Analogies in the  Classroom


With funding from the National Science Foundation’s CAREER program, the Learning Lab has embarked on a 5 year study to explore how students draw connections between concepts and compare representations in a live classroom context. Our research seeks to identify specific teaching practices such as making student responses and key ideas visible, visually organizing lesson to highlight comparisons, and using gestures between connected student responses, that help students scaffold comparative thinking and increase conceptual understanding in mathematics.

Recent Studies:

In a recent study, students watched a rate and ratio lesson that had been edited to manipulate the amount of visual support the student received in the lesson.

We found that students who viewed the “Part Visible” lesson demonstrated lower procedural understanding and flexibility than did students who viewed the “All Visible” or “Not Visible” conditions. Additionally, students who viewed “Part Visible” were less likely to use the most efficient strategy to solve problems, and more likely than either the “All Visible” or Not Visible” to routinely use incorrect solution strategies.

Classroom implications:

This finding has important implications for the way we think about classroom instruction.  It indicates that when a teacher writes only the most recent solution strategy on the board-- a very common practice in US classrooms-- his/her students will be less likely to make effective comparisons that yield a deep understanding of the content. In fact, this study shows that students who see only the most recent problem on the board are actually worse off than students who see none of the board and rely only on the verbal lesson.


Richland, L.E., Bengoli, K. (anticipated publication Spring 2013) Learning to make mathematical connections.

Research Funded By :

The National Science Foundation and the Office of Naval Research


Learning to Make Conceptual Connections: Analogical Reasoning in Classroom Mathematics

All Visible- High Support

Edited so that all solution strategies are visible

Part Visible- Some Support

Edited so that only the most recent solution strategy is visible

  1. Not Visible- Low Support

  2. Edited so that no solution strategies are visible