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…

A customized guide about liberatory design thinking processes that have been tested within college settings to support changes that enhance equity in policies and practices within institutions. This research is based on case studies of several institutions, including focus group interviews with the campus design teams and an analysis of artifacts.…

The purpose of this study was to gain insight into 30, first year calculus students' understanding of the relationship between the concept of vertex of a quadratic function and the concept of the derivative. APOS (action-process-object-schema) theory was applied as a guiding framework of analysis on student written work, think-aloud and follow up…

How children play around with new numerical concepts can provide important information about the structure and patterns they notice in number systems. In this chapter, we report on data from 243 second graders who were asked to fill in missing numbers on a number path (encouraging them to play around with numbers less than zero) and to solve…

Success in Algebra I often predicts whether or not a student will pursue higher levels of mathematics and science. However, many students enter algebra holding persistent misconceptions that are difficult to eliminate, thus, hindering their ability to succeed in algebra. One way to address these misconceptions is to implement worked-examples and…

Background: Engaging students in computer-assisted guided inquiry learning has great potential to scaffold their scientific understanding: Students are expected to improve their scientific problem-solving skills, and at the same time gain a deep conceptual understanding of the subject-matter. Additional generative activities such as creating video…

Quantum mechanics has completed century since its genesis. Quantum mechanics is taught at various levels-starting from school and colleges to universities. Regression methods are introduced at under graduate and post graduate levels to solve Schrodinger equation for finding solutions of various trivial and non-trivial physical problems. The common…

Introducing new concepts to learners in an order of increasing complexity appears to be beneficial for learning, but typically introduction of concepts does not always adhere to this principle. We examined whether introducing new algebra concepts in a contrasted manner or in an order of increasing complexity instead of a different more typical…

In this article, the authors present the use of digital tape diagrams--implemented using GeoGebra (2001) dynamic mathematics software--as a support to static diagrams to pose and solve proportional reasoning tasks. They show how dynamic sketches can allow students to explore standard tasks in proportional reasoning in ways that emphasise…

This informal essay is based on a presentation James Tanton gave at the Australian Association of Mathematics Teachers (AAMT) 'Why Maths?' Conference in 2019. It begins by offering two first steps to problem-solving that Tanton believes are key for finding success--and joy--in doing mathematics: (1) Be human! Have an emotional reaction to the…

Background and Context: In today's increasingly digital world, it is critical that all students learn to think computationally from an early age. Assessments of Computational Thinking (CT) are essential for capturing information about student learning and challenges. When programming is used as a vehicle to foster CT skills, assessment of CT…

As algebra teachers, the authors explore the following question in this article: "How can algebra 1, algebra 2, and precalculus teachers support students to develop algebraic reasoning and understanding of structure that can serve them in day-to-day algebraic computation?" The article shows how the algebraic identity "(a +…

In the study reported on here I evaluated the alignment between the Annual National Assessment (ANA) and Trends in International Mathematics and Science Study (TIMSS). Theoretical perspectives were drawn from the Survey Enacted Curriculum (SEC), while quantitative correlational methods were used to determine the alignment between ANA and TIMSS…

Understanding equivalence is fundamental to STEM disciplines, yet misunderstandings and misconceptions inhibit students from fully appreciating or leveraging the concept. Using the game-based algebraic notation system, From Here to There! (FH2T), students explore ideas of equivalence by dynamically transforming expressions or equations among…

Purpose: Most literature has focused solely on either knowledge about number sense or understanding of fractions. To fill the research gap, this study examined pupils' abilities in both number sense and fractions. In particular, it investigated Year 4 and Year 5 pupils' use of strategies in developing their fraction sense. Methodology: This study…