Over the past thirty years, research on teachers' mathematical knowledge for teaching (MKT) has developed and grown in popularity as an area of focus for improving mathematics teaching and students' learning. Many scholars have investigated types of knowledge teachers use when teaching and the relationship between teacher knowledge and student…

In the last two decades, studying the possible relations between the history of mathematics and mathematics education has revealed the importance of certain foundational issues concerning the nature, relevance and validity of historical knowledge vis-à-vis problems of teaching and learning, which call for deeper exploration. Reviewing aspects of…

The mathematics education literature indicates a consensus regarding the importance of developing algebraic thinking in elementary school mathematics. However, the approaches used to implement this concept vary around the world. This study examines how a popular standards-based elementary mathematics textbook series in China provides opportunities…

Teacher knowledge is particularly important in middle school mathematics to enhance the meaningful transition from arithmetic to algebra. Developing a solid understanding of algebra requires teachers to unpack the meaning underlying the basic concepts, make clear and explicit distinctions among concepts, and facilitate students to connect these…

When designing an instructional tool and using it in pedagogical activities, it is essential that designers and users understand what pedagogical affordances and constraints the tool provides to support its successful integration into targeted pedagogical activities. Toward this end, we developed "Pedagogical Affordance Analysis (PAA)."…

While it is commonly accepted that Learning Analytics (LA) tools can support teachers' awareness and classroom orchestration, not all forms of pedagogy are congruent to the types of data generated by digital technologies or the algorithms used to analyse them. One such pedagogy that has been so far underserved by LA is exploratory learning,…

The overarching aim of this article is to exemplify and analyse how some algebraic aspects of equations can be theoretically explored and reflected upon by young students in collaboration with their teacher. The article is based upon an empirical example from a case study in a grade 1 in a primary school. The chosen lesson is framed by the…

This paper reports a study developed with twenty-six students from a 7th-grade class and was carried in the context of teaching experience in the school year of 2016/2017, using an applet, Equation Buster, on the learning of solving single-variable linear equations. The research objectives are to assess how this applet can help students to see the…

This paper is based on the presumption that teaching multiple ways to solve the same problem has academic and social value. In particular, we argue that such a multifaceted approach to pedagogy moves towards an environment of more inclusive and personalized learning. From a mathematics education perspective, our discussion is framed around…

in this paper we focus on the link between the use of dynamic geometry software and student understanding for the solution of systems of linear equations from an instrumental genesis perspective. Three task-based interviews were conducted with an undergraduate linear algebra student majoring in mathematics education and proficient in using dynamic…

A growing number of Introductory Physics for Life Sciences courses have been developed to prepare biology, premedicine, and prehealth majors for cross-disciplinary connections between physical principles and biological systems. Many students find it challenging to apply idealized algebra-based general physics to more complex biological systems. A…

Multiple representations of a given mathematical object/concept are one of the biggest difficulties encountered by students. The aim of this study is to investigate the impact of the use of visual representations in teaching and learning algebra. In this paper, we analyze the transformations from and to visual representations that were performed…

Responsive instruction--or instruction that foregrounds and takes up the disciplinary substance of student thinking--is both a hallmark of recent STEM education reforms and challenging to enact. This kind of instruction may be especially challenging in instructional contexts that mandate or rely on curriculum with set, structured learning…

In this study we explore possible long-term effects of an adaptation of the El'konin­-Davydov elementary grades curriculum, Measure Up or MU. The objectives for the study are to assess how students relate an equation of nonnumeric quantities to a length representation, and if former MU students develop and retain a perspective characteristic of…

The year students take Algebra I historically determines how far they progress in secondary mathematics, creating complex equity issues around access to this course. By examining a case study of one large, urban school district adjusting to the Common Core State Standards in Mathematics (CCSS-M), we demonstrate how district leaders' interactions,…