About MAPs (Mathematical Analysis Papers)
Mathematical Analysis Papers (MAPs) are an important part of your mathematical learning
opportunities. They will give you experience in carrying out extended investigations of complex
problems. These problems will not necessarily be connected to the rest of the unit.
You will generally have several days to complete a MAP, but you should begin working on these
problems as soon as you get them, since they take more time than an ordinary homework
assignment. In fact, working on the problem a little bit each night is sometimes better than working
a lot at one time, because each new look at the problem may provide a new perspective. You may
want to think about the problem at odd moments, such as, while waiting in line at the store or while
sitting on the bus on your way home from school. You might discuss the problem with your family
at the dinner table or collaborate with your classmates over the phone.
It is not considered cheating to work with someone else on the problem, as long as you
acknowledge that collaboration in your write-up. You should not, however, allow others to simply
copy your work, nor should you copy from them. Your final write-up should be in your own words
and reflect your own thinking. When working with others, it is more helpful to give them a hint or
ask them a leading question rather than just giving them the answer. Otherwise, you will deprive
your friends of much of the learning experience.
MAPs give you a chance to work on your mathematical writing. You will be expected to explain
your thinking more fully in these assignments than in regular class activities or homework. Be sure
to leave ample time for this writing. To prepare for your written analysis, you will want to take
careful notes as you work on the problem. Your notes will remind you of the things you attempted
– including strategies you may have tried and abandoned – and how these initial attempts ultimately
gave you greater insight into the problem. The accompanying “Standard MAP Write-Up
Instructions” list the categories and directions you should follow when creating your formal
Mathematical Analysis Papers.
While working on the MAP problem, you may want to consider the thinking strategies that all
proficient learners utilize:
Schema – using prior knowledge
Drawing inferences – based on what I have observed I think this will happen
Asking questions
Determining what is important in the text
Monitoring meaning and comprehension
Evoking images
Synthesizing information
Using fix-up strategies
Looking at a simpler problem
From Interactive Mathematics Program Problems of the Week, Key Curriculum Press
Standard MAP (Mathematical Analysis Paper) Write-Up Instructions
Mathematical Analysis Papers give you a chance to work on your mathematical writing. You will
be expected to carefully explain your thinking about a significant problem. The following
instructions list the categories and directions you should follow when creating your formal MAP
write-ups.
1.
PROBLEM STATEMENT
State the problem clearly in your own words. Your problem statement should be clear enough that
someone unfamiliar with the problem could understand what it is that you are being asked to do.
2.
PROCESS
Describe what you did in attempting to solve the problem, using your notes as a reminder. Include
things that didn’t work out or that seemed like a waste of time. Do this part of the write-up even if
you didn’t solve the problem. If you get assistance of any kind on the problem, you should indicate
what the assistance was and how it helped you.
3.
SOLUTION
State your solution as clearly as you can. Explain how you know that your solution is correct and
complete. If you obtained only a partial solution, give that. If you were able to generalize the
problem, include your results. Your explanation should be written in a way that will be convincing
to someone else – even someone who initially disagrees with your answer.
4.
EVALUATION
Discuss your personal reaction to the problem. For example, you might respond to the following
questions:
 What did you find difficult about the problem? What was easy about the problem?
 What did you learn from doing the problem?
 Can you invent some extensions or variations to the problem? That is, what other kinds of
problems are related to this one?
 How have you grown as a mathematician by doing this problem?
5.
SELF-ASSESSMENT
Based on your effort and your results on this problem, what grade do you think you deserve and
why? What evidence have you included to support this self-assessment?
From Interactive Mathematics Program Problems of the Week, Key Curriculum Press