The Math Forum: 2000 Summer Institute - sum2000

July 25 - August 11, 2000 - Swarthmore, Pennsylvania

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2000 Summer Institute || Agenda || List of Participants
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MidPoW Conversation Notes

Dave, Eva, Suzanne, Jo, Kristina and Shelly looked at the "working model" of categories already listed in the problems library, comparing it to two other lists. They considered the following:

  1. How can the input from the two lists enhance (if at all?) the working model?
  2. Is the working model missing any topics?
  3. Is the working model the vocabulary of the teacher?
  4. If you add a topic to the list, explain the type of problem you would expect to see.
When the AlgPoW group met they recommended that several topics should be included in the MidPoW list and we also took those into account.
order of operations
algebraic expressions
integers
scientific notation
We discussed various ways that we could refer to "arithmetic" and we discussed the following possibilities:
fundamental mathematics
basic
pre-algebra
number sense
operational skills
number and operations
numeracy
Kristina shared the categories that were done by the elementary group yesterday. We looked at their categories as a starting point and eventually we generated the following for the MidPoW:
Number/Operations
operations
estimation
factors, factoring, prime numbers
fractions, decimals, percents
measurement
ratio/proportion
Algebraic Reasoning
distance/rate/time
variables
functions
equations (realizing that problems are requiring algebra)
inequalities ?
Geometry
pi
area
circumference and perimeter
Pythagorean theorem
volume
angle relationships
Applications and More
Patterns
Logic
Probability/Statistics
Permutations/combinations
Graphs/Charts/Tables
Discrete Math (we think itıs pathways)
Discussion items:
As we look at specific MidPoWs to decide what categories they fit under, if the topic is completely contained in it but there are other topics as well, it would be in another category because it would require other skills to be successfully completed.

What is number sense? - reasonable answer? Number sense is a confusing term. Can we find a better term that will help the teacher? What kind of problems would we expect to see there? Weıre looking for filters and that might not be a good one because it wouldnıt filter anything out.

Properties of equality/inequality - Jo thinks it's a content topic and not a problem topic. If we take off "property" can you have just equations/inequalities?

We had a discussion on the topic of discrete math and if teachers know what that is.

Pi - we put it in geometry because middle school teachers introduce pi using circles but we understand that it also fits in the same category as ratio.


As we considered topics we also made a list of possible searchwords
scientific notation
Golden ratio
Pascal's triangle
exponents
integers
commutative
associative
distributive
(as we make this list we are doubting whether these are really PoW appropriate)
triangle
square
(possible all different specific polygon words)


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