Argumentation activities, such as constructing and communicating claims, critiquing others' ideas, and evaluating the strengths and weaknesses of claims, can play a foundational role in students' educational development. Yet there is more to understand about utilising these activities for effective mathematics learning. This paper discusses an…

We report on 25 Year 5-6 students' written responses to two items taken from an assessment of mental computation fluency with multiplication, alongside their reasoning of the strategy they had employed, which may or may not have made use of the associative property. Coding of this interview data revealed four distinct levels of conceptual…

This paper articulates a stance on the study of students' meaningful mathematics understanding with multiple representations. We integrate Thompson's theory of quantitative reasoning and Dreyfus' theory of multiple representations in our approach to frame and conduct empirical investigations of the study of meaningful understanding of function. We…

Research findings and reform-oriented standards emphasise the importance of mathematical connections in support of students' conceptual development. Previous research on teachers attending to mathematical connections has tended to focus on expert teachers' practice. Complementing previous research, this study describes how a cohort of twelve…

This paper explores misconceptions and errors (M/Es) of eighth-grade students in Nepal with a quasi-experimental design with nonequivalent control and experimental groups. The treatment was implemented with teaching episodes based on different remedial strategies of addressing students' M/Es. Students of control groups were taught under…

"Where Mathematics Comes From" (Lakoff & Núñez 2000) proposed that mathematical concepts such as arithmetic and counting are constructed cognitively from embodied metaphors of actions on physical objects, and four actions, or 'grounding metaphors' in particular: collecting, stepping, constructing and measuring. This article argues…

Feedback in exploratory learning systems has been depicted as an important contributor to encourage exploration. However, few studies have explored learners' interaction patterns associated with feedback and the use of external representations in exploratory learning environments. This study used Fractions Lab, an exploratory learning environment…

Problem solving is at the heart of mathematics, and is known to support learning for a diverse range of children. However, challenges can be encountered when teaching mathematics through problem solving. This article provides insights from research literature into: (1) the nature of the challenges; and (2) some ways that problem solving can be…

Students thrive when presented with tasks that are approachable, challenging, and interesting. Remembering to challenge all students is essential, not just those who excel in mathematics; teachers need to open the door to meaningful mathematics for every learner. In this exploration into subtraction patterns, teachers will see how curious young…

Teaching meaningful and productive mathematical argument in school requires teachers who are comfortable with diverse forms of mathematical justification. This study examines the written and oral justifications of pre-service middle school teachers (PSTs) in a single classroom, focusing on the types of justifications they use during the patterns…

This study aims to discover the effectiveness of the blended learning model in mathematics learning to improve the achievement of mathematical concepts. This study employed a quasi-experimental design with a non-equivalent control group. The experimental class was taught through blended learning, while the control class was taught through the…

Conceptual appropriation is central to the teaching-learning and development processes. The intellectual stage is expressed by writing, verbalization and the use of the object under construction, among other means of expression. This paper discusses the conceptual appropriation by means of the creation of collaborative situations in which the…

Many studies have reported on the influence of teachers' conceptions of variability on different aspects of their professional knowledge for teaching statistics and their classroom practices. However, research on these kind of conceptions is still scarce, particularly in Latin American countries like Venezuela. In an effort to help fill this gap,…

This paper analyzes the content and tasks involving quadratic equations in eight mathematics textbooks published during the period 2000-2012 at the uppersecondary level in Sweden. The study applies the theoretical "hypothetical learning trajectory" (HLT) framework combining "conceptual" and "procedural" knowledge. The…

One desired outcome of introductory physics instruction is that students will develop facility with reasoning quantitatively about physical phenomena. Little research has been done regarding how students develop the algebraic concepts and skills involved in reasoning productively about physics quantities, which is different from either…