The teachers of mathematics education in China have gradually demonstrated the need for the systematic theory about mathematics education. However, the philosophy of mathematics education is biased towards the academic level, and there are few "readable materials" for direct application in practice. This paper prepares a curriculum…

Teachers of mathematics and researchers in mathematics education are recommended to be engaged in a creative endeavor. However, creativity cannot be thought of independent of imagination. This article analyzes the relation between imagination and the philosophy of mathematics. The later concept is inclusively concerned with arguments on whether or…

In this article, educational and psychological perspectives are used to examine how anxiety and uncertainty in the mathematics classroom can be reframed to benefit mathematical teaching and learning. Links between anxiety and uncertainty are discussed and from this discussion, two methods are proposed for reducing the negative impact of…

The aim of this pseudo-longitudinal study is to investigate pre-service teachers' beliefs about (1) the nature of mathematics and (2) mathematics teaching and learning and the development of both beliefs over the course of their studies. A quantitative belief questionnaire was completed by 142 participants divided into three groups based on their…

The widely used Draw a Scientist Test was revised to focus on statistics and 110 Elementary Statistics students were asked to draw a statistician. In addition, to better understand students' drawings and have some relative comparison, 173 College Algebra students were asked to draw a mathematician. A detailed analysis of students' images and…

If the goal is to move beyond the shape of the graph to consider the dynamic aspects of functions, students need to explore dynamic representations of functions. To address this, the authors combined the use of a dynamic representation of function with the instructional routine, Which One Doesn't Belong? [WODB]. In this article, they briefly…

The calls for reasoning and proof to have a prominent place in secondary mathematics classrooms raise the question of knowledge that teachers need to support student learning of reasoning and proof. Several conceptualizations of Mathematical Knowledge for Teaching Proof (MKT-P) have been proposed over the years, yet some key questions about the…

Curiosity is essential to scientific discovery and innovation, and more universally, it is a natural and unavoidable characteristic of children. It is shown as a process in which efforts are made to fill the knowledge gap. It is an important element of learning and it increases math achievement. This research reveals the level of curiosity in…

The purpose of this study was to examine the mathematical creativity of gifted and non-gifted students through the indicators of creativity (fluency, flexibility, and originality). The study involved 12 secondary school students (six gifted and six non-gifted) from different cities in the Black Sea Region of Türkiye. The data were collected…

This theoretical, methodological, and empirical networking study investigated the potential of inferentialism to contribute to the study of meaning and collective argumentation in mathematics. I carefully attended to my worldview and explicated my philosophical process for identifying inferentialism as my theory of choice. I then drew on Prediger…

Polyiamonds are the 'and so on' when unit-squares are replaced with unit-equilateral triangles. Polyiamonds are used to play the satisfying Blokus variant, Blokus Trigon, where the playing grid is also hexagonal, and the playing pieces are all the polyiamonds from mono- to hex. This article discusses the use of polyiamonds in puzzles.

In this paper, the construct of 'uncertainty' in professional mathematics is investigated in relation to mathematical creativity. Specific focus is on 'Big C' research mathematicians' conceptions of what uncertainty means and ways in which it influences their research. Based on the hypothesis that uncertainty is both a catalyst and a necessary…

Backward transfer refers to the influence on prior knowledge of the acquisition and generalisation of new knowledge. Studies of backward transfer of mathematical knowledge have focused on content that is closely related in time and in curricular sequencing. Employing the notion of thickening understanding, we describe instances of transfer that…

Children are active and creative mathematical learners in the early years. This article reports part of a Teacher-led Innovation Fund (TLIF) project that investigated children's mathematical activity at an early childhood centre and the first year of school. Teacher-researchers were from each site, and mathematical opportunities were identified in…

In this article, we discuss the process of understanding continuity, which is one of the most fundamental concepts in mathematics. The continuity of mathematical functions is formally defined in terms of abstract symbols and operations. This representation of continuity is very abstract or dis-embodied. Therefore, it is difficult to acquire a…