This study explores relationships among prospective secondary teachers' skills of attending to relevant mathematics elements in students' answers, interpreting students' mathematical understanding, and proposing instructional actions. Thirty prospective secondary mathematics teachers analyzed three high school students' answers to three problems…

This paper analyzes some of the ambiguities that arise among statements with the copular verb "is" in the mathematical language of textbooks as compared to day-to-day English language. We identify patterns in the construction and meaning of "is" statements using randomly selected examples from corpora representing the two…

Reform-based discourses in mathematics education have fabricated different subjectivities for teachers such as the "traditional" and the "new" teacher. Professional development programs are proposed as effective mechanisms to fabricate the "new" teacher. However, this teacher has proved hard to produce. Thus, the…

We examine opportunities and challenges of applying a single, explicit definition of multiplication when modeling situations across an important swathe of school mathematics. In so doing, we review two interrelated conversations within multiplication research. The first has to do with identifying and classifying situations that can be modeled by…

Inspired by the entering of computer algebra systems (CAS) in the Danish upper secondary school mathematics program, this article addresses, from a theoretical stance, what may happen when traditional procedures are outsourced to CAS. Looking at the commands "solve" and "desolve," it is asked what happens when such CAS…

In this paper, we propose a way of thinking about ritual that is new to mathematics education research and that challenges the more common approaches to ritual that dichotomise thinking and acting. We argue for a material, monist conceptualisation of ritual, which we refer to as ritualisation. In the context of early number work, we show that…

In this paper, learning is conceptualized as a process of routinization of learners' actions. We begin by operationalizing the keyword "routine." Two categorizations of routines are then offered. First, we distinguish between "practical" and "discursive" routines, discuss the process of their historical…

We employ Sfard's ("Thinking as communicating," 2008) "ritual towards exploration" idea to theorize the learning trajectory of two middle school teachers attending a professional development (PD) program designed around the "5 Practices for Orchestrating Productive Discussions" and Accountable Talk. Data included four…

Non-mathematics specialists' competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students…

The thinking of language as resource in mathematics education research has been more metaphorical than conceptual so far. This article provides grounds and reasons for the theorization of language as resource. Based on views from sociolinguistics and functional grammar, I propose a theorization that considers the social languages of learners and…

This paper responds to the burgeoning literature on mathematics teacher noticing, arguing that its cognitive orientation misses the cultural and ideological dimensions of what and how teachers notice. The author highlights Goodwin's concept of "professional vision" as a way of bringing analyses of culture and power into studies of…

In this paper, we present and discuss a framework for considering the quality of primary teachers' mediating of primary mathematics within instruction. The "mediating primary mathematics" framework is located in a sociocultural view of instruction as mediational, with mathematical goals focused on structure and generality. It focuses on…

This article is concerned with cognitive aspects of students' struggles in situations in which familiar concepts are reconsidered in a new mathematical domain. Examples of such cross-curricular concepts are divisibility in the domain of integers and in the domain of polynomials, multiplication in the domain of numbers and in the domain of vectors,…

Part of the international reflection on the use of history in mathematics teaching consists in a quest of frameworks and models suitable for empirical studies. Following this demand, this paper explores the way Balacheff's cK? model, a model taken from the didactics of mathematics, can be used in the analysis of learning at student level. In the…

In this article, I consider the question: why did numeracy become a relevant and sensible thing to consider in mathematics education? I historicize the numeracy discourse by writing a genealogy of how the concept of "numeracy" emerged in scholarship, with a focus on the USA. I argue that numeracy descends from three mathematics education…