Descriptions of expertise have focused on knowledge and characteristics of mathematics teacher educator (MTE) practice. To contribute to discussion of MTE expertise we share findings from a study of MTE discussion practice with prospective teachers (PTs) concerning pedagogy of teaching mathematics. Research on MTE discussion practices have shown…

Covariational reasoning, essential for understanding functions and modeling dynamic situations, is traditionally introduced in secondary education. This paper proposes introducing covariational reasoning in primary school settings through an artifact, the Tracer. Previous studies investigate a covariational approach to functions with younger…

A central aspect of reform-minded mathematical teaching is training and developing teachers' ability to notice vital aspects in the classroom and more specifically, students' mathematical thinking. As there is an abundance of evidence and research that support the benefits for teachers to elicit and use students' ideas and thinking during…

Mathematics learning in higher education today focuses on the need to enhance students' diverse creativity through learning process. To address this challenge, this study introduces the Differentiated Instruction based on Lateral Thinking Techniques (D-LTT) framework. It provides an overview of D-LTT, demonstrates its application in a numerical…

The aim of this study is to reveal and evaluate the attending and interpreting skills of student thinking of prospective teachers, as well as their instructional suggestions as responding skills. The current study was conducted with 29 prospective mathematics teachers (PMTs) within a qualitative design in the context of probability. First, three…

Reasoning is the process of thinking used to make claims and reach conclusions. It is among the first skills that should be taught to students in mathematics lessons and contributes to the creation and development of mathematical foundations. This study identifies evolution and trends in research on mathematical reasoning over the last four…

Research on teachers' noticing of student mathematical thinking has typically focused on how a teacher attends to, interprets, and determines a response to an individual student contribution in isolation from the broader mathematical classroom context. This research focus is not nuanced enough, however, to fully account for the complex noticing…

This extensively updated teaching resource provides over 100 engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K-8. Readers are provided with a strong mathematical background, downloadable copies of…

Despite substantial research exploring multiplicative thinking and students' difficulty in the domain, the topic of multi-digit multiplication is under-researched. In this paper, I share a learning trajectory for multi-digit multiplication that combined social and cognitive perspectives of learning. Using Design Research methods and involving 45…

The interactions young children have with adults are of vital importance in developing mathematical reasoning. This paper describes the behaviours of teachers who work with young children in school yet manage to have individual and natural mathematical conversations with children. These mathematical interactions young children have with their…

Secondary mathematics preservice teachers enrolled in a methods class at a large Midwestern University were supported to develop their TPACK knowledge. Instructional tasks included engaging with explorations using technology to support reasoning and sense making, creating entries for a technology portfolio, studying theoretical constructs about…

Secondary mathematics teachers' use of formative assessments have shown promise for developing models of their students' mathematical thinking and informing their instruction. While the complexities of secondary mathematics teachers' formative assessment practices are often captured in qualitative research, there is a critical need for synthesized…

The reasons for teaching programming in school are indeed manifold. Programming can for example be utilized as a vehicle for understanding and learning particular mathematical subject matter, or as a tool for solving mathematical problems. In this paper, however, we propose to utilize programming as a vehicle for developing mathematical…

With the aim of engaging more students in meaningful thinking in mathematics, a cohort of Year 7 students were introduced to a 'Building Thinking Classrooms' framework for learning in mathematics. In this paper, the authors outline the key features of the implemented framework and share reflections on challenges and benefits.

GeoGebra is a dynamic software that is frequently used and of increasing importance in mathematics teaching processes in our digital age. Accordingly, in this study a new perspective has been brought to the proofs of the "two square difference identity" expressed for the square, which is a flat polygon, made with different approaches.…