This paper explores students' ways of thinking about the average rate of change of a multivariable function and how they generalize those ways of thinking from rate of change of single-variable functions. I found that while students thought about the average rate of change of a multivariable function as the change in the independent quantity with…

Multiplicative thinking is a critical stage in mathematical learning and underpins much of the mathematics learned beyond middle primary years. Its components are complex and an inability to understand them conceptually is likely to undermine students' capacity to develop beyond additive thinking. Of particular importance are the ten times…

Researchers have identified challenges students face when modeling dynamic situations. This report discusses the results of semi-structured clinical interviews with ten prospective secondary mathematics teachers who were provided with a dynamic image of a growing and shrinking cone. We asked the students to graph the relationship between the…

This paper reports on a study of choices about the use of a computer algebra system (CAS) or pen-and-paper (p&p) by a class of seven Year 11 Mathematical Methods (CAS) students as they completed a calculus worksheet. Factors that influenced students' choices are highlighted by comparing and contrasting the use of CAS and p&p between…

The new curriculum introduced in the Malaysian primary students; the Primary School Standard Curriculum (Kurikulum Standard Sekolah Rendah-KSSR) together with the school-based assessment (SBA) is a step taken by the Malaysian government to encourage thinking skills to students, specifically critical thinking skills. The study explores teachers'…

This study examined how small groups of second-grade children developed understandings of the concept of congruence while collaboratively exploring and solving problems with dynamic representations of triangles using Sketchpad on the iPad. One case study is presented to illustrate how young learners can infer geometrical relationships between…

The ubiquitous practice of providing worked solutions to exercises in mathematics education has been under-researched. Little is known about what elements of a worked solution are valued by students. This exploratory study sought in-depth feedback from six undergraduate students who experienced a range of worked solutions designed to encourage…

This proposal reports the findings from interviews with construction science students about their visualization of problems in a two-dimensional and a three-dimensional task. The specific research questions focused on the individual characteristics that students identify as influencing their spatial ability to generate internal and external…

Theories of collaboration exist at the interfirm and intergroup level, but not the intragroup or team level. Team interactions are often framed in terms of leadership and followership, a categorization which may, or may not, accurately reflect the dynamics of intragroup interactions. To create a grounded theory of collaboration, the Farmer's…

Although students' difficulties in developing and understanding proofs in mathematics is well documented, less is known about how students' example use may support their proof practices, particularly at the middle school level. Research on example use suggests that strategic thinking with examples could play an important role in exploring…

The goal of this study was to explore the educational potential of Minecraft. This project was conducted with 118 elementary-school students from Canada during the 2016-2017 school year. To explore the educational potential of Minecraft on the students, we designed a "Minecraft challenge" for students. 10 game levels of ascending…

In the current reform of mathematics classrooms teachers are charged with the role of facilitating collaborative groups during problem-solving activity. The challenge is for teachers to engage students in making mathematical meaning during collaborative group discussions. In this paper we draw on the concept of adaptive expertise to report on…

As a pedagogical approach, problem-based learning (PBL) has shown success for average and gifted students (HmeloSiver, 2004) and there are numerous incentives for its implementation in online learning environments (Savid-Baden, 2007; Chernobilsky, Nagarajan, & Hmelo-Silver, 2005). However, little research has been conducted regarding the…

This study explores how teachers understand and translate curriculum statements into concepts that are better suited to supporting student progress with rich mathematical problem-solving tasks. We report the actions of one experienced teacher of primary mathematics in charting the sequence of concepts and processes relevant to the above issue. We…

Questioning and discussion techniques are effective instructional methods that develop critical thinking and problem solving skills. There is often inconsistent implementation of these techniques, which can result in a negative effect on student achievement. This case study explored elementary, middle, and high school teachers and evaluators'…