## Wednesday, March 28, 2012

### Escape From the Textbook Winter Meeting

Below are some lightly edited notes from the most recent Escape meeting at Willard Middle School in Berkeley. Our next meeting is tentatively set for Saturday, June 2nd somewhere in San Francisco.
----------
Escape from the Textbook meeting: March 24, 2012

Introductions

We spent the first part of the session exploring the game of Set. Over the course of the morning there were a few other games/ideas mentioned including Eleusis, Attributes Blocks (similar to set except with physical blocks), Spot It and Ricochet Robot.

We played the game for a bit, but then worked on solving and creating mathematical puzzles. Below are some examples:
* What is the maximum number of cards you can have without a set?
* Can you make a strip (a train) where any three cards next to one another are share the same number of characteristics?
* Games could be created with these cards similar to dominoes
* Start with some number of cards in your hand. Continue to play cards that do NOT make a set with the cards on the table.
* How many cards are in the deck?
* How many different sets can one card be a part of?
* How many different sets can 2 cards be part of? What if only 3 characteristics need to match (or be different)?
* Is it possible for all the cards to be used? What is the probability of this happening?
* Can a subset of the deck be organized in a way to make sets with no extra cards left over?

Our group then began working on "magic square" problems. We determined that if cards are on the four corners of a magic square, the entire square is determined. We then saw that this was also the case with 3 corners (and that it would be impossible to create the entire magic square if the 3 starting cards made a set).

We then shared our work with other tables and talked about. Some comments of note:

*Students who do well anticipate teacher questions and understand why they're being asked.

Ways SET can be used:
*the big picture of "Here's our universe. What is true in this universe?" Parallels other axiomatic systems.
*sorted attributes, categorizing
*union/intersection

Interesting to maybe think about how the cards are exactly the same mathematically as just having the 4-tuple (0,2,1,1) with four dimensions (four different attributes) and values that can be 0, 1 or 2 (three different options for each attribute).
Kim then shared (and asked us to reflect on how this could be done with students in a more meaningful way than just telling them) a way to determine which card is missing after playing a full game and ending up with a number of remaining cards that is not a multiple of three.

Break

Shared some summer opportunities:
Promoting Algebraic Thinking Summer Institute: Lawrence Hall of Science
Center For Innovative Teaching: Hands on Geometry

Assessment
How do we assess content learning? (I would add habits learning too)
Rigor?
How do we evaluate assessments?
Am I testing what I think I'm testing?
How can we use assessment to understand what sense students are making of instruction?
What are we looking for and how do we measure it?
Targeted, selected observation...
Engaging students in self-assessment

Some assessment ideas:
* Give assessments with lots of questions and then at the end tell students that their top scores on 5 (or whatever) problems will be the only ones graded.
* Ask students to solve 2 of 4 and give different point values for more complicated problems
* Have small skills, concepts, and pushing quizzes that students take weekly (with a choice of which quiz they take) and can retest until they show proficiency

Big question: assessing what?
*students making good choices
*have you learned this skill
*access

Next time, talk about different kinds of assessment. Thinking about bringing assessment questions around a particular topic/skill/concept (probably one middle school topic, maybe proportions, and one high school topic, maybe systems of equations).
Brainstorm ideas on how to make assessment a better tool for learning? What do you do after assessment?

1. Just some clarification about attribute blocks: they are not actually isomorphic to the Set cards. They have four attributes: five shapes, three colors, two sizes, two thicknesses. So a total of 60 blocks.

To the best of my recollection, the two main activities (for K-1 students) were:

- take turns placing blocks correctly in one-, two-, or three-loop Venn diagrams (for example one loop for triangles, another loop for thin blocks, and the intersection for thin triangles)

- make 1-, 2-, 3-, or 4-difference "trains", where each block differs from the previous one in that many dimensions

An interesting question would be whether a decent Set-like game could be devised using attribute blocks.

--Henri

PS: