# 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.