Multiple Models

[paulm]

The use of multiple models always seemed to be a recognition of the fact that people learn differently – some visually, some verbally, some kinesthetically, etc., etc. The different ways in which whole number place value can be taught is a good example, with Base 10 Blocks, bundles of straws, drawings representing tens and hundreds, verbal naming (e.g., 4 Tens + 6 Ones), expanded notation, all used to help students understand place value. These different methods were employed primarily so we could be sure we gave all our students their best chance at grasping concepts.

It now seems that representing mathematical concepts in multiple ways is considered an end in itself, and that students are expected to have (and will be assessed on) the ability to create those multiple representations for themselves. I’m thinking in particular about Practice 3: “…construct arguments using concrete referents such as objects, drawings, diagrams, and actions…, ” though there are other examples.

Is this perception accurate? Has anyone else wondered about this?

Thanks,

PaulM

[Bill McCallum]

No, I don’t think this is quite accurate. The full sentence is “Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions.” The “can” indicates that arguments using concrete referents are acceptable, not that they are required. And the “such as” indicates that objects, drawings, diagrams and actions are examples of possible concrete referents; not a list of requirements.

By the way, over the last few years there have been articles discrediting the whole theory of learning styles, e.g., this 2010 one in the New York Times.

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