The project we’re currently undertaking seeks to determine whether unit concepts, as measured by spatial, relational, and counting tasks are related to math outcomes in K-4th grade. Students are assessed with a specialized test battery that seeks to isolate variables related to place value concepts, conventional measurements skills, fractions, working memory, and performance on traditional calculation and arithmetic measures. We believe these tasks will help us gain insight into aspects of mathematics learning that have been difficult to isolate in previous academic literature. Evaluating this assessment’s relation to standardized mathematics assessment scores will allow us to identify latent skills utilized in fraction, measurement, and comparative spatial tasks. Ultimately data from this portion of the experiment will be used to generate a specialized curriculum for teaching unit concepts in a more universally-accessible manner.
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.