# Transition Matrices: A Tool to Assess Student Learning and Improve Instruction

## TL;DR

This paper presents a spreadsheet tool using transition matrices to analyze student answer patterns in assessments, offering deeper insights into learning progress and instructional effectiveness beyond traditional scoring methods.

## Contribution

It introduces a novel, easy-to-use spreadsheet method for analyzing pre- and post-test data with transition matrices to better understand student learning.

## Key findings

- Transition matrices reveal detailed student answer transitions.
- The tool helps identify effective teaching strategies.
- Deeper insights than traditional dichotomous scoring.

## Abstract

This paper introduces a new spreadsheet tool for adoption by high school or college level physics teachers who use common assessments in a pre-instruction/post-instruction mode to diagnose student learning and teaching effectiveness. The spreadsheet creates a simple matrix that identifies the percentage of students who select each possible pre-/post-test answer combination on each question of the diagnostic exam. Leveraging analysis of the quality of the incorrect answer choices, one can order the answer choices from worst to best (i.e., correct), resulting in "transition matrices" that can provide deeper insight into student learning and the success or failure of the pedagogical approach than traditional analyses that employ dichotomous scoring.