Mathematical Communication Skills (MCS) refer to the students' ability to (1) arrange and link their mathematical thinking through communication; (2) communicate their logical and clear mathematical thinking to their friends, teachers, and others; (3) analyze and assess mathematical thinking and strategies used by others; and (4) use mathematical…

Research has indicated that students can be taught self-regulated learning (SRL) in scaffolding programs focusing on a fixed continuous practice (e.g., metacognitive question prompts). However, the fading role of scaffolding to prepare autonomous learning is often an overlooked component. A unique approach for fading is suggested that offers a…

We present a synthesis of the Onto-semiotic Approach (OSA) theoretical system to mathematical knowledge and instruction, while highlighting the problems, principles and research methods that are addressed in this approach and considering the didactics of mathematics as a scientific and technological discipline. We suggest that Didactics should…

When exposed to principal components analysis for the first time, students can sometimes miss the primary purpose of the analysis. Often the focus is solely on data reduction and what to do after the dimensions of the data have been reduced is ignored. The datasets discussed here can be used as an in-class example, a homework assignment, or a…

Whether one engages in truth-seeking and whether he or she is open-minded are indicative of his or her critical behavior when responding to problems at hand. This research sought to determine the behavioural tendencies of pre-service mathematics teachers in the solution of non-routine problems based on the indicators of truth-seeking and…

This chapter focuses on the development of concepts that children draw on as they work toward understanding negative numbers. Framed from a conceptual change lens, I discuss different interpretations children have of minus signs, numerical order, numerical values, and addition and subtraction operations and how children draw on these varied…

Literature on learning trajectories is reviewed, and challenges in developing designs to support responsive instruction are highlighted. A distinctive form of design called a "multi-dimensional instructional framework" is introduced. These frameworks span key dimensions of mathematisation, such as notating and distancing the setting,…

This paper reports on an investigation of the student interaction and group development of a four-student group during collaborative mathematics problem solving. Video and written transcript of the group interaction were analysed. The group problem solving has been described by the flow of negotiative events in terms of topics discussed within the…

This paper reports on a study of the instructional situation in high school Geometry that Hsu (2010) called Geometric Calculation in Algebra (GCA). In particular, we conducted a virtual breaching experiment in order to examine the extent to which high school teachers recognized breaches of two norms that we conjectured to describe geometry…

Many people are discussing the issues surrounding mathematics at all levels of education. Politicians, parents, students, universities, education departments all have a view about what the problem is and all have ideas about what should happen. This article represents a synthesis of the issues and implications of one of the problems evident in…

The aim of this study is to examine the mathematical problem-solving beliefs and problem-solving success levels of primary school teacher candidates through the variables of academic success and gender. The research was designed according to the mixed methods technique in which qualitative and quantitative methods are used together. The working…

Mathematics is not just memorized facts, but rather it is understanding how to approach and solve problems, and problem-solving requires linguistic proficiency. Too often, English learners' (ELs) relatively low math performance is dismissed due to their supposed "limited" English proficiency. Taking this perspective, a constructivist…

This study aims to identify the level of knowledge and practice on the implementation of higher-order thinking skills (HOTS) among mathematics teachers at a secondary school in the district of Terengganu. The study focused on the aspects of curriculum, pedagogy and assessment and compared them with demographic factors of the respondents. It used…

This study investigated the impact on Year 10 students' attitudes towards mathematics when learning mathematics in a sporting context. A closed ended, self-reported questionnaire with Likert type statements was used to collect data. Individual statements were analysed by comparing the percentage of students agreeing or disagreeing pre-teaching and…

Proficiency in mathematics involves the seamless synchronization of conceptual understanding, procedural knowledge, computational fluency, and problem solving (NMAP, 2008). Clearly, fluency with mathematics facts is one element embedded within mathematical proficiency and important for students with disabilities to develop. As more and more…