Learning by Analogy in Mathematics
Analogies between old and new concepts are common during classroom instruction. While previous studies of transfer focus on how features of initial learning guide later transfer to new problem solving, less is known about how to best support analogical transfer from previous learning while children are engaged in new learning episodes. Such research may have important implications for teaching and learning in mathematics, which often includes analogies between old and new information. Some existing research promotes supporting learners' explicit connections across old and new information within an analogy. In this talk, I will present evidence that instructors can invite implicit analogical reasoning through warm-up activities designed to activate relevant prior knowledge. Warm-up activities "close the transfer space" between old and new learning without additional direct instruction.
Categories, language, and visual working memory: how verbal labels change capacity limitations
The limited capacity of visual working memory constrains the quantity and quality of the information we can store in mind for ongoing processing. Research from our lab has demonstrated that verbal labeling/categorization of visual inputs increases its retention and fidelity in visual working memory. In this talk, I will outline the hypotheses that explain the interaction between visual and verbal inputs in working memory, leading to the boosts we observed. I will further show how manipulations of the categorical distinctiveness of the labels, the timing of their occurrence, to which item labels are applied, as well as their validity modulate the benefits one can draw from combining visual and verbal inputs to alleviate capacity limitations. Finally, I will discuss the implications of these results to our understanding of working memory and its interaction with prior knowledge.
Relational Reasoning in Curricular Knowledge Components
It is a truth universally acknowledged that relational reasoning is important for learning in Science, Technology, Engineering, and Mathematics (STEM) disciplines. However, much research on relational reasoning uses examples unrelated to STEM concepts (understandably, to control for prior knowledge in many cases). In this talk I will discuss how real STEM concepts can be profitably used in relational reasoning research, using fraction concepts in mathematics as an example.