Due to the learning paradox, students cannot have real difficulty in understanding a mathematical concept that they have not yet understood. There is a gap between real difficulties, directly experienced by students, and illusionary ones, only observed by researchers. This paper aims to offer a critical reflection on our understanding of the term…

Although there has been extensive research on students' understanding of the particulate nature of matter (PNM), there is still a lack of research on contexts that can be used to teach this challenging topic. In a previous design-based research study, the authors developed a teaching-learning sequence (TLS) on the PNM in the context of crystal…

Circle and disc are fundamental concepts introduced in middle school, forming the basis for many other mathematical ideas. Students often face challenges in comprehending circles, discs, and their basic elements. This research examines the processes of sixth-grade students in constructing circles, discs, and their essential components within a…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

Instructional quality dimensions of cognitive demands and instructional support have been shown to have an impact on students' learning gains. Existing operationalizations of these dimensions have mostly used comprehensive ratings that combine various subdimensions of task quality and interaction quality. The current study disentangles interaction…

This study examined a cohort of middle school pre-service mathematics teachers' understanding of the rate of change as they engaged in a model development sequence. By adopting a design-based research perspective, a model development sequence on the concept of rate of change has been designed and implemented as part of a mathematical modeling…

A wide array of conceptual change strategies attempted to address students' persistent alternative conceptions, yet there remained ubiquitous struggles of teachers teaching abstract and highly contentious science concepts. This study investigated the effectiveness of the novel Conceptual Change Framework of Instruction (CCFI) in teaching eclipses…

The field of science education has put effort into providing opportunities for students to position themselves as epistemic agents pursuing the goal of making sense of natural phenomena. However, students often struggle in adapting scientific practices to achieve the sense-making goal. In this position paper, we conceptualise students'…

Common divisor is one of the concepts that started to be learned in secondary school and forms the basis of many concepts. But students generally have difficulty in making sense of it. The purpose of this study is to investigate concept formation processes of common divisor through a case study on seven sixth grade students. To do this, we…

This paper describes a pilot study that explores students learning how to program via a multi-disciplinary approach. The study participants were eleven 6th grade students who learned programming fundamentals via music activities in a Scratch 3.0 environment. These activities included the programming of familiar melodies and the development of…

Using a randomized controlled trial, we examined the effect of a fractions intervention for students experiencing mathematical difficulties in Grade 5. Students who were eligible for the study (n = 205) were randomly assigned to intervention and comparison conditions, blocked by teacher. The intervention used systematic, explicit instruction and…

Background: Prior work has shown that middle school students struggle with algebra and that game-based educational technologies, such as DragonBox and From Here to There!, are effective at improving students' algebraic performance. However, it remains unclear which aspects of algebraic knowledge shift as a result of playing these games and what…

This study investigated relations between the distribution of practice problems in textbooks and students' learning of decimal arithmetic. In Study 1, we analyzed the distributions of decimal arithmetic practice problems that appeared in 3 leading math textbook series in the United States. Similar imbalances in the relative frequencies of decimal…

At present, environmental issues are of concern to all countries, especially for developing countries, and education on waste sorting is urgent. However, it remains a challenge to improve students' learning achievement and engagement in environmental education. Researchers have pointed out the potential of digital games for promoting students'…

Cognitive development of eighth-grade students, as identified by Jean Piaget, occurs during a time when many of them are transitioning between concrete operations and formal operations where the ability to think in abstract concepts becomes possible. Because of this period of transition, many eighth-grade students find difficulty in demonstrating…