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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ElemPoW Conversation Notes

Varnelle, Eva, and Kristina looked at the "working model" of categories already listed in the problems library, comparing it to two other lists.

  • List 1: Varnelle had created a list while looking at the problems already collected under the ElemPoW category of "Algebraic Reasoning". She went through them connecting them to math topics from the NCTM Standards.
  • List 2: Kristina had made a list referring to an elementary text book, choosing topics she thought teachers would want to find on the topics list.

Discussion points:

  • What topics will teachers hope to see?
  • What language do teachers use? (Teachers don't use the word "Arithmetic" much anymore, but "Mathematics" is too general.)
  • Do we keep "Algebraic Reasoning" to show teachers that they are actually teaching it? Or do we categorize problems by "variables, equality, etc." and then add an explanation about Algebra?
  • How can we be thorough without overwhelming a teacher who is searching?

Conclusions:

The elementary curriculum is very broad. Students learn concepts like pattern, measurement, number sense, and multiplication. They learn skills for computing answers using the four basic operations, as well as finding eqivalent fractions, decimals, etc. They also learn to use tools such as calculators, graphs, and charts. Therefore, there is a lot to include.

At the same time, elementary teachers want information to be very easy to access. They do not want to search down a list of words that may or may not make sense. Therefore, the list should be organized into 3-4 conceptual groups.

Some teachers teach to Standards (NCTM, state, district). Some teachers focus more on skills and follow the sequence of traditional text books series. Some teachers use PoW's for enrichment. Some teachers use them for the whole class. All of these teachers should be able to find what they want.

Recommendations:

After looking at the organization for the Trig/Calc PoW, the elementary group would like to see the ElemPoW structured similarly. There might be four main categories with 3-8 topics listed under them. With a few exceptions, the group kept the terminology of the "working model".

Elementary Mathematics/Arithmetic

  • Addition/subtraction problems
  • Multiplication/division problems
  • Number sense
  • Estimation
  • Factors, factoring, prime numbers
  • Fractions, decimals, percents
  • Measurement
  • Ratio/proportion

Geometry

  • Area
  • Circumference & perimeter
  • Volume
  • pi

Algebraic Reasoning

  • Properties of Equality
  • Variables
  • Equations
  • Functions

Applications

  • Logic
  • Patterns
  • Probability
  • Statistics
  • Discrete math
  • Graphs, tables, charts

Where do we go from here?

  1. It is time to look at 16 problems and see if they fit these categories.
  2. The discussion needs to include context labels (weather, environment, money, families)


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