Math Projects

Project (9pts)

Choose one of the following projects. The deadline for submission is November 30th. Early
and electronic submissions are encouraged, you’ll get immediate feedback if you send it
electronically. All projects must be word processed (unless otherwise stated) to earn full
credit (text: font size not exceeding 12, single or 1.5 line spacing). State your ideas clearly
using complete sentences and correct grammar and spelling. Extent: 1.5 – 2 pages.

1. Math Autobiography (individual project, no groups!)
Project description: Write a description of how you have learned mathematics from the
time you remember learning to count up through your most recent college math
class(es). It includes pre-school, elementary, middle school, high school and college
experience. Discuss how your experience may or will influence the way you will be
teaching mathematics someday.

Write your own definition of mathematics (use your own words). What is your opinion
on “the importance of mathematics” in school and life? Is it important? Why or why
not? Based on your own experience, what is the best way to teach mathematics? What
is the best way to learn mathematics? Note that the last two questions are different and
you need to address both of them.

2. Problem Solving Interview (individual or group project)
This is a research project. Choose a subject. Your subject may be a friend, roommate,
family member etc. but not a student currently enrolled in MTH 151 class. Do not
identify your subject by name in the report. Provide only background information (age,
attitude towards mathematics, etc.).

Pick any (one) problem we have done in class in chapter 1 (you may refer to the Chapter
1 review sheet). Ask your subject to solve the problem. Ask him/her to think out loud.
Take notes on how your subject solves the problem. If your subject was not able to solve
it in reasonable amount of time, just keep track of what he/she was able to do. Keep
track of all questions the subject asked (you may answer them only with “yes” or “no”).
Keep track of all strategies the subject attempted to use. Do not forget to specify
conditions: amount of time, available resources (calculator, manipulatives etc.).

Discuss your findings. Was the problem difficult for you subject? What were the biggest
obstacles in his/her problem solving process? Was there any effective hint you (could
have) used? Etc. If you interviewed more than 1 subject, compare their strategies,
obstacles etc. Record differences in initial conditions.

If it is a group project, state clearly each student’s role and/or input. You must interview
at least one subject for every two group members (that is, if your group has 6 members,
you must interview at least 3 subjects using the same problem)

3. Division in non-base-10 numeration system. (individual or group project – 4
students maximum)
This is a theoretical project. Choose a numeration system with base different from 10
(base-2, base-5 etc.). Solve several division problems in your numeration system without
converting any numbers into base 10. You must solve and explain at least 4 division
problems:

· Start with a division of a two-digit number by a one-digit number. Solve the
problem and explain the solution (draw cubes, base-n pieces, etc.).
· Continue with division of a two-digit number by a one-digit number but now use
the table of basic multiplication facts to explain your solution.
· Continue with division of a three-digit number by a two-digit number with a
non-zero remainder. Explain the solution.
· Perform a long division algorithm with two numbers of your choice.

If it is a group project, state clearly each student’s role and/or input. If you use a lot of
drawings, you may hand in a neat handwritten report.

4. Nonstandard Algorithms (group project)
This is a research project. Its objective is to teach one of the nonstandard
algorithms to at least 3 people (per group member – in group of 4 you need at
least 12 people). None of your subjects should be or have been enrolled in MTH
151. If possible, one of your subjects should be a child.

Teach the algorithm of your choice (it must be nonstandard) and give your
subjects a problem or two to practice it. Then give them two more problems and
tell them that they can use any method they want. Observe your subject’s
method and result.

Keep track of all questions the subject asked and do not forget to specify
conditions: amount of time, available resources etc.

In your write-up, do not identify your subject by name in the report. Provide
only background information (age/gender, attitude towards mathematics, etc.).

Explain briefly which operation you used and the algorithm you taught.

Discuss your findings. Did your subjects know the algorithm before? Was the
algorithm difficult for you subject to learn? Were your subjects comfortable to
use it even for problems, in which they were allowed to use any method? What
were the biggest obstacles? Compare strategies of all your subjects.