Mathematics Learning
mathematics learning
Comparing Multiple Strategies to Improve Mathematics Learning and Teaching
Comparison is a powerful learning process that improves learning in many domains. For over 10 years, my colleagues and I have researched how we can use comparison to support better learning of school mathematics within classroom settings. In 5 short-term experimental, classroom-based studies, we evaluated comparison of solution methods for supporting mathematics knowledge and tested whether prior knowledge impacted effectiveness. We next developed supplemental Algebra I curriculum and professional development for teachers to integrate Comparison and Explanation of Multiple Strategies (CEMS) in their classrooms and tested the promise of the approach when implemented by teachers in two studies. Benefits and challenges emerged in these studies. I will conclude with evidence-based guidelines for effectively supporting comparison and explanation in the classroom. Overall, this program of research illustrates how cognitive science research can guide the design of effective educational materials as well as challenges that occur when bridging from cognitive science research to classroom instruction.
Analogies, Games and the Learning of Mathematics
Research on analogical processing and reasoning has provided strong evidence that the use of adequate educational analogies has strong and positive effects on the learning of mathematics. In this talk I will show some experimental results suggesting that analogies based on spatial representations might be particularly effective to improve mathematics learning. Since fostering mathematics learning also involves addressing psychosocial factors such as the development of mathematical anxiety, providing social incentives to learn, and fostering engagement and motivation, I will argue that one area to explore with great potential to improve math learning is applying analogical research in the development of learning games aimed to improve math learning. Finally, I will show some early prototypes of an educational project devoted to developing games designed to foster the learning of early mathematics in kindergarten children.
Abstraction and Analogy in Natural and Artificial Intelligence
Learning by analogy is a powerful tool children’s developmental repertoire, as well as in educational contexts such as mathematics, where the key knowledge base involves building flexible schemas. However, noticing and learning from analogies develops over time and is cognitively resource intensive. I review studies that provide insight into the relationship between mechanisms driving children’s developing analogy skills, highlighting environmental inputs (parent talk and prior experiences priming attention to relations) and neuro-cognitive factors (Executive Functions and brain injury). I then note implications for mathematics learning, reviewing experimental findings that show analogy can improve learning, but also that both individual differences in EFs and environmental factors that reduce available EFs such as performance pressure can predict student learning.