Specific acts of problem solving with rates and ratios were interpreted using a journey metaphor derived from Skemp's (1979) construct of director systems. To successfully undertake a problem solving journey a learner must recognise their starting place (present state), have a sense of destination (goal state), and co-ordinate sub-routes along the…

Inservice teachers, participants in a prior study on mathematics anxiety, were revisited to determine whether their levels of mathematics anxiety still existed and/or continued to change after 5 years teaching experience. A 98-item Likert-type survey, informal discussions, informal interviews, and questionnaire-guided narrative interviews were…

Fractions are a well-researched area; yet, student learning of fractions remains problematic. We outline a novel path to initial fraction learning and document its promise. Building on Freudenthal's analysis of the fraction concept, we regard "comparing," rather than "fracturing," as the primary activity from which students are…

A growing body of literature has identified quantitative and covariational reasoning as critical for secondary and undergraduate student learning, particularly for topics that require students to make sense of relationships between quantities. The present study extends this body of literature by characterizing an undergraduate precalculus…

Previous studies have shown that intentional learning through explicit instruction is effective for the acquisition of collocations in a second language (L2) (e.g. Peters, 2014, 2015), but relatively little is known about the effectiveness of incidental approaches for the acquisition of L2 collocations. The present study examined the incidental…

This paper reports results of a design experiment regarding young children's concepts of mass measurement. The research built on an earlier study in which a framework of "growth points" in early mathematics learning and a related, task-based, one-to-one interview to assess children's understanding of the measurement of mass…

This report describes the longitudinal development of one student, Drew, in terms of his unit concepts in area and volume measurement situations across Grades 2 through 5. Data were collected during individual interviews and an open-response assessment within the context of a four-year longitudinal teaching experiment. Results indicate that Drew's…

The technological pedagogical content knowledge (TPACK) framework is a nuanced lens to study teachers' 21st century professional knowledge and practice (Mishra & Koehler, 2006). Veteran teachers in 1:1 settings have not been the focus in TPACK research. In this mixed-methods study, veteran teachers were surveyed to determine their self-reported…

The Effective Classroom Practice project aimed to identify key factors that contribute to effective teaching in primary and secondary phases of schooling in different socioeconomic contexts. This article addresses the ways in which qualitative and quantitative approaches were combined within an integrated design to provide a comprehensive…

This study investigated children's understanding of area measurement, including the concept of area and the area formula of a rectangle, as well as their strategic knowledge for solving area measurement problems. Twenty-two fourth-graders from three classes of a public elementary school in Taipei, Taiwan, participated in a one-on-one interview.…

The aim of this research is to describe the development of the Science Teachers' Pedagogical Discontentment Scale, an instrument that measures the discontentment that arises in teachers as they recognize a mismatch between their own pedagogical beliefs and goals and their actual classroom practices. From a conceptual change perspective, we explore…

Multicultural education includes the design of learning environments according to different cultural characteristics and learners' respectful attitudes towards these characteristics. One of the teachers' expected competencies in multicultural education is recognizing learners' cultural characteristics and being respectful of these during the…

Why has large-scale standardised testing attracted such a bad press? Why has pedagogic benefit to be derived from test results been downplayed? The paper investigates this question by first surveying the pros and cons of testing in the literature, and goes on to examine educators' responses to standardised, large-scale tests in a sample of low…

This study aimed at investigating the progress of students' learning on multiplication fractions with natural numbers through the five activity levels based on Realistic Mathematics Education (RME) approach proposed by Streefland. Design research was chosen to achieve this research goal. In design research, the Hypothetical Learning Trajectory…

One of the objectives of any government is the establishment of an effective solution to significantly control crime. Identity fraud in Nigeria has generated global attention and negative publicity toward its citizens. The research problem addressed in this study was the lack of understanding of the dynamics that influenced the adoption and…