February 11, 2024

# Learning and reasoning with mathematical symbols: Connecting contextual mathematical thought to abstract, symbolic mathematical operations

Principal Investigator:

Jeffrey Bye, Ph.D.

Department of Psychology

jkgye@ucla.edu

Participants: Rooms 4, 5 & 6 – Students ages 10-12

Keywords: Purpose Driven Progressive Formaliztion (P-PF), interactive multi-media videos for algebraic learning

The concept of an *algebraic variable* is both important in its own right and foundational for higher levels of mathematics, but many students struggle to understand the *meaning* and *purpose* of a variable. Common math education practices often fail to support students in making meaningful insights about the interpretation of a variable, its mathematical purpose, or its relevance in solving real-world problems. Such conceptual impoverishment prevents these students from appreciating algebra and from building on its concepts in more advanced math. This project seeks to assess new educational materials, in the form of online multimedia videos, that encourage and support students’ discovery of the meaning and purpose of a variable, guided by principles from educational psychology and the cognitive psychology of learning.

The concept of an *algebraic variable* is both important in its own right and foundational for higher levels of mathematics, but many students struggle to understand the *meaning* and *purpose* of a variable. Common math education practices often fail to support students in making meaningful insights about the interpretation of a variable, its mathematical purpose, or its relevance in solving real-world problems. Such conceptual impoverishment prevents these students from appreciating algebra and from building on its concepts in more advanced math. This project seeks to assess new educational materials, in the form of online multimedia videos, that encourage and support students’ discovery of the meaning and purpose of a variable, guided by principles from educational psychology and the cognitive psychology of learning.