Disciplinary differences between cognitive psychology and mathematics education: A developmental disconnection syndrome. Reflections on 'Challenges in Mathematical Cognition' by Alcock et al. (2016)

As the participants in this collaborative exercise who are mathematics education researchers espouse a cognitive perspective, it is not surprising that there were few genuine disagreements between them and the psychologists and cognitive neuroscientists during the process of generating a consensual research agenda. In contrast, the prototypical mathematics education researcher will mostly likely find the resulting list of priority open questions to be overly restrictive in its scope of topics to be studied, highly biased toward quantitative methods, and extremely narrow in its disciplinary perspectives. It is argued here that the fundamental disconnects between the epistemological foundations, theoretical perspectives, and methodological predilections of cognitive psychologists and mainstream mathematics education researchers preclude the prospect of future productive collaborative efforts between these fields. [Commentary on: Alcock, L., Ansari, D., Batchelor, S., Bisson, M.-J., De Smedt, B., Gilmore, C., . . . Weber, K. (2016). Challenges in mathematical cognition: A collaboratively-derived research agenda. Journal of Numerical Cognition, 2, 20-41. doi:10.5964/jnc.v2i1.10]

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The Portrayal of Parents in the School Mathematics Reform Literature: Locating the Context for Parental Involvement

Journal for Research in Mathematics Education ◽

10.5951/jresematheduc.29.5.0555 ◽

1998 ◽

Vol 29 (5) ◽

pp. 555-582

Author(s):

Dominic D. Peressini

Keyword(s):

Mathematics Education ◽

Parental Involvement ◽

Education Reform ◽

Research Agenda ◽

School Mathematics ◽

Mathematics Reform ◽

Mathematics Educators ◽

And Mathematics

In this article, using reform recommendations that call for parental involvement as a springboard, I provide an analysis of the positioning of parents in the school mathematics reform literature. Employing Foucault's (1980) conception of “regimes of truth,” I demonstrate how the literature has created the accepted discourse for mathematics education reform. I then argue that the professionalization of teachers has distanced parents from schools and led to conflict between parents and mathematics educators and that to reconcile this conflict, ways in which parents can be included in mathematics education must be considered. It is essential first, however, to understand issues central to involving parents in mathematics education. A research agenda for parental involvement in mathematics education is presented.

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The Cultural Challenge in Mathematical Cognition

10.31235/osf.io/tqj6b ◽

2021 ◽

Author(s):

Sieghard Beller ◽

Andrea Bender ◽

Stephen Chrisomalis ◽

Fiona Jordan ◽

Karenleigh A. Overmann ◽

...

Keyword(s):

Cognitive Science ◽

History Of Science ◽

Research Agenda ◽

Numerical Cognition ◽

Mathematical Cognition ◽

Cultural Dimension ◽

Science History ◽

Specific Research ◽

History Of ◽

Research Questions

In their recent paper on “Challenges in mathematical cognition”, Alcock and colleagues (Alcock et al. [2016]. Challenges in mathematical cognition: A collaboratively-derived research agenda. Journal of Numerical Cognition, 2, 20-41) defined a research agenda through 26 specific research questions. An important dimension of mathematical cognition almost completely absent from their discussion is the cultural constitution of mathematical cognition. Spanning work from a broad range of disciplines – including anthropology, archaeology, cognitive science, history of science, linguistics, philosophy, and psychology – we argue that for any research agenda on mathematical cognition the cultural dimension is indispensable, and we propose a set of exemplary research questions related to it.

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Integrating numerical cognition research and mathematics education to strengthen the teaching and learning of early number

British Journal of Educational Psychology ◽

10.1111/bjep.12421 ◽

2021 ◽

Author(s):

Zachary Hawes ◽

Rebecca Merkley ◽

Christine L. Stager ◽

Daniel Ansari

Keyword(s):

Mathematics Education ◽

Teaching And Learning ◽

Numerical Cognition ◽

Early Number ◽

And Mathematics

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Challenges in teaching mathematics: Perspectives from students’ learning difficulties. Reflections on 'Challenges in Mathematical Cognition' by Alcock et al. (2016)

Journal of Numerical Cognition ◽

10.5964/jnc.v2i1.26 ◽

2016 ◽

Vol 2 (1) ◽

pp. 53-56 ◽

Cited By ~ 1

Author(s):

Steve Chinn

Keyword(s):

Research Agenda ◽

Numerical Cognition ◽

Learning Difficulties ◽

Mathematical Cognition ◽

Teaching Mathematics ◽

Research Topics

Alcock et al (2016, this issue) have set out and discussed a potential research agenda for mathematical cognition. It is timely that research topics, along with knowledge uncovered to date, should be incorporated into a coordinated agenda for further research. This commentary focuses on the perspectives that learning difficulties, and dyscalculia, reveal. These perspectives potentially add much to that research agenda. [Commentary on: Alcock, L., Ansari, D., Batchelor, S., Bisson, M.-J., De Smedt, B., Gilmore, C., . . . Weber, K. (2016). Challenges in mathematical cognition: A collaboratively-derived research agenda. Journal of Numerical Cognition, 2, 20-41. doi:10.5964/jnc.v2i1.10]

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The cultural challenge in mathematical cognition

Journal of Numerical Cognition ◽

10.5964/jnc.v4i2.137 ◽

2018 ◽

Vol 4 (2) ◽

pp. 448-463 ◽

Cited By ~ 2

Author(s):

Sieghard Beller ◽

Andrea Bender ◽

Stephen Chrisomalis ◽

Fiona M. Jordan ◽

Karenleigh A. Overmann ◽

...

Keyword(s):

Cognitive Science ◽

History Of Science ◽

Research Agenda ◽

Numerical Cognition ◽

Mathematical Cognition ◽

Cultural Dimension ◽

Science History ◽

Specific Research ◽

History Of ◽

Research Questions

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Integrating numerical cognition research and mathematics education to strengthen the teaching and learning of early number

10.31234/osf.io/ta8gh ◽

2019 ◽

Cited By ~ 1

Author(s):

Zachary Hawes ◽

Rebecca Merkley ◽

Daniel Ansari

Keyword(s):

Mathematics Education ◽

Teaching And Learning ◽

Numerical Cognition ◽

School Context ◽

Intervention Group ◽

Number Line ◽

Control Group ◽

Number Line Estimation ◽

Teachers And Students ◽

And Mathematics

This study reports on the design, implementation, and effects of a 16-week (25-hour) mathematics Professional Development (PD) model for K-3 educators (N=45) and their students (N=180). A central goal of the PD was to better integrate numerical cognition research and mathematics education. The results of the first iteration (Year 1), indicated that compared to a control group, both teachers and students benefitted from the intervention. Teachers demonstrated gains in self-perceived and actual numerical cognition knowledge, while students demonstrated gains in number line estimation, arithmetic, and numeration. In Year 2, teachers in the intervention group demonstrated greater improvements than the control group on a measure of self-perceived numerical cognition knowledge, but no gains in actual numerical cognition knowledge. At the student level, there was some evidence of gains in numeration. Given the mixed findings, questions remain as to why the model may be effective in one school context but not another.

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Some Ideas about Research Methodologies in Mathematics Education

Journal for Research in Mathematics Education ◽

10.5951/jresematheduc.10.3.0228 ◽

1979 ◽

Vol 10 (3) ◽

pp. 228-232

Author(s):

Frank K. Lester ◽

Donald R. Kerr

Keyword(s):

Mathematics Education ◽

Problem Solving ◽

Quantitative Methods ◽

Letters To The Editor ◽

Laboratory Methods ◽

Learning And Teaching ◽

Working Groups ◽

Considerable Controversy ◽

And Mathematics ◽

Natural Settings

There is growing interest among educational researchers in general, and mathematics education researchers in particular, in methodological issues. This interest is due in part to the influence of Piaget and Krutetskii who eschewed strictly controlled laboratory methods in their investigations in favor of less carefully controlled case studies, careful observations in natural settings, and other nonexperimental techniques. Also, there has been a slow shift in emphasis from using quantitative methods to using qualitative techniques to complement, supplement, or even replace quantitative ones. This trend is evidenced by the urging of authorities like Bronfenbrenner (1976) and Shulman (1970), the recent research on problem-solving processes by Kantowski (1977), and the problem-solving working groups of the Georgia Center for the Study of Learning and Teaching Mathematics (Hatfield, Note I). Considerable controversy surrounds this shift in emphasis (see “Letters to the Editor” in the March, May 1977 and May, November 1978 issues of this journal). We wish to discuss this shift toward using nonexperimental paradigms in mathematics education research with the hope of promoting much needed dialogue.

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