Using a mixed methods approach, we explore a relationship between students' graph reasoning and graph selection via a fully online assessment. Our population includes 673 students enrolled in college algebra, an introductory undergraduate mathematics course, across four U.S. postsecondary institutions. The assessment is accessible on computers,…

Students' evidence-based reasoning was examined across two studies. In Study 1, students were asked to evaluate newspaper excerpts including anecdotal, descriptive, correlational, and causal evidence provided in support of causal claims as well as to justify their quality ratings for two of these excerpts. In Study 2, students' justifications for…

Solving organic chemistry reactions requires reasoning with multiple concepts and data (i.e., multivariate reasoning). However, studies have reported that organic chemistry students typically demonstrate univariate reasoning. Case comparisons, where students compare two or more tasks, have been reported to support students' multivariate reasoning.…

This study aims at elaborating a well-established theoretical framework that distinguishes three modes of thinking in linear algebra: the analytic-arithmetic, the synthetic-geometric, and the analytic-structural mode. It describes and analyzes the bundle of signs produced by an engineering student during an interview, where she was asked to recall…

Since statistical inference is a probabilistic generalization about a population analyzed on the basis of a sample, inferential reasoning demands producing reasons ("statistical" and "contextual") to substantiate and validate generalizations. To convey an understanding of students' inferential reasoning, we present a…

Critical thinking is embedded in national university graduate outcomes and included in international bodies' statements on higher education. At the same time, there are tensions surrounding critical thinking in higher education, such as its commodification, Eurocentrism, and relationship to rapidly digitalising cultures. Drawing from the…

This article draws on the philosophical work on dialogic rationality offered by Charles Taylor as well as qualitative studies of dialogues between politically opposed college students to argue that these conversations succeed as tools of democracy precisely because they fail as interventions. That is, the democratic strength of such dialogue is…

The basis for mastering neurophysiology is understanding ion movement across cell membranes. The Electrochemical Gradients Assessment Device (EGAD) is a 17-item test assessing students' understanding of fundamental concepts of neurophysiology, e.g., electrochemical gradients and resistance, synaptic transmission, and stimulus strength. We…

Abstraction is essential to learning mathematics because the mathematical concepts obtained through abstraction will be more meaningful than directly receiving these concepts. This study aims to describe the pre-service teachers' abstraction in constructing relationships among quadrilaterals. This research method was explorative qualitative…

In order to learn more about student understanding of the structure of proofs, we generated a novel genre of tasks called "Proof Without Claim" (PWC). Our work can be viewed as an extension of Selden and Selden's (1995) construct of "proof framework"; while Selden and Selden discuss how the structure of a proof can be discerned…

An important consideration in the design and development of numeracy-focused coursework is ensuring that one meets students where they are with respect to both their mathematics background and their existing numeracy practices in relation to public issues. The latter consideration is especially important, given that students already think about…

The purpose of this proposed quantitative, ex post facto, comparative study with a pretest-posttest design was to assess gains in overall Critical Thinking (CT) skills, and particularly in the Hypothetical-deductive Reasoning (HDR) skills, for pre-health college students tested before and after a Critical Analyses in Science course they attended…

This article reports on a qualitative investigation into students' thinking about a differential equations problem posing task; i.e. an initial value problem. Analysis of written and verbal responses to the task indicate that only four of the 34 students who participated in the study were successful in posing problems. Furthermore, only one of the…

University students are often asked to learn abstract concepts. Abstract concepts are hard to learn. Giving specific examples can help learning abstract concepts. These examples might limit understanding to the similarities between the abstract domain and particular examples. The primary purpose of this study was to test whether exposure to…

Education researchers are deeply interested in understanding the way students organize their knowledge. Card sort tasks, which require students to group concepts, are one mechanism to infer a student's organizational strategy. However, the limited resolution of card sort tasks means they necessarily miss some of the nuance in a student's strategy.…