Growth in two subscales, Informal and Formal Mathematics Skills, of the "Test of Early Mathematics Abilitity-3" (TEMA-3) was explored in a sample of 281 children. Children were identified as either typically developing (TYP; n = 205) or having mathematics difficulties (MD; n = 76) based on their total TEMA-3 score at the end of…

This paper describes a research project implemented in a course of Real Analysis II. The aim of this project is to analyse students' comprehension of the limiting behaviour of a function from "R"[superscript 2] to "R" at a point "P"[subscript 0] focusing on the formal definitions. Alternative definitions and other…

We analyze the process of constructing a definition within the theoretical framework of "Abstraction in Context." Pairs of students were engaged in a task designed to engender a need for a definition of a tangent to a graph at a given point, and lead to constructing a definition following that need. The results of our analysis point to…

Tensions are an integral part of mathematics teachers' practice and have been recognised as playing a pivotal role in guiding teachers' choices, and in driving teacher change. Professional development particularly elicits dilemmas. Tensions appear to be a crucial aspect of mathematics teacher education and therefore a deeper understanding of…

Although there is extensive research on attrition in gatekeeper courses and students' cognition about calculus concepts, there is one population in introductory calculus that remains understudied: those who failed their initial course and chose to repeat it rather than change majors. These students can provide insight into overcoming poor…

Inside the discipline, mathematical work consists of the interplay between stating and refining conjectures and attempting to prove those conjectures. However, the mathematical practices of conjecturing and proving are traditionally separated in high school geometry classrooms, despite some research showing that students can successfully navigate…

Students studying statistics often misunderstand what statistics represent. Some of the most well-known misunderstandings of statistics revolve around null hypothesis significance testing. One pervasive misunderstanding is that the calculated p-value represents the probability that the null hypothesis is true, and that if p < 0.05, there is…

We describe the use of student-generated video content to assess students' engagement with, and understanding of, problem-solving skills. In this framework, students are tasked with using technology to create videos that show them working through, and explaining solutions to, challenging calculus exercises. The videos are then posted online,…

At the college level, it can be difficult to engage students outside the classroom through the use of effective homework assignments. Although it is straightforward to create assignments that test the ability to carry out computations as discussed in class, it is more challenging to create assignments that encourage students to think more…

The fundamental theorem of calculus (FTC) plays a crucial role in mathematics, showing that the seemingly unconnected topics of differentiation and integration are intimately related. Indeed, it is the fundamental theorem that enables definite integrals to be evaluated exactly in many cases that would otherwise be intractable. Students commonly…

How students' rigid perceptions of mathematics persist over years has been a conundrum. Students not only think that only one solution exists for a mathematical task (Schoenfeld 1985) but also rigidly fuse mathematical concepts with specific tasks. Students deserve to learn a variety of mathematical strategies to flexibly deploy at will. Teaching…

"Wheel spinning" is the phenomenon in which a student fails to master a Knowledge Component (KC), despite significant practice. Ideally, an intelligent tutoring system would detect this phenomenon early, so that the system or a teacher could try alternative instructional strategies. Prior work has put forward several criteria for wheel…

The motivation behind this examination is to present the theoretical structure of Modeling Activities, which is believed to be a vital device for mathematics instruction. Modeling activities are defined as activities to figure out complex problems faced in real life situations that require the creation of a mathematical model as a product. In…

Experienced teachers, researchers and mathematics community members, contributed to the documentation of the professional vocabulary of teachers to describe the pedagogical practice of the middle school mathematics classroom. In this paper we use this Australian Lexicon to study which terms teachers deem essential for their classroom practice. We…

Quantifying angularity is critical for the study of K-12 school mathematics and beyond; yet, quantifying angularity is challenging for individuals across these grade levels. Using data from a yearlong teaching experiment with ninth-grade students, I address the role of attentional motion in quantifying angularity and present four such motions…