A Conceptual Blend Analysis of Physics Quantitative Literacy Reasoning Inventory Items

TL;DR

This paper uses Conceptual Blending Theory to analyze physics reasoning items, aiming to improve assessment of students' flexible mathematical reasoning in physics contexts.

Contribution

It introduces a novel application of Conceptual Blending Theory to develop and validate physics reasoning assessment items that capture expert-like blended reasoning.

Findings

Analysis reveals hierarchical reasoning patterns

Potential to track reasoning development over physics courses

Supports creation of more nuanced assessment tools

Abstract

Mathematical reasoning flexibility across physics contexts is a desirable learning outcome of introductory physics, where the math world and physical world meet. Physics Quantitative Literacy (PQL) is a set of interconnected skills and habits of mind that support quantitative reasoning about the physical world. The Physics Inventory of Quantitative Literacy (PIQL), which we are currently refining and validating, assesses students proportional reasoning, covariational reasoning, and reasoning with signed quantities in physics contexts. In this paper, we apply a Conceptual Blending Theory analysis of two exemplar PIQL items to demonstrate how we are using this theory to help develop an instrument that represents the kind of blended reasoning that characterizes expertise in physics. A Conceptual Blending Theory analysis allows for assessment of hierarchical partially correct reasoning patterns, and thereby holds potential to map the emergence of mathematical reasoning flexibility throughout the introductory physics sequence.