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…

Decimals and the related areas of ratio and proportion are recognised as one of the most challenging and complex areas of mathematics for young children to learn. In this study, four dynamic digital representations were used by Year 4 (9-10 years old) students in a set of video-recorded, individual task-based interviews to explore key concepts of…

While proof has been studied from different perspectives in the mathematics education literature for decades, students continue to struggle to build proof comprehension. Complicating this, the manner in which proof comprehension is assessed largely remains to be the definition-theorem-proof format in which students are asked to reproduce proofs or…

Entrepreneurship education is critical in encouraging students' innovation, creativity, and entrepreneurial spirit. It provides essential skills and knowledge, enabling them to open their creative potential and apply innovative thinking across diverse professional fields. With the widespread application of large language models in education,…

The aim of this paper is to describe and analyze how a group of prospective teachers create problems to develop proportional reasoning either freely or from a given situation across different contexts, and the difficulties they encounter. Additionally, it identifies their beliefs about what constitutes a good problem and assesses whether these…

This article presents a case study that explores digital experiences in statistics teaching within Danish lower secondary school, focusing on the development of students' statistical concepts. The study tracks the progress of a student named Frida, who engages with the digital tool TinkerPlots over the span of a year. Frida developed a unique…

Mathematics educators and researchers have increasingly integrated social justice-oriented tasks into their classrooms. Teaching mathematics for social justice (TMfSJ) aims to help students develop mathematical knowledge in ways that promote students' abilities to critique the communities of which they are members (Ellis & Malloy, 2007;…

The evolution of mathematics coincided with advancements in its teaching. The 19th and 20th centuries marked a pedagogical revolution in mathematics education. This paper argues that Bruner's (1966) model, Gagné's (1985) taxonomy, innovative teaching methods emphasizing research and problem-solving, and the inclusion of data analysis topics have…