The Math Forum: 2000 Summer Institute - sum2000

July 25 - August 11, 2000 - Swarthmore, Pennsylvania

2000 Summer Institute || Agenda || List of Participants

Day 4 Summary

Shelly and Suzanne led the participants in thinking about the Library of Math Forum Problems, a new feature being developed for the Math Forum site. Jody Underwood attended to take notes and participate in the discussion.

Shelly began by telling the participants, "Think about a course that you've taught that you like or that you find challenging. Think of the top ten most important concepts, ideas, or relationships that are inherent in the course design. What ten things do you want the kids to get? Write it down."

Some people focused on particular courses like geometry and algebra, Jeanne focused on high school math in general.

Now, go into the PoW environment and search for things on your list. You can partner up or do it alone. We're going to focus on how to make the PoW archives, in particular, useful to you. You'll have an impact on the design of the site.

Round robin sharing:

Susan: congruent triangles. Checked all the hits for which ones are really congruent triangles -- 2. With area: 3. Another bit: 3. The rest were not relevant. In one case, a kid used "congruent triangles" as a wrong solution. It was the 5th one to come up. (Someone accused her of taking a scalpel knife to do this exercise.)

Dave took a more general approach. PoWs are not instructional in nature. He felt Susan wanted to use them as instruction; he wants to use them for enrichment.

Varnelle couldn't find anything particularly in the PoWs. So she went to the Teacher's Place, did elementary math search and found a lesson. Found something by Suzanne also that was appropriate.

Matt took a year at random in the GeoPoWs. Went week by week to see what fit into the topics he teaches. As he got later in the year, the PoWs hit 5-6 categories. Circles, Pythagorean Theorem, and area and volume were hit by most. He's not sure this is the best way to do it. (There weren't many on proofs, but kids wouldn't want to do that anyway.)

PoWs are like proofs, because they have to explain their answers.

Eva went to an FAQ page, and it took her a whole page on how to do square and cube numbers by hand and by calculators. She would bookmark that page for a lab so students could use it, because it would provide reinforcement. "Absolute value" took her to a great site. It gives lesson by lesson on how to turn on the calculator she uses, how to graph things, how to turn it off.

Face value. Algebra 2. Shirley went to various sites that had puzzles that showed the way different kids solved the problems. She was interested in what puzzles would help her with these concepts.

Jo. Tried to play naïve as if she didn't know anything about the site. She searched for main topics -- volume. It came up with a number of different levels of PoWs. It didn't just give her the geometry problems, which is what she would have wanted.

Algebra 1. Danielle looked in the AlgPoW section, went through the problems. As she scanned, she checked to see if it would reinforce the topics that she'd written down. She looked a little at the solutions that students submitted. If you want to categorize, it should be done on the concepts from a teacher's point of view, not on the strategies that students used. She found other topics that the pows reinforced, and there others in addition to her top 10, often covering more than one concept.

Jeanne. General high school. She was looking at the PoWs from an assessment perspective. She wanted problems with multiple entries, and was interested in the student approaches. She'd like to see what has stuck (from her teaching). She looked at all the PoWs, not just the high school ones. She typed in "variety". She was looking for the administrator's comments -- "students tried a variety of approaches". It gave her a lot of appropriate PoWs.


Then we shared our PoWs library. The goal is to outline tasks that could come out of it that the teachers would be interested in doing. It was presented as a sample; everything can be changed.

It didn't bother Susan to see the different PoW levels once she did a search.

Some thought the search words were related to Pythagorean theorem, in Special Topics. That got cleared up.

Could the user decide how to sort the PoWs for individual view?

They like having the PoWs sorted by level (geo, alg…) and difficulty.

They don't like the catalog words; they want language that teachers use.

Suggested Search Words aren't necessary, but should be hot links in the Special Topics.

There could be a myriad of suggested search words.


If PoWs are used as enrichment, then you don't need to worry about Standards.

People vary on whether they use the Standards, local, or none. Some people's curriculum needs to be Standards-driven. California has Standards, but they don't seem to align to what's in the classroom even though they have good ideas.

Wouldn't go for a Standards code. The keywords are more important.

Have a page that has the NCTM Standards, and from each heading have a link to sample PoWs that meet that Standard.

We're assuming that the Process Standards, like communication and logical reasoning, are included in all the PoWs.

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