The examples used in the teaching-learning process of mathematics have a crucial role in fostering conceptual understanding, and some variables can affect instructors' qualified example usage. This longterm study focused on mathematics teachers' exemplification process in face-to-face and online learning environments. In this regard, the change in…

This study diagnoses and explores year eight students' misconceptions and mistakes in algebra. An in-depth exploration of students' misconceptions were carried out by conducting interviews based on the students' work as outlined in a cognitive map. Based on the cognitive maps, it can be seen that the students emphasize procedural knowledge rather…

It was aimed to reveal the informal statistical inferences of primary school students on the concept of variability. A phenomenographic research approach was adopted. A task was adapted and used as a data collection tool. Clinical interviews were conducted with 20 primary school students from each grade level. Data were analyzed within the context…

This action research study examined the effects of professional development on teaching for conceptual understanding in Algebra I. "Conceptual knowledge refers to knowledge of the underlying structure of mathematics-the relationships and interconnections of ideas that explain and give meaning to mathematical procedures" (Eisenhart et…

Research focusing on the home mathematics environment has shown mixed results across age groups. Using data from a large online survey, we explored parents' perceptions of the age appropriateness of home mathematics activities for their children. Children's ages ranged from one to 6 years old (N = 958). Activities spanned multiple domains of early…

On the one hand, mathematical software is ubiquitous in mathematics education. On the other hand, word problems are an important part of the curriculum, and they often require modelling skills. This is especially true with optimisation and extrema problems proposed to high school and undergraduate students. We propose two activities around extrema…

Proof is a fundamental aspect of mathematics. However, in the high school curriculum, it often receives uneven attention that is focused on form rather than understanding. One avenue for addressing this issue is to change and strengthen teachers' conceptions of proof. To explore this idea, we followed a group of teachers as they participated in a…

Research studies are abundant in pointing at how the transition from additive to multiplicative thinking acts as a core challenge for students' understanding of proportionality. This said, we have yet to understand how this transition can be supported, and there remains significant questions to address about how students experience it. Recent work…

We used citation cartography to answer the question, "what research agendas should we pursue, with respect to engagement and learning needs, to ensure that all students reach their potential?" First, we found that current research studying engagement and learning needs were located on the periphery of the field with few connections…

For students to develop adequate conceptual understanding about fractions, they require experiences that afford them opportunities to think flexibly about multiple interpretations of fractions. This article presents a sequence of lessons designed to offer such experiences for students in Years 3 and Year 4. The lessons adopt a challenging tasks…

Differential equations are widely used tools for modelling the world around us, making a course in differential equations a natural place for students to connect concrete mathematical applications to abstract concepts. Since students grasp the concepts better by applying them, introducing differential equations through modelling becomes essential.…

The purpose of this study was to examine the effects of a number line intervention with supported self-explanation on student understanding of fraction magnitude and quality of explanation. Participants were three U.S. middle school students with significant behavior problems. Participants were given eight lessons containing explicit instruction…

Engineering design is being increasingly included in elementary education, typically to provide students with opportunities to apply science and mathematics concepts while developing their engineering practices. An important question is how to prepare teachers who can help students develop more informed engineering practices during classroom…

Students' understanding of the meaning of the equal sign develops slowly over the primary grades. In addition to updating their representations of equations to recognize that the equal sign represents an equivalence relation rather than signaling an operation, students need to move beyond full computation to efficiently solve equivalence problems.…

Research has shown that there is a need to examine prospective teachers' development trajectories related to noticing expertise. An important content in the Spanish high school curriculum (16-18 years old) is the limit concept. Given the importance of this concept in the curriculum and the difficulties some prospective teachers have, developing…