This qualitative research study uses middle-grades students' numerical reasoning to model their symbolic representations of the relationship between two multiplicatively related unknowns on an algebra task. Students in sixth grade through ninth grade participated in clinical interviews that assessed their numerical reasoning using the Number…

Successful integration of problem-solving in mathematics classrooms lies mostly with the assistance and support teachers get. Many studies have been conducted on the strategies teachers can use to integrate problem-solving in their teaching of mathematics, however, few studies have been conducted on frameworks/models that can assist teachers and…

This paper explores the affordances of mobile learning in developing frameworks for discourse analysis. Specifically, this paper examines the commognitive analysis of classroom discourses in virtual learning environments (VLEs) and how it resolves the challenges of discourse analysis in face-to-face (F2F) settings. With the ongoing social turn of…

The rapid development of large language models (LLMs) presented opportunities for the transformation of science and STEM education. Research on LLMs was in the exploratory phase, characterized by discussions and observations rather than empirical investigations. This study presented a framework for incorporating LLMs into Science and Engineering…

Self-regulated learning (SRL) is a critical component of mathematics problem solving. Students skilled in SRL are more likely to effectively set goals, search for information, and direct their attention and cognitive process so that they align their efforts with their objectives. An influential framework for SRL, the SMART model, proposes that…

We re-examine a Malawian teacher's lessons which, using the framework of mathematic problem-solving developed by Polya, the typology of levels of task demand from Stein and colleagues and Malawi's description of learner-centred education (LCE), were described as teacher-centred and evaluated as 'not good'. We studied seven video-recorded circle…

Problems of developing subject education and science have become more acute during different social changes. The most problematic is the teaching of exact disciplines, including mathematical disciplines (mathematics, algebra, geometry), which form knowledge for working in high-tech industries. It is worth noting that the methodology of teaching…

When teachers, researchers, and students describe productively responding to moments of failure in the learning process, what might this mean? Blending prior theoretical and empirical research on the relationship between failure and learning, and empirical results from four data sets that are part of a larger design-based research project, we…

Fractions are perceived as one of the most difficult areas in school mathematics to learn and teach. The most frequently mentioned factors contributing to the complexity are fractions having five interrelated constructs (part-whole, ratio, operator, quotient and measure) and teachers' pedagogical approaches to address these constructs. The present…

A historical review of mathematics textbooks suggests a canonical method to solving equations that teachers often see as "the" way to solve equations. In this paper, we examine data from a nationally-distributed sample of 524 secondary mathematics teachers who responded to scenario-based survey items that represent the instructional…

In this paper, we present a novel approach to defining, teaching, and assessing creativity by examining its origins and delineating the processes involved. The rationale for introducing this framework developed from studying existing thinking and questioning the current metrics for measuring creativity, which we posit are unfit for purpose. We…

Similar content has tremendous utility in classroom and online learning environments. For example, similar content can be used to combat cheating, track students' learning over time, and model students' latent knowledge. These different use cases for similar content all rely on different notions of similarity, which make it difficult to determine…

This study proposes a framework for investigating how preservice mathematics teachers notice students' reasoning about comparing distributions, including preservice teachers' attention to statistical elements used by students, interpretation of students' understanding, and decision about how to respond to students' statistical reasoning. The…

Science education has an important role to play in supporting our young people to meet the complex challenges of the modern age. Students need a curriculum that can prepare them to work collaboratively, competently and confidently to address the wicked "glocal" problems of our time. Rangatahi themselves recognise this - those involved in…

This conceptual paper proposes a model to describe the quality of student dialogue during participative collaborative problem solving. Drawing on the participation metaphor of learning, we argue that the construct of mathematical sophistication is useful to describe the quality. We then present two frameworks, mathematical competencies and…