This paper aims to shed light on an overlooked but essential aspect of informal reasoning and its radical implication to mathematics education research: Decentralising mathematics. We start to problematise that previous studies on informal reasoning implicitly overfocus on what students infer. Based on Walton's distinction between reasoning and…

This paper presents the results of a systematic scoping literature review of higher education mathematics and statistics support (MSS) evaluation focusing on its impact on students. MSS is defined as any additional organised mathematical and/or statistical aid offered to higher education students outside of their regular programme of teaching by…

In this paper, we offer a comparative review of research on understanding and promoting students' mathematical thinking. The sources for the review are papers that were published in "Educational Studies in Mathematics" ("ESM") during two windows of time: 1994-1998 and 2014-2018. Selection of these two time periods enables us to…

Research in mathematics education is a discursive process: It entails the analysis and production of texts, whether in the analysis of what learners say, the use of transcripts, or the publication of research reports. Much research in mathematics education is concerned with various aspects of mathematical thinking, including mathematical knowing,…

The author remarks on the purpose(s) and content of existing geometry courses and offers alternative purposes and goals for geometry courses and some consequences of this alternative point of view. (JG)

In recent years several mathematics education researchers have attempted to analyse students' arguments using a restricted form of Toulmina's ["The Uses of Argument," Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate mathematics students,…

A tentative approach to geometry by the Comprehensive School Mathematics Program (CSMP) is discussed. Included are descriptions of the content for courses in the elementary, middle, and secondary school mathematics. Both Euclidean and affine plane geometry are included. (JG)

The author surveys some aspects of both product evaluation and process investigation as they impinge on mathematics education and curriculum development. Discussion includes summative and formative evaluation, investigating the learning process, and problems inherent in both areas. (JG)