Teaching for Conceptual Change

Topic/question: Using CIMM to teach algebra for 9th grade students on a 4th grade level

Convener: Janet

 

Attendees: Seth, Janet, Dan, Jennifer

 

Proceedings:

Janet, CIMM approach

Background:

•    What is a "concept" and what is a "system"?
•    Is math purely abstract? or
•    Math is a way to represent things in the real world
•    Kids stumble over trying to explain the meaning of mathematical formulas
•    How do you match an object with its relationship?

Use representative systems:
Example with negative and postive numbers:

•    Come up with a system of pictures (e.g. dots) which can be positive or negative (e.g. filled dots or unfilled dots)
•    Have students convert this made up visual system into a mathematical formula
•    After students practice with the visual system, matching symbols to math, they are better at relating math to the real world
•    The dot system is so decontextualized, students are more able to see how math relates to different contexts

Seth: proportional reasoning
3 dollars gets you 2 donuts, 3s=2d or 3s/2d = 1

Janet: There are 3 students for every professor, P=3S?
The mind tries to set up equivalency relationships.
This representative system help students with proportional reasoning.

Seth: difference between speaking formally like a physicist (2 meters in 1 second) vs. colloquially (2 dollars gets me one hamburger)

Janet: Connect visual system with its structures (e.g. parentheses) to algebraic expression.
Meta language connects different contexts

Jennifer: Can this be applied to other subjects, like social studies.  Students can create a solution to a historical problem, for instance scapegoating, and use symbols to represent.

Janet: Last year 3 school districts in Arizona  adopted CIMM
This summer, CIMM will be taught as a workshop at ASU

Seth: There has to be something more to this system than a visual representation for counting things, such as “I have 3 apples”

Janet: This system shows different reasoning processes that are at work, such as proportional reasoning.

Janet: Students don't intuitively understand conservation. If you have 6 objects and you put them into 2 groups, students still count the individual objects rather than understanding that the number is conserved.