Decomposing and Rehearsing Explanations of Algorithms in Mathematics

The major activities carried out during the grant period included (1) developing a psychometric instrument for measuring preservice elementary teachers’ knowledge and beliefs for teaching multidigit subtraction, (2) designing an interactive online environment for authoring storyboard explanations and to facilitate learning to use concrete materials to support explanations, (3) a descriptive interview study of preservice teachers learning during their methods class, and (4) an experimental study of an intervention that used the online authoring tool and included outcome data from the psychometric instrument.

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Harnessing human perception and gesture to develop sharable expertise in algebra

Our IUCRG project will recruit undergraduate education majors to experimentally test whether kinesthetic perceptual learning improves integration with conceptual knowledge and enhances the communicability of resulting perceptual expertise relative to non-kinesthetic perceptual learning. Data will include standard measures of perceptual and conceptual learning and novel measures of shareable expertise, such as gesture frequency and elementary student learning in response to undergraduate explanations. This pilot is the first step towards understanding how means of gaining perceptual expertise influence the ability to share it.

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