This paper presents the results of a systematic review of the empirical literature, reported in research journals, on Mathematics Learner Identity (MLI). In the mathematics education research field, arguments have been made that the conceptualization of Mathematics Identity (MI) is inconsistent and this makes the literature as a whole incoherent.…

In this paper, a focus is made on defining processes at stake in an unfamiliar situation coming from discrete mathematics which brings surprising mathematical results. The epistemological framework of Lakatos is questioned and used for the design and the analysis of the situation. The cognitive background of Vergnaud's approach enriches the study…

Many mathematics education researchers have suggested that asking learners to generate examples of mathematical concepts is an effective way of learning about novel concepts. To date, however, this suggestion has limited empirical support. We asked undergraduate students to study a novel concept by either tackling example generation tasks or…

It is widely recognized that purely cognitive behavior is extremely rare in performing mathematical activity: other factors, such as the affective ones, play a crucial role. In light of this observation, we present a reflection on the presence of affective and cognitive factors in the process of proving. Proof is considered as a special case of…

Observations and interviews with (n=16) undergraduate mathematics and mathematics education majors learning to do formal mathematical proofs found three major sources of students' difficulties: concept understanding, mathematical language and notation, and getting started on a proof. (25 references) (MKR)

Two books ("The Mathematical Experience" and "Mathematics Tomorrow") raise many issues about mathematics and education, including how mathematics education must be disciplined by focusing on the real world. Examined are ways the books take adequate account of the constraints present in problems they consider. (JN)

Reviews the Lakoff and Nunez's book, "Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (2000)," which provided many mathematics education researchers with a novel and startling perspective on mathematical thinking. Suggests that several of the book's flaws can be addressed through a more rigorous establishment of…

Describes a research project whose major aim was to evaluate first-year teacher-education students' understanding of subject matter knowledge in the domain of area measurement. This study focuses on the student teachers' substantive knowledge, knowledge about the nature and discourse of mathematics, mathematics in society, and their disposition…