glossary, you may want to make your own vocabulary list. Include terms you find yourself looking up repeatedly, or that you often get confused. Give examples or applications as well as definitions, if that would be helpful to you. For instance, my vocabulary list would include the names for types of division (which we'll get to in Chapter 3), including all the alternative names and sample problems of each type.
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Most recently updated on December 3, 2010.