Generalizing is a critical aspect of mathematics learning, with researchers and policy documents highlighting generalizing as a core mathematical practice. It can also be challenging to foster in class settings, and teachers need access to better resources to teach generalizing, including an understanding of effective forms of instruction. This…

Inquiry-based mathematics education (IBME) includes features such as: (a) Using tasks with authentic problem contexts, (b) building on students' everyday resources, (c) relying on small-group and whole-class discussions, and (d) establishing certain norms of participation for the inquiry classroom community (Laursen & Rasmussen, 2019). Prior…

Inquiry-based mathematics education (IBME) includes features such as: (a) Using tasks with authentic problem contexts, (b) building on students' everyday resources, (c) relying on small-group and whole-class discussions, and (d) establishing certain norms of participation for the inquiry classroom community (Laursen & Rasmussen, 2019). Prior…

Well-designed online educational games can improve students' math knowledge, skills and engagement; however, more research is needed to understand how to formatively assess components of students' mathematical understanding and learning as students solve problems in online educational games. In this study, we examined how 7th-grade students' (N =…

School closures during the COVID-19 pandemic have resulted in substantial learning gaps in students' mathematical abilities. The problem was self-enrollment against teacher recommendation among Honors Algebra 2 students in 9th, 10th, and 11th grade students at a local high school. The purpose of the quantitative, quasi-experimental study was to…

Secondary course assignment substantially determines a teacher's day-to-day work life, incentivizing them to realize their personal desires, which prior work shows tend to be working with more advanced students. Teachers have varying abilities to enact these desires, potentially due to their political capital, which is largely influenced by…

This research delves into the attitudes, perceptions, and motivations of student-athletes enrolled in Intermediate Algebra courses. It focuses on the distinct challenges they encounter in juggling academic and athletic responsibilities at a southeastern university in the United States. Employing a mixed-methods approach, the study gathered…

The purpose of the present article is to investigate the definition of matrix multiplication as a central issue in linear algebra courses. Applying both historical and pedagogical approaches, it focuses on the philosophy of generating the usual matrix multiplication, as a special binary operation, with its partly unexpected form compared with the…

We propose some generalizations of the classical Division Algorithm for polynomials over coefficient rings (possibly non-commutative). These results provide a generalization of the Remainder Theorem that allows calculating the remainder without using the long division method, even if the divisor has degree greater than one. As a consequence we…

This report proposes a framework for describing student analogical reasoning activities in abstract algebra that moves beyond the traditional literature-based treatment of analogical mapping. The Analogical Reasoning in Mathematics (ARM) framework captures the activities that students engage in when anticipating, creating, and reasoning from…

George Spencer-Brown's Laws of Forms was first published in 1969. In the fifty years since its publication, it has influenced mathematicians, scientists, philosophers, and sociologists. Its influence on mathematics education has been negligible. In this paper, I present a brief introduction to the theory and its philosophical underpinnings. And I…

In this paper, we focus on two particularly problematic concepts in teaching mathematics: the complex unit i and angles. These concepts are naturally linked via De Moivre's theorem but are independently misused in numerous contexts. We present definitions, notations, and ways of speaking about these terms from mathematics education that are not…

The study aimed to determine the mistakes of students in operations with algebraic expressions, and their misconceptions that may lead to errors. The study adopted case study method, one of the qualitative research models. The participants were composed of 48 (24 boys, 24 girls) randomly selected among 8th grade students in three different classes…

Many mathematics teachers and students are familiar with the typical "box problem." In this type of problem, one takes a rectangular (or a square) sheet of paper and cuts out four squares from the four corners of the sheet and then folds the four strips up to form a box. Math problems like this are seen in middle school, high school,…

This work aims at investigating the educational potentialities of mathematical memes, digital objects belonging to students' out-of-school culture, in combination with classic educational objects as GeoGebra applets. To pursue our goal, we observed a group of 29 12th-grade students who design, create and interact with mathematical memes and…