Use of three-force member concept for rigid bodies whenever possible, to circumvent the more taxing use of equilibrium equations has been long-established. However, most students fail to reap its benefits due to a number of reasons, including the fact that its importance is hardly emphasized to them; skills and details needed for the concept are…

The Department of Mathematics and Computer Science at Adelphi University engaged in a year-long program revision of its mathematics major, which was initiated by a longitudinal study and the publication of the 2015 Curriculum Guide by the MAA's Committee on Undergraduate Programs in Mathematics. This paper stands as a short story, so to speak, of…

This article chronicles the author's positive experience of conducting a liberal arts mathematics course with no testing whatsoever. The format of the course is discussed, and student responses to the format are summarized.

Productive failure has shown positive effects on conceptual and transfer measures, but no clear effects on procedural measures. It is therefore an open question whether, and to what extent, productive failure methods may be used to enhance the learning of procedural skills. A typical productive failure study focuses on a single, complex concept;…

Common divisor is one of the concepts that started to be learned in secondary school and forms the basis of many concepts. But students generally have difficulty in making sense of it. The purpose of this study is to investigate concept formation processes of common divisor through a case study on seven sixth grade students. To do this, we…

Making meaning with math in physics requires blending physical conceptual knowledge with mathematical symbology. Students in introductory physics classes often struggle with this, but it is an essential component of learning how to think with math. Teaching the dimensionality of measured quantities and dimensional analysis (DA) is a valuable first…

The appropriateness of guess and check as a problem-solving strategy has been debated. This qualitative study examines the use of guess and check by middle-grades students to solve linear systems of equations. Students' reasoning is examined within the number sequences framework, which is based in part on students' units coordination. Only…

Research on elementary students' reasoning on patterning problems with pictorial representations has illustrated that students can visualize structure in patterns in different ways. In this paper, we offer a characterization of students' spatial structures and numerical structures and explain how the link between these two structures can support…

This research shares progressions in thinking about equations and the equal sign observed in ten students who took part in an early algebra classroom intervention across Kindergarten and first grade. We report on data from task-based interviews conducted prior to the intervention and at the conclusion of each school year that elicited students'…

This paper reports on one aspect of a bigger project: teachers' design of instructional materials. We found a number of design moves used by the teachers in our study. In this paper, we report three of them: Making things explicit, making connections, and resequencing practice examples. [This paper is the fourth in a symposium of four papers. For…

This paper investigates two specific probabilistic biases which middle graders usually exhibit when reasoning about probability and randomness on assessment items. We discuss how students' reasoning about key probability concepts undergirds statistics literacy related to randomness, independence, and the likelihood of future events based on past…

Research has shown the majority of students who have completed a university calculus course reason about the definite integral primarily in terms of prototypical imagery or in purely algorithmic and non-quantitative ways. This dissertation draws on the framework of Emergent Quantitative Models to identify how calculus students might develop a…

This research addressed increasing understanding of how players make meaning during play of a complex STEM game and explores to what extent player mental models of STEM concepts shift as a result of interacting with the game simulation. Game based learning is attracting increased attention and interest as a novel platform for experiential…

Abstract algebra has been identified as an important course for preservice secondary mathematics teachers because much of the abstract algebra content is connected to, and thus relevant for, secondary mathematics teaching (Wasserman et al., 2017). However, many preservice teachers do not recognize the usefulness of an undergraduate abstract…

In this study, the evaluation of mathematical proficiency (MP) in one NSW Year 12 standardised exam paper was investigated. By considering the multi-strand model of MP, a literature-based criteria for scoring the assessment of MP in individual exam questions was first developed. The criteria were then applied to quantitatively evaluate the 2023…