This exploratory study reports on characteristics of proof production and proof writing observed in the work of first-year university students who took part in workshops on the theorem prover LEAN (https://leanprover.github.io). These workshops were voluntary and offered alongside a transition to proof module in a UK university. Through…

In this article, the authors share frameworks for problem types and students' reasoning about integers. The authors found that all ways of reasoning (WoRs) were used across grade levels and that specific problem types tended to evoke particular WoRs. Specifically, students were more likely to use analogy-based reasoning on all-negatives problems…

This study was conducted to examine whether newly enrolled 9th grade students were ready to directly engage in the theoretical discursive process from the perspective of Duval's Cognitive Model. The sample of the study was comprised of 51 newly enrolled 9th grade students between the ages of 14 and 15, who had not received any prior geometry…

This study explores Saudi students' perceptions of their motivation to learn Mathematics using metacognitive strategies. Data were collected using a qualitative case study design among 13 Saudi secondary school students. The findings from the data collected through semi-structured interviews show that several motives encourage the participants to…

This research focuses on ways in which balance scales mediate students' relational understandings of the equal sign. Participants included 21 Kindergarten-Grade 2 students who took part in an early algebra classroom intervention focused in part on developing a relational understanding of the equal sign through the use of balance scales. Students…

We introduce a ruler and compass activity designed around Islamic Geometry and provide a detailed description of the various components of the activity along with ideas for students exhibitions in both digital and print form. In our experience, this activity helps students to "buy into" actively doing mathematics, making it an ideal…

Objective: In numerous calls for reform to community college math instruction, contextualization has been identified as an effective approach to teaching and learning. Yet, little is known about how faculty contend with math contextualization and how they make decisions about its adoption. This study explored how community college faculty teaching…

This qualitative research study sought to help community colleges aid math faculty in making a transformation in their teaching practices. The research questions were: (a) What did it take for faculty to change their teaching style from traditional lecture-based instruction to one that incorporates low-stakes collaborative practice, just-in-time…

As identity becomes more discussed within education, it becomes crucial to understand identity in relation to power and social justice. In this paper, we discuss the identity frameworks of figured worlds and rightful presence to operationalize the critical consideration of identity within mathematics learning environments. We argue that by…

Productive use of student mathematical thinking is a critical aspect of effective teaching that is not yet fully understood. We have previously conceptualized the teaching practice of building on student mathematical thinking and the four elements that comprise it. In this paper we begin to unpack this complex practice by looking closely at its…

Covariational reasoning and the creation and interpretation of graphs of covariational situations are important skills in math and science. Unfortunately, research shows that students often struggle to make meaningful connections between graphs and the covariational situations they represent. Educational activities designed to help students…

Advances in technology are helping reshape how students learn, communicate, and interact in higher education; this change may assist universities as they address the developmental course crisis. This study sought to increase understanding of how computer-assisted instruction (CAI) impacted students' perception of their experience in a…

This article explores the effectiveness of the pedagogical practices associated with the cognitive load theory and the van Hiele theory, which are two theories from cognitivism and constructivism perspectives, respectively. Following a quasi-experiment, the quantitative analysis of 157 high school students' responses to pre, post, and retention…

This paper draws on numerous data sources to better understand the shift from additive to multiplicative thinking in years 4 to 9. Research studies that have used the Scaffolding Numeracy in the Middle Years assessment tasks have found that while students can be supported to move through the early and upper zones of the Learning and Assessment…

Supporting students of all levels to move beyond empirical arguments, which employ example based reasoning to endorse universal truths and are thus mathematically invalid, remains a challenging goal in mathematics education. Arguments that make use of generic examples are both mathematically valid and accessible for even young learners. However,…