This paper reports on five secondary school mathematics prospective teachers' conceptions of "extreme point." The analysis of the data addressed students' definitions, examples, and evaluation of given examples, with special attention to the related domain. Written assignments and individual interviews uncover salient, erroneous concept…

The invention of problems is a fundamental competence that enhances the didactic-mathematical knowledge of mathematics teachers and therefore should be an objective in teacher training plans. In this paper, we revise different proposals for categorizing problem-creation activities and propose a theoretical model for problem posing that, based on…

Teaching that attends to and builds on students' resources and treats students as capable mathematical sense makers has been referred to as responsive teaching. A body of research reports teachers' tendency to overlook students' mathematical thinking when their answer is correct and to correct it procedurally when students make a mistake. This…

Understanding fractions, especially their magnitude, is essential for success in mathematics. Unfortunately, fractions are one of the most challenging mathematics concepts to teach and learn. Several studies have examined preservice teacher (PST) knowledge of fractions, but very few studies have looked for ways to improve this knowledge. This…

Mathematics traditionally has been taught in a way that reifies the cultural belief that it is discrete in nature and, therefore, irrelevant to other content areas and the real world. National Council of Teachers of Mathematics, inclusive of mathematics teacher educators, views this belief as unproductive to learning and has stressed the need for…

Proficiency in solving mathematical problems is essential for preservice elementary teachers, as they will teach foundational math concepts and foster problem-solving abilities among young learners. However, many studies found low problem-solving performance among preservice teachers. In line with this, the present study examined how…

Providing opportunities for students to talk directly with their peers is a critical dimension to facilitating discussions in mathematics and science, including argumentation-focused discussions in which students construct arguments and critique others' arguments. Research suggests that supporting student-to-student talk and facilitating…

We suggest that writing lesson plays can be a valuable approach in learning to teach proving in teacher education. A lesson play is an imagined discussion between a teacher and some students about a particular mathematical content, written verbatim. In this paper, we investigate novice teachers' opportunities to work on teaching practices related…

Harmful and inaccurate narratives about the nature of mathematics, and about the mathematical incapability of historically marginalized groups, are pervasive and longstanding. The persistence of these narratives, and their documented negative impacts in school, the discipline, and beyond, have led some scholars to conclude that there is something…

Mathematics is a core academic subject, regardless of grade level or setting. Everyone uses mathematics in their everyday life, so being competent in basic mathematics is critical to independent living. One thing teachers can do to ensure learners are learning the mathematics concepts being taught is to diagnose and remediate the errors they are…

Research has shown there are algebra concepts elementary teachers can introduce that help prepare elementary students for the eventual transition to algebra (e.g., the relational interpretation of the equal sign). "Early algebra" refers to the use of informal approaches to introduce such concepts to elementary students. "Strip…

Reform in teacher education seeks to engage preservice teachers (PSTs) in authentic classroom situations that explore equitable practices by connecting theory to professional practice. One way for PSTs to examine how equity and inequity operate in schools is with the aid of equity-related case-based instruction. This study reports on mathematics…

Preservice elementary teachers' attitudes towards mathematics are often negatively influenced by their K-12 education. Accordingly, teacher educators must allow preservice elementary teachers to experience mathematical instruction differently to change their attitudes toward mathematics and their conceptions about what it means to teach and learn…

This paper details an integrated inquiry-based mathematics and science method course for preservice teachers designed around STEM problem-based learning. It documents how problem-based learning (PBL) activities supported PSTs' envisioning of equitable approaches for diverse children. The overarching research question was: "How did preservice…

Considering the content of history of mathematics textbooks, it's evident that their emphasis is primarily on the illustrative aspects of recurring numerical sequences, with a particular focus on the Fibonacci sequence. Unfortunately, this limited approach results in the neglect of other sequences akin to the Fibonacci numbers, thus rendering the…