While multiple theories exist to explain the diagnostic process, there are few available assessments that reliably determine diagnostic competence in trainees. Most methods focus on aspects of the process of diagnostic reasoning, such as the relation between case features and diagnostic hypotheses. Inevitably, detailed elucidation of aspects of…

Despite the increasing amount of research on students' quantitative reasoning at the secondary level, research on students' quantitative reasoning at the undergraduate level is scarce. The present study used task-based interviews to examine 16 high-performing undergraduate calculus students' quantitative reasoning in the context of solving three…

Children and adults appreciate that physical action is typically the conduit between individuals' desires and the fulfillment of those desires. However, certain forms of petitionary thought -- e.g., wishing and praying -- are believed by many people to influence the external world and fulfill desires without direct physical action. We examine…

This report proposes a framework for describing student analogical reasoning activities in abstract algebra that moves beyond the traditional literature-based treatment of analogical mapping. The Analogical Reasoning in Mathematics (ARM) framework captures the activities that students engage in when anticipating, creating, and reasoning from…

This chapter illustrates the main warning signals that could help us to detect the flaws of an explanation in physics: internal contradiction (two examples); direct contradiction of a law of physics (one example); indirect contradiction of a law of physics (one example); logical incompleteness of an explanation (three examples); overgeneralization…

The mathematics classroom is particularly vulnerable to these judgments of perfectionism, with endless evidence of students and teachers believing that mathematics is based on an ultimate truth or a single, objective, unique answer. School mathematics still favors students' participation in rote procedures, memorization, and using only a few…

Out-of-school time (OST) science, technology, engineering, and math (STEM) programs have gained recognition for their potential to enhance youth engagement, motivation, and skills by addressing young people's needs for autonomy, competence, and connection (Faust & Kuperminc, 2020; Hoffman et al., 2021; Mulvey et al., 2023; Yu et al., 2022; Yu…

This study examined age-related differences in the effectiveness of two generative learning strategies (GLSs). Twenty-five children aged 9-11 and 25 university students aged 17-29 performed a facts learning task in which they had to generate either a prediction or an example before seeing the correct result. We found a significant Age × Learning…

Collaborative argumentation in education, where students work together to construct and critique arguments, is an important social practice in many disciplines and can also develop conceptual understanding. This article addresses the evolution of my research agenda on collaborative argumentation from just scaffolding the generation of…

Analogies are useful pedagogical tools to introduce new and difficult concepts to students by building connections to familiar things from our daily life. Research has shown that applying analogies during the learning process facilitates the development of higher order thinking. In this article, we present a number of analogies that have been…

Exploratory data analysis (EDA) is an iterative, open-ended data analysis procedure that allows practitioners to examine data without pre-conceived notions to advise improvement processes and make informed decisions. Education is a data-rich field that is primed for a transition into a deeper, more purposeful use of data. This article introduces…

Although geometric transformations are functions, few studies have examined students' reasoning about these two important concepts. The purpose of this study was to examine the various ways students reasoned about functions in the context of pre-constructed, dynamic sketches of geometric transformations. We found that, regardless of prior…

This study examines through action research whether blended instruction in an upper-level philosophy course in introductory symbolic logic can help undergraduate philosophy students to achieve better learning outcomes than undergraduate philosophy students in a traditional, face-to-face version of the same course. The authors conclude that the…

Comparison is a powerful and important way that we learn. To support teachers in the use of comparison in their instruction, the authors developed an instructional routine called compare and discuss multiple strategies (CDMS). Similar to other instructional routines, CDMS is a structured, specific, repeatable minilesson that teachers can use to…

The capacity to reason critically and negotiate ideas and differences lies at the heart of quality education. Through critical reasoning we construct, organise, and justify knowledge; and we create new ideas and practices. Despite the emphasis on teaching argumentative writing in school curricula, existing research consistently shows that arguing…