Calculus has frequently been called one the greatest intellectual achievements of humankind. As a key transitional course to college mathematics, it combines such elementary ideas as rate with new abstract ideas--such as infinity, instantaneous change, and limit--to formulate the derivative and the integral. Most calculus texts begin with the…

The modelling approach to teaching and learning mathematics emphasizes the usefulness of mathematics in the real-world. The aim of the current study is to examine whether engagement in modelling activities provides learners an opportunity to expand their knowledge of a specific concept -- the "average" concept. Our data include…

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…

Teacher professional learning occurs across various contexts. Previous studies on teacher learning and changes in practice have focused on either classroom contexts or learning communities outside of school, but have rarely investigated teacher learning across multiple contexts. Investigating teacher learning across the double contexts of…

This study examines how joint exploration is established and maintained among students and the teacher in secondary mathematics classrooms. We use the theoretical perspective of positioning to conceptualize joint exploration as involving the negotiation and coordination among participants to position students with epistemic agency and authority.…

The Common Core State Standards for Mathematics emphasize the importance of developing students' conceptual understanding, mathematical reasoning, and problem solving skills. This is a shift from the traditional approach to teaching mathematics and many teachers rely on curriculum resources to help them meet these new standards and expectations.…

In response to restrictions on visitors within school buildings during the COVID-19 pandemic, the evidence-based math fact fluency procedure known as the taped problems intervention was adapted for use in a virtual setting. The present study used a multiple-probe across participants design to evaluate the effects of the adapted intervention on the…

This study investigated preservice middle school mathematics teachers' (PSTs) understanding of proportional and nonproportional relationships and their abilities to differentiate these relationships from each other. The PSTs' abilities to interpret and represent proportional and nonproportional situations and solution strategies were also…

The number sequences describe a hierarchy of students' concepts of number. This research uses two defining cognitive structures of the number sequences--units coordination and the splitting operation--to model middle-grades students' abilities to write linear equations representing the multiplicative relationship between two unknowns. Results…

The authors start from the premise that mathematical understanding and skills are fundamentally important in STEM education as they underpin the three other discplines of STEM. They describe how contextualised integrated STEM projects can bring mathematics into the foreground with digital technologies--such as Kitsi blocks. They outine a project…

The authors describe activities designed to teach the concept of weight to five and six year old children, using the imaginary 'Measureland' and its brand-new ride 'The Zipline Balancer'. They explore how they addressed misconceptions and insights are provided into the evolving measurement understandings of young children.

Although numerous studies have investigated how technology affects academic achievement, very few have focused on the purpose of the use of technology in mathematics education. This current study examines how student teachers (STs) benefit from GeoGebra as one of the Dynamic Geometry Software (DGS) while solving continuity problems. In order to…

Professional problem-solving practice in physics and engineering relies on mathematical sense making--reasoning that leverages coherence between formal mathematics and conceptual understanding. A key question for physics education is how well current instructional approaches develop students' mathematical sense making. We introduce an assessment…

The low performance of Grade 4 learners in the mathematical concept of word problems involving multiplication remains a concern for many researchers in mathematics education. Several studies conducted have largely focused on improving learners' performance on bare problems involving multiplication, with little focus on contextual problems. The…

This article describes a study of how Chinese preservice teachers unpacked a learning goal pertaining to adding fractions and understanding the concepts underlying the operation. Based on work in the USA by Morris, Hiebert, and Spizter ("Journal for Research in Mathematics Education," 40(5), 491-529, 2009), 50 Chinese preservice teachers…