This study investigates geometry teachers' evaluations of problems that use visual arts contexts. We ask, "how do teachers' evaluations relate to the four arguments justifying the geometry course?" and "How do teachers draw on the APPRAISAL system to evaluate sample geometry problems from textbooks?" Nine high school teachers…

Teaching children with autism spectrum disorder (ASD) academic skills supports their future opportunities. For example, early number sense skills are predictive of future mathematical success for all children including children with ASD. Yet, research on foundational early childhood mathematics skills of children with ASD is limited. This study…

Performance tasks enable the development of not just the knowledge but also the skills of students. Unfortunately, teachers find it challenging to prepare their performance tasks. To help teachers, an authentic framework for the preparation of performance tasks should be utilized. GRASPS, as an assessment model, can help teachers develop authentic…

Adverse childhood experiences (ACEs) can impact an individual physically, emotionally, and socially while also influencing cognitive development and academic outcomes. Mathematics learning requires cognitive clarity and the ability to solve problems and make decisions. Guided by the contemporary theory of trauma, the theory of allostasis, and…

Comparing health risks that include ratios of integers (e.g., 12 in 1,000) is challenging. We tested whether a worked-example intervention with number-line visual displays improved adults' risk-comparison accuracy, whether pretest confidence moderated learning, and which individual differences related to accuracy. Replicating prior work, U.S.…

In this article, we seek to understand how university students learn to use programming as an instrument for 'authentic' mathematical investigations. We use the instrumental approach as a framework, focusing on how the transformation of the programming language into an instrument requires that the user develops or mobilizes multiple schemes at…

The Action-Process-Object-Schema (APOS) theory is applied to study student understanding of implicit differentiation in the context of functions of one variable. The APOS notions of Schema and schema development in terms of the intra-, inter-, and trans-triad are used to analyze semi-structured interviews with 25 students who had just finished…

This research aimed to determine the differences of mathematical communication skills based on cognitive styles and gender. This research was a mixed-method with sequential explanatory design. The population was grade XI students at Senior High School in Jambi City consisting of 53 male and 72 female students. The study used a total sampling. The…

Practices within research mathematics can and do serve as models for mathematics education. However, typically such inspirations impose a devastating narrowness in relation to reflections on mathematics. This narrowness I refer to as the "banality of mathematical expertise". Reflections on mathematics can be expressed through a…

In this study, we propose the notion of a socio-mathematical norm to explore the affective aspects of a classroom in the context of problem posing. Our case is a gifted and talented mathematics classroom with twelve students. The primary source of data consists of forty-three mathematics lessons. Our theoretical stance defines two dimensions of a…

Play is central to children's learning and development in the early years, including the learning of mathematics. The aim of the present study was to explore how play skills are related to mathematical skills in toddlers by examining the correlations between different kinds of play skills and mathematical skills, and how level of play skills is…

Creativity is an understudied topic in elementary school mathematics research. Nevertheless, we argue that creativity plays an important role in mathematics, but that more research is needed to understand this relation. Therefore, this study aimed to investigate this relation, specifically between domain-general creativity, domain-specific…

Spurred by Kilpatrick's (1987) "Where do good problems come from?", this study explores problem-posing triggers of experienced problem posers for mathematics competitions. Triggers are conceived as instances of noticing, where an impulse draws a poser's attention and "triggers off" a mathematical re-action, one of the outcomes…

Long have we known that reasoning abilities are linked to learning, and specifically to learning mathematics. Even intelligence, considered a controversial construct, plays a significant role in the research on the explanation of academic performance. This article intends to highlight some important cognitive abilities or dimensions relevant to…

There is a growing knowledge base in mathematics education highlighting the importance of teachers' cognizance about what and how they are noticing, namely considerations about their attending, interpreting, and decisions to respond on the basis of students' thinking. However, less focus has centered on those in teacher leader positions and how…