Precalculus and single-variable calculus courses are a critical early juncture for the success of science, technology, engineering, and mathematics (STEM) students in the United States (US). The default course structure is often a required three-term sequence of precalculus, differential calculus, and integral calculus. In this paper we analyse…

Argumentation activities, such as constructing and communicating claims, critiquing others' ideas, and evaluating the strengths and weaknesses of claims, can play a foundational role in students' educational development. Yet there is more to understand about utilising these activities for effective mathematics learning. This paper discusses an…

Previous studies indicated that calculus courses are considered 'weed-out' courses as a lot of students in STEM majors struggle to pass. Instructors and researchers explored various instructional methods to facilitate calculus learning, however, more tailored instructional strategies are still needed. Inventing Contrasting Case is a strategy that…

This study investigated the effectiveness of using a sequence of worked examples as part of the feedback cycle. Worked examples were either presented as full worked examples or partial worked examples (single-step and completion formats). In two experiments, grade 8 students completed a learning phase on a mathematics topic, which was immediately…

This article begins by describing a class scenario in which a teacher gives her students the L problem (Watanabe 2008), which involves finding the area of a composite figure. Her students inappropriately extend the area formula for rectangles (A = L x W) to composite figures by multiplying all given dimensions. After class, the teacher concluded…

Understanding how struggling students approach math is vital to designing effective math lessons. Many low achieving students rely on a weak knowledge of procedures and attempt calculations without adequate consideration of the problem. We investigated how enabling or preventing premature calculations affected learning math. Students were…

Ginsburg (1977) observed that children typically develop surprisingly powerful informal (everyday) knowledge of mathematics and that mathematical learning difficulties often arise when formal instruction does not build on this existing knowledge. By using meaningful analogies teachers can help connect new formal instruction to students' existing…

We present a question bank consisting of over 250 multiple-choice and true--false questions covering a broad range of material typically taught in an introductory undergraduate course in numerical analysis or computational science. The questions are ideal for polling students during lectures by means of a student response system that uses…

Using data from 23 statistics instructors and 1,924 students across 11 post-secondary institutions in the United States, we employ multilevel covariate adjustment models to quantify the sizes of instructor and instructional effects on students' statistics attitudes. The analysis suggests that changes in students' statistics attitudes vary…

Although visual representations are generally beneficial for learners, past research also suggests that often only a subset of learners benefits from visual representations. In this work, we designed and evaluated anticipatory diagrammatic self- explanation, a novel form of instructional scaffolding in which visual representations are used to…

High school students often ask questions about the nature of infinity. When contemplating what the "largest number" is, or discussing the speed of light, students bring their own ideas about infinity and asymptotes into the conversation. These are popular ideas, but formal ideas about the nature of mathematical sets, or "set…

Students' ability to reason for themselves is a crucial step in developing conceptual understandings of mathematics, especially if those students are preservice teachers. Even if classroom environments are structured to promote students' reasoning and sense-making, students may rely on prior procedural knowledge to justify their mathematical…

Analogies between old and new concepts are common during classroom instruction. Previous transfer studies focused on how features of initial learning guide later, spontaneous transfer to new problem solving. We argue for a shift in the focus of analogical-transfer research toward understanding how to best support analogical transfer from previous…

Research Findings: This study investigated teachers' Concept development (CD) strategy use in whole-group math teaching and its associations with children's higher-order thinking processes in 25 Chinese preschool math lessons. We utilized the CD dimension within the Classroom Assessment Scoring System (CLASS) to guide our exploration. CD…

The quality of curriculum resources and teaching practices can constrain or promote students' opportunities for mathematics learning, in particular, students with diverse language proficiency. The video study investigates 18 classes that all used the same curriculum resources aimed at developing 367 seventh graders' conceptual understanding of…