ZDM

The participation of students in processes of collective argumentation is seen as a fundamental condition for enabling mathematics learning in classroom settings. Using data from a finished research project on argumentation in primary mathematics classrooms it will be shown, that in elementary education these processes are of a narrative character.

Teacher dashboards in mathematics classrooms tend to provide teachers with information on student performance that are often linked to classroom management systems, online course systems, or peer-tutoring software. Teacher dashboards also tend to emphasize features that support teachers using a “transition” or “direct instruction” model. In our approach, we iteratively designed, developed, tested, and refined a teacher dashboard that is linked to a student digital collaborative environment with an embedded problem-based mathematics curriculum. In this study, we investigate teacher dashboard features that support teacher enactment of problem-based mathematics curriculum embedded in a digital collaborative platform. We report on design principles that guided the development of three teacher dashboard features: (1) monitoring evidence of student thinking in real-time or after class, (2) accessing workspace for whole-class discussions of the problem, and (3) creating and sending “just-in-time” supports. The pedagogical advantages and challenges teachers face throughout the iterative development process are also discussed. Evidence from observational data and teacher interviews suggests that the organic synergism generated from the student and teacher digital platform offers several ways that teachers are provided with new and timely information from teacher dashboards that supports problem-based mathematics teaching.

Dual-process theories posit two distinct types of cognitive processing: Type 1, which does not use working memory making it fast and automatic, and Type 2, which does use working memory making it slow and effortful. Mathematics often relies on the inhibition of pervasive Type 1 processing to apply new skills or knowledge that require Type 2 processing. In two studies, we demonstrate that giving participants a difficult task (Raven’s Matrices) before a task that requires the inhibition of intuitive responses (the Cognitive Reflection Test) significantly improves performance. Our findings suggest that encountering a difficult task that requires Type 2 processing before completing a task that requires inhibition of Type 1 processing may encourage an enduring ‘Type 2’ mindset, whereby participants are more likely to spontaneously use Type 2 processing for a period of time. Implications for mathematics education are discussed.

This paper starts from some observations about Presmeg’s paper ‘Mathematics education research embracing arts and sciences’ also published in this issue. The main topics discussed here are disciplinary boundaries, method and, briefly, certainty and trust. Specific interdisciplinary examples of work come from the history of mathematics (Diophantus’s Arithmetica), from linguistics (hedging, in relation to Toulmin’s argumentation scheme and Peirce’s notion of abduction) and from contemporary poetry and poetics.

The relationship between acquisitionism and participationism is a challenge in research on and with teachers. This study uses a patterns-of-participation framework (PoP), which aims to develop coherent and dynamic understandings of teaching as well as to meet the conceptual and methodological problems of other approaches. The paper presents PoP theoretically, but also illustrates its empirical use. It presents a novice teacher, Anna, who often engages with mathematics and with aspects of ‘the reform’ in ways that link well with how she builds relationships with her students and positions herself in her team of teachers. However, in other situations her engagement with mathematics is overshadowed by her involvement in other practices. The study suggests that there is some potential in PoP in spite of methodological difficulties.

This paper provides on-the-ground accounts of epistemic violence against Black immigrant children in mathematics classrooms. From a critical feminist perspective, we introduce Dotson’s notion of silencing as an enactment of epistemic violence. According to Dotson, one way to enact epistemic violence is to damage a particular group’s ability to speak and be heard. A successful act of communication depends on the audience’s willingness and ability to “hear” the speaker. Therefore, denying this reciprocity in communication is a form of epistemic violence. Using this conceptualization, we conducted a secondary data analysis from a larger study aimed at enhancing teachers’ knowledge and abilities to implement problem-solving teaching. We identify and characterize three practices of silencing Black immigrant students in Chilean mathematics classrooms that damage their agency as knowers and doers of mathematics. Beyond language issues, we show that silencing is a form of anti-Black onto-epistemic violence that prevents Black immigrant students from being recognized as legitimate subjects of knowledge in mathematics classrooms.

In this study we investigated the development of 245 kindergarteners’ mathematics problem solving (MPS) at two time points within 7 months using a cognitive diagnostic test, which measured three cognitive components (mathematical knowledge and skills, semantic understanding, and quantitative reasoning) with eleven cognitive attributes. The effects of five influencing factors [language ability, mathematics application ability, calculation ability, approaches to learning (ATL) and socio-economic status (SES)] on the children’s MPS ability at the two time points were examined. The results indicated that the 245 children’s mastery of mathematical knowledge and skills was much better than their mastery of semantic understanding and quantitative reasoning. Furthermore, they achieved significant progress in set comparison and addition and subtraction within the range of natural numbers to ten (two of the three cognitive attributes of mathematical knowledge and skills), additive composition reasoning and one-to-many correspondence reasoning (two of the three cognitive attributes of quantitative reasoning). Only their mathematics application ability significantly predicted their mastery of the three cognitive components of MPS ability at the two-time points. Their language and calculation abilities predicted only their mastery of mathematical knowledge and skills at the two time points. Their ATL predicted their mastery of the three cognitive components of MPS only at the first time point, and their SES predicted only their mastery of semantic understanding 7 months later.

This study investigates US teachers’ cultural beliefs concerning effective mathematics teaching using semi-structured interviews with 11 experienced teachers. For US teachers, effective teaching is student-centered. Cognitively appropriate mathematical content should be understood through many hands-on activities that allow students to explore by themselves the relationship between mathematical knowledge and their life experiences. Correspondingly, the US teachers view an effective teacher as a facilitator who is sensitive to student social and cognitive needs and is skillful at organizing collaborative learning. The result of this study helps researchers and educators understand the student-centered learning model in US classrooms.

Statistical modeling is a core component of statistical thinking and has been identified by several countries as a curricular goal for secondary education. However, many secondary teachers have minimal preparation for teaching this topic. The goal of this research study is to learn about teachers’ perceptions of the role statistical models play in statistical inference and how these perceived purposes affect their reasoning about statistical models and inference. Problem-solving interviews were conducted with four in-service teachers who had recently taught a modeling and simulation-based introductory statistics course. Teachers’ responses suggest they may not see modeling variation as the primary purpose of statistical modeling and instead substitute two other purposes: making a decision and replicating the data collection process. Suggestions for how to build on teachers’ transitional conceptions and refocus attention on modeling variation are discussed.