In this paper, we examine the relationships between teachers' subject matter preparation and experience in teaching and their performance on an instrument measuring mathematical knowledge for teaching Algebra 1. We administered the same instrument to two different samples of teachers-high school practicing teachers and community college…

Understanding how young learners come to construct viable mathematical arguments about general claims is a critical objective in early algebra research. The qualitative study reported here characterizes empirically developed progressions in Grades K-1 students' thinking about parity arguments for sums of evens and odds, as well as underlying…

This qualitative research study explores how students negotiate their identities as mathematics learners in a college algebra quadratics unit that implements asset-based frameworks that reframe mathematics curriculum to support student awareness of their capacities. This study adds to existing research discourse on teaching and learning…

This large-scale study characterizes the algebraic learning of a cohort of nearly 800 French students during the last year of middle school (9th grade, 14-15 years old) and examines their evolution in relation to the composition of the classes to which the students belong. Based on the Anthropological Theory of the Didactic (ATD), the study is…

This study contributes to the literature on linear algebra instruction by designing and researching a teaching sequence based on APOS Theory to introduce engineering students to vector spaces. The sequence offers students multiple opportunities to understand the concept. Another contribution is the evidence that introducing prerequisite…

This quantitative study examines how support facilitation instruction affects high school students without disabilities end-of-course assessment scores and Algebra l-B grades using descriptive statistics, t-test two-sample assuming equal variances, F-test two-sample for variances, and Pearson correlation coefficient (r) analysis. The two-sample…

This paper is part of broader research being conducted in the area of algebraic thinking in primary education. Our general research objective was to identify and describe generalization of a 2nd grade student (aged 7-8). Specifically, we focused on the transition from arithmetic to algebraic generalization. The notion of structure and its…

To be successful in algebra, students need access to high-quality instruction that includes opportunities to develop their algebraic understanding. Yet research on algebra teaching suggests that instruction remains procedurally focused, indicating that teachers may need additional support to provide students such opportunities. One possible lever…

Despite the growing popularity of both flipped classrooms and digital manipulatives, there is a need for empirical research to examine the impact of combining these instructional strategies in the context of an Algebra 1 course (Alsaeed, 2017; Brown et al., 2001). This study is grounded in Kolb's learning cycle, the Technological Pedagogical…

In agreement with the main tenets of the anthropological theory of the didactic (ATD), this study uncovers dependencies between what students can learn, the established curriculum and the current state of mathematicians' mathematics ('scholarly mathematics'). One main result is that the mathematics taught, too often taken for granted by curriculum…

Mathematics continues to be one of the most significant barriers to student success, particularly in the community college sector. Many students are placed into the algebra-based track, which is often viewed as the "safe" or most desirable option, when they likely would have been better served in an alternative mathematics pathway more…

The presented article is dedicated to a new way of teaching substitution in algebra. In order to effectively master the subject matter, it is necessary for students to perceive the equal sign equivalently, to learn to manipulate expressions as objects, and to perceive and use transformations based on defining their own equivalences. According to…

The design principles of cognitive load theory and learning by analogy has independently contributed to our understanding why an instruction will or will not work. In an experimental study involving 97 Year 9 Australian students conducted in regular classrooms, we evaluated the effect of the unguided problem-solving approach, worked examples…

Teachers choose to supplement their curriculum for various reasons (Drake, 2010) and use online resources to search for and choose these supplements for their curriculum (Silver, 2022). TeachersPayTeachers.com (TPT) is a popular choice for online curriculum resources. TPT is a virtual resource pool that allows teachers to create and share…

Topology is considered an advanced field in mathematics, and it might seem off-putting to people with no previous experience in mathematics. The classification theorem, which lies within the field of algebraic topology, is fascinating, but understanding it requires extensive mathematical knowledge. In this manuscript, we present a modular object…