The variational thinking of high school students based on mathematical connections was analyzed through a laboratory on linear functions. This qualitative research based on design was developed in three phases: diagnostic test, implementation of the mathematics laboratory and final test, with students from a public institution in Barranquilla,…

This case study explores how 12-13-year-old students encounter proportional reasoning while working with geometric patterning tasks using concrete materials. The focus is on the students' use of spontaneous concepts when first dealing with such patterns in the context of collaborative work. Based on video recordings of a single lesson, a…

This article revisits and expands upon a previous phenomenographic study characterising the qualitatively different ways in which South African undergraduate physics students may experience the use of +/- signs in one-dimensional kinematics (1DK). We find the original categorisation as applicable for interpreting Swedish university-level students'…

This article aims to analyze the process of the progressive mathematization of the concept of the function by secondary school students through the resolution of a free fall situation. A free-fall mathematical situation was designed and experimented using the Tracker software to obtain movement data. Worksheets and conversations were collected…

The mathematical representation ability is essential in solving mathematical problems, especially in algebraic expressions problems. Therefore, it is crucial to have a valid design of learning activities to support students' mathematical representation ability. Several previous studies claimed that realistic mathematics education is one of the…

This article provides insights into Grade 11 learner understanding of the roots of quadratic equations, how learners used solution strategies to find equations with given roots, how they determine the unknown values and the other root when one root is given and how they determine the unknown values when two roots of the equation are given. The…

In this paper, we explore student solutions to a free response mathematical assessment task which had opportunities for students to notice structural properties in the context of number systems. In total, 308 students aged between 10 years to 13 years participated in the study. Their responses were analysed to determine whether they noticed…

The mathematics curricula of countries such as the United States, Singapore, Australia and New Zealand have started to incorporate the teaching of algebra in early childhood education. From this perspective, our study has two objectives: (a) to design a learning trajectory and teaching itinerary introducing patterns for children between the ages…

This article uses the concurrent mixed methods design to explore the errors made by 171 Grade Seven learners in algebraic problem-solving within the Assin Central Municipality in Ghana. The participants were categorized into low-achieving and high-achieving groups based on their performance in a pretest, to help provide a detailed examination of…

The purpose of this study is to identify the teaching styles and problems faced by teachers as they attempt to cultivate higher-order thinking skills (HOTS) in the topic of quadratic equations. This study used a qualitative approach via structured interview involving four participants who are experienced mathematics teachers from three districts…

Generalisation is a skill that enables learners to acquire knowledge in general, and mathematical knowledge in particular. It is a core aspect of algebraic thinking and, in particular, of functional thinking, as a type of algebraic thinking. Introducing primary school children to functional thinking fosters their ability to generalise, explain and…

In this paper, we explore how students' algebraic noticing's and explanations changed across a two-year period with the introduction of designed instructional material. The data in this report is drawn from n=53 Year 7-8 students' responses to a free-response assessment task across two different years. Analysis focused on how students noticed and…

The purpose of this study was to determine the extent to which professional development on assessment for learning improves pre-service teachers' self-regulated learning. Helping students develop self-regulation abilities in learning and assessment remains difficult due to the widespread culture of summative assessment in teacher education. A…

The learning of algebra represents a difficulty within the mathematics learning process. Precisely because of their epistemological and ontological nature, semiotics provides a good key to understanding the main difficulties that hinder the learning of algebraic objects. The answers to a large scale assessments task that requires a treatment in…

Majority of the students regarded algebra as one of the difficult areas in mathematics. They even find difficulties in algebraic expressions. Thus, this investigation was conducted to identify common errors in algebraic expressions of the preservice teachers. A descriptive method of research was used to address the problems. The data were gathered…