This lecture reports on aspects of a larger research programme focused on studying mental mathematics in elementary and secondary mathematics classrooms. It specifically addresses an unplanned aspect that became salient through the work conducted in these classrooms. In this research programme, mental mathematics sessions are designed on a variety…

We report on and validate a system for ranking the cognitive demand of mathematical tasks. In our framework, task rankings are determined by the sequences of units and unit transformations students might use to solve each task. Using this framework, we ranked a set of 10 fractions tasks. We then interviewed 12 pre-service teachers to assess the…

To allow prospective teachers to see mathematics as a useful tool to make sense of the world we redesigned a university mathematics content course for prospective elementary school teachers in the context of exploring income distribution in the United States. This allowed the prospective teachers to learn mathematics in a meaningful context and…

The purpose of the present study is to examine the effects of an intervention in which mathematics e-book (EB) activities were supported by metacognitive scaffolding on kindergarten children's mathematics knowledge and mathematics reasoning. Participants were 60 Israeli children who studied in three intact kindergarten classrooms in the Arab…

We present an investigative activity that was set as part of a course of pre-service teachers of mathematics. The emphasis in the course was set on the importance of using the computerized technological tool for teaching the subject. The activity focused on investigating interesting geometrical conservation properties which are not known to the…

This paper studies how four primary-school in-service teachers develop the mathematical practices of conjecturing and proving. From the consideration of professional development as the legitimate peripheral participation in communities of practice, these teachers' mathematical practices have been characterised by using a theoretical framework…

Making connections between the representations of trigonometric functions and an interpretation of graphs of the functions are major challenges to many students. This study explores the effectiveness of the GeoGebra on grade 12 students' success in making connections between the representations of trigonometric functions and the interpretation of…

In this paper, differences in the implementation of a number activity called the snake game are studied. Nine Swedish preschool teachers worked in collaboration with a research team, enacting the same activity with their groups of 5-year-old children over a 3-month period. Variation theory forms the basis for the analysis of 67 videorecorded…

Purpose of the study is to investigate the effectiveness of the use of Realistic Mathematics Education (RME) approach on sixth grade students' statistical thinking levels. Mooney's (2002) statistical thinking framework describing four thinking levels across four different statistical thinking processes was used. This study utilized a…

Tasks play a central role in the mathematics classroom. Especially when teaching in a heterogeneous mathematics class, teachers should be able to find, select, modify, and assign tasks adequately. The focus in this paper is on adaptivity to cognitively activate all learners at the individual level, and on teachers' abilities to allow for such…

School life in England (and beyond) is temporally structured, with learning planned as a time-limited activity, both within lessons and across units of work. Discourses of performativity and measurement pervade school life in many societies and, what we call "regulated time" controls school-based learning. In particular, primary…

Active learning in mathematics can lead to deeper understanding than passively listening to a lecture, yet recent studies indicate that didactic teaching dominates online tutorials. This study investigated student participation in three types of activity: solving mathematical problems via polling, on-screen activities on a shared whiteboard and…

Background: Previous research has shown that students often struggle to understand algebraic expressions and solve equations, and that traditional instructional approaches may not be sufficient to address these challenges. While the use of technology and physical manipulatives independently has been shown to support students' conceptual…

The facts show that the mathematics achievement of Indonesian students is still very low. One of the causes of this problem is that the learning model used by the teacher is still conventional. This study aims to describe the activities of Mathematics Prospective Teachers (MPT) in completing assignments/projects using the Outdoor Learning…

Algebra as a study of quantitative relationship is one of four conceptions of school algebra which serves as a foundation for the concept of function. However, there is still a lack of attention to this particular relationship, especially in early algebraic reasoning. This study aims to investigate how the aspect of quantitative relationship in…