Survey on Mathematics Problem Solving and Proof
NAME: __________________
NOTE: All responses will be kept confidential by Professors Dewar and Bennett.
Check, if true: I have taken MATH 190 ______ .
I have taken MATH 191 ______.
I am currently enrolled in the following MATH classes: ___________________________
1. Briefly describe the most interesting problem you have ever worked on.
2. Briefly describe what you think mathematics is
3. Briefly describe what features you think make a mathematics problem interesting.
4. Briefly describe what you think the purpose(s) of proof in mathematics is (are).
Survey on Mathematics
Circle the underlined word in Statements 1 - 28 that most closely describes your approach to and
attitudes toward problem solving.
1. If I am given a problem quite a bit different from the examples in the book, I can
Always
Usually
Sometimes
Rarely
Never
figure it out myself.
2. Drawing pictures or imagining real physical situations
Always
Usually
Sometimes
Rarely
helps me do mathematics.
Never
3. Reading a problem more than once is
Always
Usually
Sometimes
a waste of time.
Rarely
Never
4. When I have finished working a problem, I
Always
Usually
Sometimes
check my calculations for errors.
Rarely
Never
5. There are
Always
Usually
Sometimes
obvious ways to solve a good mathematics problem.
Rarely
Never
Rarely
Never
7. When I get the answer to a problem, I
Always
Usually
Sometimes
Rarely
look back at the problem to see if my answer makes sense.
Never
6. I Always
Usually
Sometimes
stop thinking about a problem after I get an answer.
8. I Always
Usually
Sometimes
try to restate a new math problem in my own words.
9. Solving a mathematical problem
Always
Usually
Sometimes
involves finding a rule or formula that applies.
Rarely
Never
Rarely
Never
10. I am
Always
Usually
Sometimes
Rarely
Never
interested in knowing how mathematical formulas are derived or where they came from.
11. I Always
Usually
Sometimes
Rarely
have trouble getting started on a problem that is new to me.
Never
12. I Always
Usually
Sometimes
enjoy exploring mathematical relationships.
Never
Rarely
13. I Always
Usually
Sometimes
Rarely
Never
enjoy solving problems that require me to figure out my own individual approach.
14. I Always
Usually
Sometimes
Rarely
Never
learn mathematics best when someone shows me exactly how to do the problem and I can
practice the technique.
15. When I have finished working a problem, I
Always
Usually
Sometimes
check my calculations for errors.
Rarely
Never
16. For the math problems I have encountered, there are
Always
Usually
Sometimes
Rarely
obvious ways to solve them.
Never
17. After reading a problem, I
Always
Usually
Sometimes
Rarely
try to remember if I have ever done a similar problem before.
Never
18. I Always
Usually
Sometimes
Rarely
Never
enjoy solving problems that are an application of a particular rule or formula.
19. I can
Always
Usually
Sometimes
Rarely
Never
think of at least one way to begin to work on a math problem that I have never seen before.
20. I Always
Usually
Sometimes
Rarely
Never
enjoy solving problems that are similar to a problem I have seen solved.
21. After obtaining a correct answer, I
Always
Usually
Sometimes
Rarely
want to know an explanation for why the solutions works.
Never
22. If I know a few concepts, I can
Always
Usually
Sometimes
figure out the rest.
Never
Rarely
23. I Always
Usually
Sometimes
Rarely
enjoy solving problems that require research and original thinking.
24. If I can't solve a problem in 10 minutes, I will
Always
Usually
Sometimes
be able to solve it.
Rarely
Never
Never
25. I Always
Usually
Sometimes
Rarely
Never
take time to estimate what the answer to a problem will be before actually doing the problem.
26. I Always
Usually
Sometimes
Rarely
Never
read a problem more than once to make certain I understand it.
27. After I have solved a problem, I
Always
Usually
Sometimes
try to think of a different way to solve it.
Rarely
Never
28. I Always
Usually
Sometimes
Rarely
enjoy doing large numbers of easy mathematics problems.
Never
------Circle the response that most closely indicates how you feel about each statement 1 - 24.
strongly
strongly
disagree disagree neutral agree agree
1.
2.
3.
I usually believe that I can do
well in a mathematics course.
SD
D
N
A
SA
Most good mathematics problems
can be done in a single sitting.
SD
D
N
A
SA
I frequently discuss homework and
class notes with other students.
SD
D
N
A
SA
strongly
strongly
disagree disagree neutral agree agree
4.
The main benefit from studying
mathematics is developing the ability
to follow directions.
SD
D
N
A
SA
If I do not understand something in
class, I will usually ask the teacher a
question about it.
SD
D
N
A
SA
I usually take clear and complete
notes in a mathematics class.
SD
D
N
A
SA
After a conjecture has been proven, it is
possible to find a counterexample.
SD
D
N
A
SA
I almost always make a persistent
effort to do my homework before the
next class session.
SD
D
N
A
SA
If I have questions arising from the
homework, I ask my teacher or
another student.
SD
D
N
A
SA
10. I find a way to check my solutions to homework problems before the next class.
SD
D
N
A
SA
5.
6.
7.
8.
9.
11. In mathematics you can be creative and
discover things by yourself.
SD
D
N
A
SA
12. If I have trouble understanding the textbook,
I find other ways to master the concepts. SD
D
N
A
SA
13. The average U.S. citizen rarely encounters
applications of mathematics in his/her
everyday life.
SD
D
N
A
SA
14. A person must possess a special
talent to do well in mathematics.
D
N
A
SA
15. No really new mathematical theories
have been discovered since the 1800's.
SD
SD
D
N
A
SA
strongly
strongly
disagree disagree neutral agree agree
16. Mathematics is a creative endeavor.
SD
D
N
A
SA
17. Sometimes very theoretical
mathematical results are later found
to have real world applications.
SD
D
N
A
SA
18. I work persistently in a mathematics course
regardless of how well I do on the tests.
SD
D
N
A
SA
19. I am usually enthusiastic about
learning in mathematics courses.
SD
D
N
A
SA
20. Talking over math problems with another
person is a legitimate problem solving
strategy.
SD
D
N
A
SA
21. Expert problem solvers often find trial-anderror and other seemingly haphazard
methods are necessary in mathematics.
SD
D
N
A
SA
22. I miss at most two class hours
per semester.
SD
D
N
A
SA
23. If I see five examples where a formula holds,
then I am convinced the formula is true.
SD
D
N
A
SA
24. I usually reread my class notes
carefully before the next class.
D
N
A
SA
SD
Please answer the next four questions on the back of this sheet.
1.
On the back of this sheet list as many general problem solving strategies (such as,
draw a picture) as you can (up to 10).
2.
On the back of this sheet list as many careers as you can (up to 10) that are
appropriate for a person with a college degree in mathematics.
3.
On the back of this sheet list as many famous mathematicians (living or dead) as you
can (up to 10).
4.
On the back of this sheet list as many fields or areas of mathematics as you can (up
to 10)