The transition between arithmetic and algebraic thinking is challenging for students. One notable difficulty for students is understanding algebraic symbols--pronumerals. Researchers are exploring pedagogical approaches in seeking to address this issue. The current paper is contributing to this body of literature by illustrating how an online card…

This paper reports on teachers' perceptions of students learning as part of a project examining teacher practice and student learning when using "ScratchMaths" in their classroom programmes. The project used design-based methodology, incorporating video-recorded classroom excerpts; teacher interviews; and teacher analysis and review of…

This paper discusses the design modifications of a sequence of specified learning goals for teaching early number, which characterise an instructional resource developed in a design research collaboration with teachers in Mexican preschools. Highlighted are the types of research involvement that appear to be necessary in designing resources for…

This paper will elaborate five levels of algebraic generalisation based on an analysis of students' responses to Reframing Mathematical Futures II (RMFII) tasks designed to assess algebraic reasoning. The five levels of algebraic generalisation will be elaborated and illustrated using selected tasks from the RMFII study. The five levels will be…

In Realistic Mathematics Education (RME), students should reach formal mathematics knowledge and explore mathematics based on their informal knowledge. The problems chosen in the exploration process should apply mathematics to real-life situations and be suitable for students to explore and create mathematical structures. In the current study, the…

The aim of this study is to examine the experiences of secondary school mathematics teachers facing with the distance education process for the first time due to COVID-19 regarding the mathematics lessons. Therefore, this study employs a case study, which is one of the qualitative research types. The study is conducted with 52 secondary school…

This paper presents research activity in the solution of geometric tasks by mathematics teachers and by mathematics teacher trainees at a College of Education as part of an advanced courses. This activity tested the level of knowledge and ability to apply it in the solution of problems that can be solved in a number of ways: by using various tools…

The learning of mathematics poses specific linguistic challenges. Amongst them, teachers and students need to be able to unpack the language used in mathematics word problems to understand its context, discern the relationships between the known and unknown information, and identify relevant solution strategies. Prior research has described some…

Even in the digital age, learning mathematics at an academic level still requires much reading of mathematical text. Research has shown that reading mathematical text requires readers to engage with all the structures of the book and with its pedagogical voice, making connections, and plausible reasoning. Specific practices and strategies that…

Intelligent tutoring systems (ITSs) have drawn researchers' attention as a means of providing personalized learning content, adaptive feedback, and instructional strategies based on students' characteristics and learning needs. Few studies, however, have explored how prospective and practicing teachers integrate ITSs into their lessons. This study…

Problem solving is a central focus of mathematics teaching and learning. If teachers are expected to support students' problem-solving development, then it reasons that teachers should also be able to solve problems aligned to grade level content standards. The purpose of this validation study is twofold: (1) to present evidence supporting the use…

The South African Language in Education Policy (LiEP) advocates using African languages in the Foundation Phase (FP) which is the first phase of formal schooling in South Africa. This paper seeks to identify the challenges in implementing the language provisions prescribed in the LiEP in South Africa and within the region. Using the…

Providing adequate proof is one essential mathematical method, but it is a difficult task for many school-age students. While previous studies have revealed the cognitive factors of proving the proof, the function of affective factors and learning engagement has been largely unexplored. This study examined the effects and processes associated with…

To improve understanding of identities and inverses, and to provide a stronger foundation for future mathematics, Sandra Miles designed a two-part lesson that makes the relationship between identities and inverses explicit. This article illustrates Miles' teaching of the first part of the lesson, focused on addition and subtraction, and then gives…

The aim of this research is to advance in the teaching-learning process of representing quadratic functions, both with pencil and paper and with a technological tool. For this purpose, a didactic experience is presented. Firstly, it is explained in the traditional way how to graph a quadratic function; secondly, students are introduced to the…