The current project we're undertaking attempts to operationalize and isolate an underlying/latent unit concepts structure. Unit concepts are related to how children think about units and measurement. We have designed or adapted several cognitive tasks involving concrete manipulatives that we believe align with unit concepts. Ultimately we will calculate a general model of unit concepts understanding using binomial regression to see whether it aligns with traditional mathematics outcomes. Results from this study will be used to inform a later intervention study which will investigate whether unit concepts are malleable.
Another of our goals is to help K-1 students master place value with some experimental instructional techniques. Some of these techniques are based on Montessori activities and other common place value exercises. What’s new is that we’re trying to help children see the underlying relational structure of place value symbols by comparing and mapping across different examples and representations (like from words to written symbols or from physical models to words). We think that if we scaffold these mappings in different ways, it will really help kids grasp place value at a deep level that will be beneficial when they start to learn operations like multi-digit calculation.