Cognitively demanding tasks have been shown to support students' understanding of mathematics. How a task is launched, or introduced, determines how students engage with the task, as well as the type of work the teacher engages in during the task implementation. The authors designed a unit focused on launching a task where prospective teachers…

Research indicates that investigating phenomena, rather than reproducing facts, should be a core experience in the education of prospective mathematics teachers. Corresponding with its centrality to quality teacher education, there are multiple existing methodologies for analyzing the effects of investigation tasks on teachers' mathematical…

This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration…

This study examined opportunities provided for preservice secondary mathematics teachers (PSMTs) to learn reasoning and proof in algebra from the perspective of college instructors. We analyzed interview transcripts of 15 course instructors recruited from three teacher education programs in the United States. We examined the reported opportunities…

In studies over recent years, there has been an increasing interest in teachers' predicting middle school students' thinking processes. However, as far as we are aware, there are no studies examining students' thinking in terms of mathematical thinking components. This study primarily aimed to determine the mathematical thinking of middle school…

Mathematics plays a crucial role in engineering education. Students who are good at math are often advised to consider engineering as a career. In this study, engineers, mathematics teachers, and engineering professors were asked about the type of mathematics representative of engineering, whether the engineering problems created by math…

The Modelling Dance task is a mathematical modelling task that explores the relationship between mathematics and dance. The authors share the task sequence, adaptations made to support virtual implementation, and evidence of student learning related to learning goals.

The use of tasks to promote mathematical reasoning (MR) in teaching practice is essential to meet curricular goals. However, that practice is often a huge challenge for teachers, and particularly for prospective teachers and thus it is essential to highlight it as a goal for initial teacher education. This study focuses on preservice mathematics…

In this article, the author describes a task given to pre-service secondary school mathematics teachers. By exposing them to a relatively simple mathematics process, it was hoped that their ability to plan and implement lessons for their own students would be enhanced.

In this article, we use a case study to explore the views of first-year university students on the differences between mathematics at school and at university, and on the changes to their study methods as they make the transition to university mathematics. We also consider their views on the differences and affordances of tasks that they encounter…

We propose a divisibility criterion for elements of a generic Unique Factorization Domain. As a consequence, we obtain a general divisibility criterion for polynomials over Unique Factorization Domains. The arguments can be used in basic algebra courses and are suitable for building classroom/homework activities for college and high school…

Educational mathematics researchers and educationists emphasise teaching for understanding. However, does it influence students' mathematical learning behaviour? The purpose of this study was to explore late adolescent students' views on mathematical learning behaviour in teaching-for-understanding classes. Content analysis of secondary data from…

We investigate the beliefs that influence middle and high school algebra teachers' appraisals of contextual problems having diverse mathematical and pedagogical features. We asked six teachers to analyze six contextual algebra tasks and indicate how they would apportion instructional time among the six tasks based on their structure, pedagogical…

Inherent in the Common Core's Standard for Mathematical Practice to "look for and express regularity in repeated reasoning" (SMP 8) is the idea that students engage in this practice by generalizing (NGA Center and CCSSO 2010). In mathematics, generalizing involves "lifting" and communicating about ideas at a level where the…

Algebraic thinking is a method of solving math problems that stresses the significance of general connections. Excellent algebraic thinking necessitates strong symbolization and generalization ability. Students aged 7 to 15 are at the Piaget thinking stage's formal operational stage. Teachers, especially those working with secondary school…