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Sixth-grade students’ reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis

Negative numbers are among the first formalizations students encounter in their mathematics learning that clearly differ from out-of-school experiences. What has not sufficiently been addressed in previous research is the question of how students draw on their prior experiences when reasoning on negative numbers and how they infer from these experiences. This article presents ...

Which Techno-mathematical Literacies Are Essential for Future Engineers?

Due to increased use of technology, the workplace practices of engineers have changed. So-called techno-mathematical literacies (TmL) are necessary for engineers of the 21st century. Because it is still unknown which TmL engineers actually use in their professional practices, the purpose of this study was to identify these TmL. Fourteen semi-structured interviews were conducted ...

An inferentialist perspective on the coordination of actions and reasons involved in makinga statistical inference

. Acknowledgements This research is made possible with the financial support of a grant from the Educational and Learning Sciences Utrecht to Arthur Bakker and a grant DP120100690 by the Australian Research Council to

Inferentialism as an alternative to socioconstructivism in mathematics education

The purpose of this article is to draw the attention of mathematics education researchers to a relatively new semantic theory called inferentialism, as developed by the philosopher Robert Brandom. Inferentialism is a semantic theory which explains concept formation in terms of the inferences individuals make in the context of an intersubjective practice of acknowledging, ...

Using genre pedagogy to promote student proficiency in the language required for interpreting line graphs

The importance of language in mathematics learning has been widely acknowledged. However, little is known about how to make this insight productive in the design and enactment of language-oriented mathematics education. In a design-based research project, we explored how language-oriented mathematics education can be designed and enacted. We drew on genre pedagogy to promote ...

Scaffolding and dialogic teaching in mathematics education: introduction and review

, especially when taking advantage of the insights from the dialogic teaching literature. - & Arthur Bakker 1 Scaffolding and dialogic teaching 1.1 Why combine these topics? This special issue of ZDM

Scaffolding norms of argumentation-based inquiry in a primary mathematics classroom

Developing argumentation-based inquiry practices requires teachers and students to be explicit about classroom norms that support these practices. In this study, we asked: How can a teacher scaffold the development of argumentation-based inquiry norms and practices in a mathematics classroom? A primary classroom (aged 9–10) was videotaped during the school year to address this ...

Learning to reason from samples

to this theme (SRTL7). This conference was hosted by Arthur Bakker in the Netherlands and attended by 22 participants from 7 countries. This special issue addresses the following questions: How does

A boundary-crossing approach to support students’ integration of statistical and work-related knowledge

Vocational students and beginning professionals typically find it hard to integrate the mathematics and statistics that they have learned at school with work-related knowledge. To explore how such an integration process could be supported, we conducted an intervention in secondary vocational laboratory education. Our boundary-crossing approach was informed by the literature on ...

Meaningful statistics in professional practices as a bridge between mathematics and science: an evaluation of a design research project

Arthur Bakker 0 Jan A van Maanen 0 Harrie MC Eijkelhof 0 0 Faculty of Science, Department of Mathematics, The Freudenthal Institute for Science and Mathematics Education, Utrecht University

Crossing Boundaries Between School and Work During Apprenticeships

Sanne F. Akkerman Arthur Bakker 0 ) Department of Education, Faculty of Social and Behavioural Sciences, Utrecht University , Heidelberglaan 8, 3508 TC Utrecht, The Netherlands In vocational ... . Arthur Bakker is an assistant professor at the Freudenthal Institute for Science and Mathematics Education, Utrecht University, Princetonplein 5, 3584 CC, Utrecht, Netherlands; e-mail: . For several years

Proportional reasoning in the laboratory: an intervention study in vocational education

Based on insights into the nature of vocational mathematical knowledge, we designed a computer tool with which students in laboratory schools at senior secondary vocational school level could develop a better proficiency in the proportional reasoning involved in dilution. We did so because we had identified computations of concentrations of chemical substances after dilution as a ...

The use, nature and purposes of measurement in intermediate-level occupations

To provide a basis for thinking through how measurement can be taught in schools, this paper analyses the use, nature and purposes of measurement in intermediate-level work, i.e. occupations for which a school-level qualification is required, but not a bachelor degree or higher. In the Netherlands, senior secondary vocational education (MBO) prepares its students (aged 16+) for ...