Scientific reasoning is an important skill that encompasses hypothesizing, experimenting, inferencing, evaluating data and drawing conclusions. Previous research found consistent inter- and intra-individual differences in children's ability to perform these component skills, which are still largely unaccounted for. This study examined these…

Purpose: This paper aims to compare two types of prompts, encouraging participants to think about real-world examples or engineering principles to show how these two approaches can result in vastly different design practices. Design/methodology/approach: Two studies (N = 20, N = 40) examine the impact of two different prompts. Non-expert students,…

The purpose of this paper is to investigate students' engagement in computational thinking (CT) and programming with MATLAB when solving a mathematical task in a programming course at the undergraduate level. The data collection method is participant observation of three groups of three students presented with a mathematical task to solve. The…

The present study contributes to knowledge about how to design tasks that benefit from dynamic software in math education, comparing practice performance and learning outcomes among 129 students practicing on two different task designs using GeoGebra. The task designs differed with respect to the presence or absence of guidelines on how to solve…

Confidence and its accuracy have been most commonly examined in domains such as general knowledge and learning, with less study of other domains, such as applied knowledge and problem solving. Monitoring accuracy in real-world competencies may depend on characteristics of the domain. In this study, we examined whether monitoring accuracy, both…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

Mathematical knowledge for teaching is a complex web of knowledge domains. In this article, we share findings from an 18-month professional development project that aimed to improve middle school mathematics teachers' mathematical knowledge for teaching (MKT) of proportional reasoning by focusing on the critical analysis of mathematical tasks and…

In this article, we explore the power relationships and positioning that occurred between caregivers and teachers who engaged in mathematics tasks as a part of a year-long project involving workshops. Specifically, we explore the shifts in power and positioning that occurred when the tasks were grounded in the caregivers' funds of knowledge, in…

Research in psychology and in mathematics education has documented the ubiquity of "intuition traps" -- tasks that elicit non-normative responses from most people. Researchers in cognitive psychology often view these responses negatively, as a sign of irrational behaviour. Others, notably mathematics educators, view them as necessary…

This paper focuses on pre-service mathematics teachers' geometrical construction processes while using a duo of artefacts, namely the paper-and-pencil environment (PPE) and a dynamic geometry system (DGS). The participants of this case study were two pre-service mathematics teachers, who had limited DGS experiences in solving geometry tasks. The…

This study sought to further explain the association between general anxiety symptoms and impaired problem-solving by testing whether this occurs, in part, through a reduced ability to retrieve event-level, specific autobiographical memory (AM). Participants (N = 301; M age = 28.2 SD = 7.7, 55.8% female) completed assessments of the retrieval of…

In this report, we discuss background research on the development of student understanding of quadratic functions and present a provisional learning progression for quadratic functions and quadratic equations. We also describe task shells that are linked to the learning progression. The learning progression and task shells can be used as a…

We articulate a student perspective on task design in mathematics education, foregrounding a dynamic relationship between intentions of task designers, teachers, and students. First, we characterize a student perspective on task design. Second, we provide theoretical perspectives that we use as tools to account for different facets of task design…

A commonly accepted claim in mathematics education is that there is a relationship between the cognitive demand of mathematical task enactments and students' subsequent learning. One study often cited to support this claim is Stein and Lane (1996), and in 44% of those citations, Stein and Lane (1996) is the sole reference provided. Citation…

Both creativity and humor are high-level cognitive functions and complex concepts. Although creativity and humor are generally deemed positively correlated, it has been difficult to explicitly identify their relationship with each other. The cognitive process of creativity includes divergent thinking, insight, and remote association, whereas humor…