Research about the optimal methodologies for guiding the training of primary school instructors in the instruction of early algebra remains in the process of determination. This manuscript delineates the methodology involved in developing and validating an assessment tool to evaluate the mathematical acumen of prospective primary educators in the…

Because the failure rate for college algebra is large and sometimes up to 50%, college algebra serves as a gatekeeper to STEM fields and degree completion. Therefore, it is critical to examine students who are at risk of dropping, withdrawing, and failing college algebra help-seeking behavior. The purpose of this mixed methods study was to focus…

Online collaborative learning (OCL) based on the community of inquiry (CoI) framework is often implemented in the form of an online discussion activity for teaching subjects that require learners to revise their understandings and invent ways to solve problems. However, implementing OCL is challenging due to the difficulty of fostering…

Background: Students take many tests and exams during their school career, but they usually receive feedback about their test performance based only on an analysis of the item responses. With the increase in digital assessment, other data have become available for analysis as well, such as log data of student actions in online assessment…

As they progress to more abstract and complex levels of mathematics, students with learning disabilities (and other students who are struggling with mathematics) can face challenges related to memory and cognition, as well as potential difficulties with math anxiety. For example, quadratic functions can present several challenges for many…

Purpose: It is crucial for teachers to understand what students already know and what they are thinking, before conducting their lessons, because identification of the cause is the first step of remedy. This study analyses students' conceptions that underlie the errors they make in algebraic expressions under two categories of conceptual…

The Klein bottle and hairy ball theorem are important concepts in advanced mathematics and they are both examples of the Poincaré-Hopf theorem. Complex theories such as these usually remain unrealized in the minds of mathematicians. In this collaborative work between a mathematician and a designer, we introduce the concept of the hairy Klein…

Preservice mathematics teachers are subject to multiple influences when they make in-the-moment instructional decisions in classroom settings. Little is known about which influences make a significant contribution to decisions regarding the mathematical content knowledge (MCK) that preservice teachers decide to enact. The process by which…

This study examined how algebra teachers plan curriculum units when they actively design their curriculum. I used a case study (Yin, 2013) of five experienced high school mathematics teachers who came from school districts of varying sizes across the nation. More specifically, I analyzed the teachers' unit planning processes and products by…

This study reports on a professional learning (PL) initiative aimed at establishing a community of practice, through teacher working groups in which teachers can explore and develop their algebraic pedagogical content knowledge (PCK). Here we report on teachers' solutions to three differently represented algebraic problems and explore what the…

Many mathematics education researchers agree that students struggle to understand the key concepts in linear algebra courses. The purpose of this study was to examine in-service teachers' errors and misconceptions in the area of linear combinations. The participants were 73 Zimbabwean mathematics teachers who were enrolled in an in-service…

This paper explores Year 3 Irish students' problem-solving strategies when responding to a skyscraper growing pattern problem. Students' strategies reveal their understandings of multiplicative thinking, pattern, and algebraic reasoning. The version of the growing pattern lesson was that a 'teaching through problem solving' approach was taken,…

Several studies related to mathematics understanding found that many undergraduate students lack some basic knowledge of algebra. They memorized only a few topics, formulas, and algorithms without understanding them conceptually, even though they could manipulate those limited number of points correctly or incorrectly. In comparison, most…

Relational thinking and dealing with variables are two essential aspects of algebraic thinking. Relational thinking means viewing mathematical expressions and equations as a whole rather than as individual computing processes. It is characterized by using relationships between mathematical objects, and refers to the relations of equality and…

A substantial body of research has documented that the types of knowledge that mathematics teachers draw upon during their practice often differs from the knowledge of individuals working in other fields. Drawing on the Mathematical Knowledge for Teaching (MKT) Framework and the School Mathematics Teaching Pedagogical Content Knowledge (SMTPCK)…