In this theoretical paper, I review the history of research in educational psychology that inspired Shulman's notion of pedagogical content knowledge (PCK) and I critically examine interpretations of PCK reflected in prominent theoretical frameworks for mathematical knowledge for teaching (MKT). I propose a theory of PCK--grounded in radical…

This paper compares and contrasts two approaches that are widely used in the English- and German-speaking discourse on mathematics teacher knowledge: 'mathematical knowledge for teaching' and 'mathematics didactic knowledge'. It is proposed that these constructs are based on distinct theoretical and conceptual positions and origins. Mathematical…

This paper presents a modified approach to subject-matter didactics, in which the focus is not on the content itself, but on the students' view of the content. The introduction deals with an overview of subject-matter didactics and the notion of beliefs used in this paper. The main portion of the paper deals with presenting the concepts of a book…

The paper introduces the notion of collateral creativity as an unintended outcome of the appropriate use of technology, both physical and digital, in the teaching of mathematics. The notion is motivated by Dewey's conceptual framework of collateral learning which enables one gaining knowledge beyond the intent of the traditional curriculum.…

This paper problematizes the metaphors of unpacking, deconstructing, and decompressing mathematics that are prevalent in discourses about mathematics teacher knowledge. It is argued that the logic of these metaphors is based on the reversibility of packing, constructing, and compressing mathematics and seems to suggest the view that knowledge is…

Shulman (1986) conceptualized pedagogical content knowledge (PCK) at the intersection of content knowledge and pedagogical knowledge. In this paper, I re-explore the intersection of content--in our case, mathematics--and pedagogy, not in terms of domains of knowledge, but in terms of domains of practice. I conceptualize, describe, and exemplify…

The terms conceptual knowledge and procedural knowledge are often used by teachers and never more so than when discussing how teachers teach, and children learn mathematics. This paper will look at literature regarding conceptual and procedural knowledge and their place in the classroom, to offer teachers and teacher educators' advice on some of…

Two of the teachers' knowledge models most widely used in the literature are the Mathematical Knowledge for Teaching (MKT) and the Knowledge Quartet (KQ). We develop an analysis of the limitations of the knowledge required for teaching problem-solving published during 1990-2018 which includes these models. This analysis revealed that MKT takes…

Focussing on teachers' subject pedagogical actions over the course of a series of lessons on a mathematical topic, this paper sets out an original analytical approach to characterise the shape of mathematics teaching decisions made over time: tri-polar analysis. The notion of manifestation is introduced as a way of categorising how the teacher is…

Current gaps in achievement among students from diverse backgrounds and their culturally dominant counterparts imply that theoretical ideas, such as culturally responsive teaching (CRT), that focus on increasing the achievement of diverse populations are sound yet difficult to translate into everyday practice. CRT is intricate and complex and…

In the teaching of math-fact automaticity, most classroom teachers are unaware of research-based practices such as the use of a controlled response time, the scaffolded teaching of individual math facts, the limiting of exposure to new math facts, the separation of math facts with common operands, and even the definition of automaticity. As a…

What mathematical knowledge is required for teaching has been researched by many, with Ball et al. (J Teach Educ 59(5):389-407, 2008) and their practice-based theory of mathematical knowledge for teaching (MKT) primary among them. However, what is required in terms of mathematical knowledge for teacher educator training has been researched much…

The article aims to present an excerpt from the research that investigates knowledge to teach arithmetic in practical classes in teacher training courses. More precisely, we are looking for traces of prescriptions of practices at a knowledge systematization level that we seek to objectify in a set of articles from the journal "A Eschola…

In this paper we examine the relationship between teachers' knowledge, beliefs and instructional practices based on a study with 495 Chinese pre-service mathematics teachers. The results indicate that Chinese pre-service mathematics teachers tend to hold mixed beliefs about the nature of mathematics, and a constructivist view about mathematics…

This paper focuses on the design of tasks that situate teachers in the work of mathematics teaching. We examine a simple, yet fundamental feature of pedagogical content knowledge tasks: the extent to which pedagogical warrants are necessitated by the pedagogical context. We argue that this feature has implications for the design of tasks, as well…