This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

The sequence in which problems of different concepts are studied during instruction impacts concept learning. For example, several problems of a given concept can be studied together (blocking) or several problems of different concepts can be studied together (interleaving). In the current study, we demonstrate that the 2 sequences impact concept…

Spatial skills have been shown in various longitudinal studies to be related to multiple science, technology, engineering, and math (STEM) achievement and retention. The specific nature of this relation has been probed in only a few domains, and has rarely been investigated for calculus, a critical topic in preparing students for and in STEM…

Purpose: The purpose of this paper is to examine how elementary school teachers integrated technology into their mathematics teaching in classroom settings that were one-to-one computer environments for most of the day. Following a series of classroom observations and interviews, inductive qualitative analyses of data indicated that teachers felt…

This paper describes seven in-service teachers' interpretations of student statements about slope. The teachers interpreted sample student work, conjectured about student contributions, assessed the students' understanding, and positioned the students' statements in the mathematics curriculum. The teachers' responses provide insight into their…

This study examined the extent to which the iPad app, Spatial Temporal Mathematics (ST Math), diminished college remedial mathematics students' natural number bias and deepened their fraction conceptual understanding. In this quasi-experimental study one class played the ST Math fraction games for 8 weeks, and they were compared to a control class…

Each year, post-secondary institutions across the nation enroll thousands of students into developmental mathematics courses. Success rates are low for students placed in developmental mathematics courses employing traditional teaching practices. Secondary institutions utilizing more engaging pedagogies and high impact practices, such as…

Addition of fractions is an important foundation for students to experience success in mathematics. This mixed-methods study was conducted to measure the effectiveness of robotics as a mathematics manipulative with seventh grade students. Two groups of students were established: control and treatment. The control group received teacher-centered…

The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

This inquiry presents two fine-grained case studies of students demonstrating different levels of cognitive functioning in relation to bilateral symmetry and reflection. The two students were asked to solve four sets of tasks and articulate their reasoning in task-based interviews. The first participant, Brittany, focused essentially on three…

The new "Australian Senior Secondary Curriculum: Mathematics" contains more statistics than the existing Australian Curricula. This case study examines how a group of Queensland mathematics teachers define the word "statistics" and five statistical terms from the new curricula. These definitions are compared to those used in…

An algorithm is presented for factorising a quadratic expression to facilitate instruction and learning. It appeals to elementary geometry which may provide better insights to some students or teachers. There have been many methods for factorising a quadratic expression described in school text books. However, students often seem to struggle with…

By the time students reach the middle years they have experienced many chance activities based on dice. Common among these are rolling one die to explore the relationship of frequency and theoretical probability, and rolling two dice and summing the outcomes to consider their probabilities. Although dice may be considered overused by some, the…

In providing a continued focus on tasks and activities that help to illustrate key ideas embedded in the "Australian Curriculum," this issue focuses on the Statistics and probability strand and the sub-strand of Chance. In the Australian Curriculum (ACARA, 2015), students are not asked to list outcomes of chance experiments and represent…

This current study examined human children's and adults' automatic processing of proportion using a Stroop-like paradigm. Preschool children and university students compared the areas of two sectors that varied not only in absolute areas but also in the proportions they occupied in their original rounds. A congruity effect was found in both age…