Summer 2016. To the memory of my friend and inspiration, Jerry Bruner, October 1916-June 2016.
A new instructional procedure developed by Cynthia McCallister, called Integrative Math©, combines elements of Cooperative Unison Reading®: and modes of representation Jerome Bruner presented in his book, Toward A Theory of Instruction (1974). Students use the rules of Unison to read story problems. Then, using manipulatives, crayons, markers, and stories, they integrate enactive, iconic, and symbolic modes of representation, strengthening their mathematical thinking.
Integrative math integrates the way our minds work to unite diverse systems of memory so that they can be deployed and used for problems that come up in real-life situations.
For example, Integrative Math is an example of 'bihemispheric integration,' because the procedures let students engage both sides of their brains as they do activities focused on solving the problem at hand. The context-sensitive, receptive right brain handles the context-dependent, face-to-face, non-verbal communicative aspects of the activity, while the left-brain, logical-sequential, assertive left brain does the work of describing and encoding the experience.
After doing the activity for a half hour, one graduating senior from Urban Assembly High School for Green Careers said he didn't want to graduate now that the kids were getting to play with blocks again!
Ready to learn how to do the activity? Here’s how Integrative Math works:
Before I explain the next step, I’ll take a minute to explain how Bruner’s ideas come into play.
Bruner developed an insightful way of thinking about the way human beings represent ideas to themselves. He reasoned that people have three ways of representing information that unfold, one after the other, but also work interactively to support complex thinking.
Enactive: The first form of representative thought is stored through action. It’s in our bodies and muscles. It’s what Bruner called the enactive Mode of representation. It’s dominant at ages 0-1 years of age.
Iconic. The next type is the iconic mode of representation, in which we represent images as mental images in our minds. Diagrams and pictures are a form of iconic representation. Children ages 1-6 begin to rely upon iconic forms of representation in their thinking.
Symbolic. The symbolic mode of representation is the final form of thought, and it’s stored in our memory as a code or symbol that is able to represent something else. This ability—for the code to be flexible enough to stand for something different than the code itself—allows human beings to free up their thinking from the constraints of the ‘here and now’ boundaries of situations. This form of thinking allowed humans to conjure up the ideas that created mathematics and science and enabled civilizations to compile their histories.
Bruner thought that kids of almost any age could tackle most conceptual problems if the material were arranged in the appropriate sequence. That’s where Integrative Math as a protocol comes in. Which brings me back to Step 4.
Now you have the tools to become a math genius!
Theories embedded in this method:
Cooperative nature of human thinking and creativity (Tomasello)
Mindsight and neural integration (Siegel)
Modes of representation (Bruner)
Socio-relational theories of instruction (McCallister)
© 2016 Cynthia McCallister All Rights Reserved
Integrative Math©, Cooperative Unison Reading, and other Learning Cultures methods are featured in online courses this Fall on www.LearningCultures.net.
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In a new e-book, by Cynthia McCallister, is a brief guide to the Cooperative Unison Reading approach. It provides an innovative angle on reading instruction by looking at the reading process as a cooperative human process and applying theories from science that explain cooperation.
McCallister also looks at the reading process as a form of action, as opposed to the accumulation of discrete skills that are accumulated through linearly transmitted instruction.
The book is packed with practical applications of the method to real classroom situations, and comes alive with media assets such as audio and slideshows.
Even if you don't buy the book, you can access a free chapter that provides a training guide to the Cooperative Unison Reading method, led by an expert teacher in the method, Tara Silva.
The book is a companion to the online course, Cooperative Unison Reading/Mindful Reading, found on www.LearningCultures.net.
Visit the book's url and get yourself a copy today!