Defining Mathematical Reasoning

Project Description


To explore and operationally define types of mathematical reasoning present in elementary students.

Project Description

This project is to examine mathematical reasoning in elementary students in order to operationally define types of reasoning. For the last two years our team has worked to better understand the reasoning of elementary students in mathematics. Our primary focus has been on students in grades 3-6. Two primary studies have been conducted to meet this objective. Study 1 consisted of two phases and used a sample of students performing below the 35th percentile (N = 105) and Study 2 consisted of students in the general education population (= 418).

Study 1 used two separate analyses to examine types of reasoning that emerged based on student responses (N = 1,928) to a psychometrically validated measure of mathematical reasoning for Whole Number and Fraction items. In the first phase of Study 1 a cluster analysis was performed on 36 categories of student strategies, and the data dispersed into three clusters. Based on these results and a review of the literature on reasoning, the research team created a set of operational definitions encompassing three types of reasoning: (1) faulty reasoning, (2) algorithmic reasoning, and (3) plausible reasoning.

Study 2 was conducted to examine the reasoning of a larger, more diverse population. We replicated the cluster analysis performed in Study 1 conducted on the 36 reasoning strategies to determine the findings from Study 2 were comparable. Findings from this study were promising for our proposed categories and provide initial evidence in the development process of an evaluation tool for assessing students’ mathematical reasoning intended for research and practical application.

Research Team

  • Lindy Crawford
  • Jacqueline Huscroft-D’Angelo

Graduate Student Researchers

  • Hannah Alvis
  • Madeline Cranford
  • Pei Pei Gong
  • Shelley Shirley
  • Shayla Sigler

Research Team


Mathematics E-Text Research Center

The Mathematics eText Research Center (MeTRC) is located at the University of Oregon. Currently, under the leadership of Dr. Mark Horney and Dr. Lynne Anderson-Inman of the University of Oregon's Center for Advanced Technology in Education (CATE), the center is in the process of conducting a systematic program of research that has spanned over five years in collaboration with five teams across the country, each focusing on a specific student population, curriculum, or technology.