This article describes how mathematics may be experienced in widely different ways across mathematics and physics courses and highlights some unexpected constraints in a trigonometry curriculum. The examples and discussion are based on a study (Mateas 2020) that compares how trigonometry is portrayed in representative physics (i.e., "Holt…

Children often learn abstract mathematics concepts with concrete manipulatives. The current study compared different ways of using specific manipulatives -- base-ten blocks -- to support children's place value knowledge. Children (N = 112, M age = 6.88 years) engaged in place value learning activities in one of four randomly assigned conditions in…

The authors present a new classroom-tested lesson that was designed to engage students in the joy of mathematical inquiry through a card game, Frustration, while building number sense, understanding of uncertainty, statistical reasoning, and discourse skills. The purpose in developing and sharing these lessons is to highlight how games of chance…

Typically, mathematics lessons are shaped around mathematical tasks. However, teachers frequently modify or enhance school- or district-adopted curriculum materials, often drawing on multiple sources to develop lessons. Research shows that teachers with a large percentage of students classified as English learners report modifying their materials…

This study investigated the middle school preservice mathematics teachers' conceptualization of what it means for a problem to be mathematically rich and contextually realistic and how their conceptions evolved during a series of professional development activities. Fifteen middle school preservice mathematics teachers were involved in this…

The comparison of different languages in terms of specific mathematical ideas can provide insights into the nature of mathematics and into the learning and teaching of mathematics in both languages. This paper uses a typological perspective to contrast the language of comparison of isiXhosa and English, specifically when comparing countable…

Given the vast experiences pre-service mathematics teachers (PSMTs) have with functions, one may assume that they have existing personal definitions and concept images. The purpose of this paper is to build an understanding of the variety of images that one might associate with a definition of function that includes 'for each input there is one…

In the area of early literacy, the children learned new vocabulary to describe the attributes of triangles and shapes. Through math talk and class discussions, the children also learned about listening to others, turn taking, and voicing their ideas. Although the children described in this article were generally competent in the English language…

In the world where we always meet geometric constructions, it is a necessity to make sense of the objects belonging to these constructions. In this respect, this study aimed to examine the teaching of volume with the blending of the realistic mathematics education (RME) and GeoGebra. The study group consisted of 12 students attending lessons…

Quadratic equations are a notorious topic for the challenge it provides to students in secondary mathematics. Despite this, there is limited research, particularly in the Australian context, that explains why such challenges persist. This article details the causes of Year 11 students' difficulties in solving quadratic equations. Observing…

The aim of this paper is to identify errors and misconceptions that student demonstrated when learning linear independence and linear dependence concepts. A case study is presented involving 73 in-service mathematics teachers at a university in Zimbabwe who were studying for a Bachelor of Science Education Honors Degree in mathematics. Data was…

Human-Computer Interaction (HCI) research aims to make systems versatile, easy to use, and accessible for most people. While computer technologies have successfully remodeled and improved the learning process, students with vision impairment (SVI) are at a disadvantage due to the lack of accessibility to their learning tools. This research aims to…

For students to engage in mathematical thinking, a greater emphasis is needed on the expectations of students, by themselves and others, as active listeners and explainers. As student responsibility for mathematical thinking and participation increases, the roles of the teacher and learner change. A qualitative study of changing classroom…

This article provides an example of the implementation of school-wide professional learning as part of an Australian Research Council grant and the Catholic Schools Parramatta Diocese (CSPD) called Exploring Mathematical Sequences of Connected, Cumulative and Challenging Tasks (EMC[superscript 3] ) (Sullivan et al., 2021). By using sequences of…

Learning to calculate with natural numbers by structuring seems promising but how this can be taught in a sustainable manner remains an open question. An eight-month-long intervention based on the idea of using a structural approach to addition and subtraction, and particularly bridging through ten, was implemented in four Swedish first-grade…