The cultural challenge in mathematical cognition

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

Why frequencies are natural

Research in mathematical cognition has shown that rates, and other interpretations of x/y, are hard to learn and understand. On the other hand, there is extensive evidence that the brain is endowed with a specialized mechanism for representing and manipulating the numerosities of sets – that is, frequencies. Hence, base-rates are neglected precisely because they are rates, whereas frequencies are indeed natural

Transcriptions, Mathematical Cognition, and Epistemology

The epistemologies researchers bring to their studies mediate not only their theories but also their methods, including what they select from their data sources to present the findings on which claims are based. Most articles reduce mathematical knowing to linguistic/mathematical structures, which, in the case of embodiment/enactivist theories, undermines the very argument about the special nature of mathematical knowing. The purpose of this study is to illustrate how different transcriptions of mathematics lessons are generally used to support different epistemologies of mathematical knowing/competence. As part of our third illustration, we provide embodiment/enactivist researchers with an innovative means of representing classroom interactions that are more consistent with their theoretical claims. We offer a comprehensive transcription, which, when treated by readers in the way musicians treat their scores, allow them to enact and feel the knowledge that the article is about

Challenges in mathematical cognition: a collaboratively-derived research agenda

This paper reports on a collaborative exercise designed to generate a coherent agenda for research on mathematical cognition. Following an established method, the exercise brought together 16 mathematical cognition researchers from across the fields of mathematics education, psychology and neuroscience. These participants engaged in a process in which they generated an initial list of research questions with the potential to significantly advance understanding of mathematical cognition, winnowed this list to a smaller set of priority questions, and refined the eventual questions to meet criteria related to clarity, specificity and practicability. The resulting list comprises 26 questions divided into six broad topic areas: elucidating the nature of mathematical thinking, mapping predictors and processes of competence development, charting developmental trajectories and their interactions, fostering conceptual understanding and procedural skill, designing effective interventions, and developing valid and reliable measures. In presenting these questions in this paper, we intend to support greater coherence in both investigation and reporting, to build a stronger base of information for consideration by policymakers, and to encourage researchers to take a consilient approach to addressing important challenges in mathematical cognition

Mathematical Cognition and the Arts

This article revisits the study of mathematics in the arts, and vice versa, the arts in mathematics, with a view to connecting mathematical and artistic creativity to the same neural circuits—a proposition put forward for mathematics and language in a critical 2000 book by Lakoff and Núñez, Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. This expanded perspective would open up suggestive avenues for connecting mathematics, language, and the arts as part of an imaginative blend that comes out in different forms but having the same underlying neural source. Whether or not this can be established empirically, it is plausible and highly interesting and, thus, needs to be explored seriously in order to see if equations to theorems are born of the same mental structures that produce music, poetry and drawing, as the philosopher Max Black [4] had anticipated before the advent of contemporary neuroscience in the early 1960s. The argument put forth here is that art can be studied through a mathematical lens, and that mathematics can be studied through an artistic lens, in order to glean what the common neural substratum is like. The approach is called hermeneutic, in line with critical approaches in the arts, from visual art to literature

Challenges in mathematical cognition: a collaboratively-derived research agenda

This paper reports on a collaborative exercise designed to generate a coherent agenda for research on mathematical cognition. Following an established method, the exercise brought together 16 mathematical cognition researchers from across the fields of mathematics education, psychology and neuroscience. These participants engaged in a process in which they generated an initial list of research questions with the potential to significantly advance understanding of mathematical cognition, winnowed this list to a smaller set of priority questions, and refined the eventual questions to meet criteria related to clarity, specificity and practicability. The resulting list comprises 26 questions divided into six broad topic areas: elucidating the nature of mathematical thinking, mapping predictors and processes of competence development, charting developmental trajectories and their interactions, fostering conceptual understanding and procedural skill, designing effective interventions, and developing valid and reliable measures. In presenting these questions in this paper, we intend to support greater coherence in both investigation and reporting, to build a stronger base of information for consideration by policymakers, and to encourage researchers to take a consilient approach to addressing important challenges in mathematical cognition

Mathematical Cognition: A Case of Enculturation

Most thinking about cognition proceeds on the assumption that we are born with our primary cognitive faculties intact and they simply need to mature, or be fine-tuned by learning mechanisms. Alternatively, a growing number of thinkers are aligning themselves to the view that a process of enculturation transforms our basic biological faculties. What evidence is there for this process of enculturation? A long period of development, learning-driven plasticity, and a cultural environment suffused with practices, symbols, and complex social interactions all speak in its favour. In this paper I will sketch in outline the commitments of the enculturated approach and then look at the case of mathematical cognition as a central example of enculturation. I will then defend the account against several objections

The Neuroscience of Mathematical Cognition and Learning

The synergistic potential of cognitive neuroscience and education for efficient learning has attracted considerable interest from the general public, teachers, parents, academics and policymakers alike. This review is aimed at providing 1) an accessible and general overview of the research progress made in cognitive neuroscience research in understanding mathematical learning and cognition, and 2) understanding whether there is sufficient evidence to suggest that neuroscience can inform mathematics education at this point. We also highlight outstanding questions with implications for education that remain to be explored in cognitive neuroscience. The field of cognitive neuroscience is growing rapidly. The findings that we are describing in this review should be evaluated critically to guide research communities, governments and funding bodies to optimise resources and address questions that will provide practical directions for short- and long-term impact on the education of future generations

Analisis Kemampuan Penalaran Numerik Siswa dalam Menyelesaikan Soal Berbasis Mathematical Cognition di Sekolah Dasar

Penelitian ini bertujuan untuk menganalisis kemampuan penalaran numerik siswa kelas III SD Negeri 25 Padang dalam menjawab soal yang berbasis mathematical cognition. Subjek peneilitan ini adalah SD Negeri 25 Parupuk Tabing Padang kelas III yang terdiri dari 16 siswa. Instrumen yang digunakan berupa tes dan wawancara. Penelitian ini menggunakan pendekatan kualitatif dengan metode deskriptif. Berdasarkan analisis data dapat disimpulkan bahwa kemampuan penalaran numerik siswa masih rendah dalam menyelesaikan soal berbasis mathematical cognition. Siswa tidak mampu memahami angka dan memberikan alasan mengenai hubungan antar angka