Educators, researchers, and policy makers recognize that student participation in classroom mathematics conversations, especially explaining one's own thinking and engaging with others' ideas, can promote students' mathematics learning. However, precisely "how" participating in these ways supports learning has not often been examined in…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

Despite the introduction of Common Core State Standards and the National Council of Teachers of Mathematics urging educators to explore fundamental concepts in mathematics at a deeper level, the majority of mathematics education has remained aimed at initial skill acquisition. The result has led to students learning to mimic a standard set of…

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…

The purpose of this study is to examine cross-national differences in students' exploration strategies in a computer-simulated CPS (complex problem-solving) environment and to identify similarities and qualitative differences in the way Hungarian and Chinese students explore a CPS environment. In a sample of 187 Chinese and 835 Hungarian students…

There are various misconceptions students have when studied quadrilateral which encourages efforts needed to overcome these misconceptions. This study aims at overcoming misconceptions by designing learning trajectories in the topic of Quadrilateral applying the Realistic Mathematics Education (RME). Design research carried out at one of junior…

Retrieval practice has been widely studied as an effective strategy for enhancing memory. In this review article, we discuss how its effects on learning complex problem-solving procedures are less straightforward, however, with repeated studying of worked examples sometimes more effective than problem-solving practice. This worked example benefit…

Research has shown a bi-directional association between the (perceived) amount of invested effort to learn or retrieve information (e.g., time, mental effort) and metacognitive monitoring judgments. The direction of this association likely depends on how learners allocate their effort. In self-paced learning, effort allocation is usually data…

Background: Research indicates that implicit theories of intelligence, specifically growth mindset, are conducive to students' academic achievement and engagement. While much research has focused on the role of teachers and parents, it is unclear how implicit theories of intelligence operate in the peer context. Aims: This study examined the…

Background: The need to focus more on children's abilities to change requires new assessment technologies in education. Process-oriented assessment can be useful in this regard. Dynamic testing has the potential to provide in-depth information about children's learning processes and cognitive abilities. Aim: This study implemented a…

Transactive discussion during collaborative learning is crucial for building on each other's reasoning and developing problem solving strategies. In a tabletop collaborative learning activity, student actions on the interface can drive their thinking and be used to ground discussions, thus affecting their problem-solving performance and learning.…

Purpose: This study explores the achievements and process of a group of Chinese primary school teachers learning from a research-based school-university collaborative project. Design/Approach/Methods: We used qualitative methods to construct our research design, collecting data through participatory observations of weekly meetings, teacher…

Recent developments in language models, such as ChatGPT, have sparked debate. These tools can help, for example, dyslexic people, to write formal emails from a prompt and can be used by students to generate assessed work. Proponents argue that language models enhance the student experience and academic achievement. Those concerned argue that…

The goal of this paper is twofold. First, the paper clarifies and elaborates on an important theoretical construct called orientation with respect to understanding in mathematics, which denotes the degree to which students exhibit an inclination towards and demonstrate an earnest concern for understanding in mathematical learning. Second, the…

A solid foundation in mathematics is beneficial not only for individuals' concurrent and later academic achievement, but also for future career success and financial stability. Rational number knowledge plays a pivotal role in mathematical success, yet it is often regarded as a challenging area to grasp comprehensively. The dissertation aims to…