The paper presents findings from a study that examined, through the lens of the Image Having layer of the Pirie-Kieren model, the qualitative characteristics of the images that different children formed when engaging with eight, novel partitive quotient tasks. The Image Having layer is the first point of abstraction within the Pirie-Kieren model.…

Wheel-spinning is unproductive persistence without the mastery of skills. Understanding wheel-spinning during the use of intelligent tutoring systems (ITSs) is crucial to help improve productivity and learning. In this study, following Beck and Gong (2013), we defined wheel-spinning students (unsuccessful students in ITSs) as those who practiced…

Background: Previous research in the field of content and language integrated learning (CLIL) has not yet comprehensively investigated the interaction between learners' expertise and the instructional effectiveness. Aims: Taking cognitive load theory as the theoretical framework, a study was conducted to investigate the expertise reversal effect…

This research investigates the significance that the development of creativity in mathematics classes has for the preservice teachers from a master's program in secondary school teaching, who are not trained on how to develop creativity. In the master's final projects, preservice teachers reflect on their teaching practice at school and propose…

Mathematics teacher education programs in the United States are charged with preparing prospective secondary teachers (PSTs) to teach reasoning and proving across grade levels and mathematical topics. Although most programs require a course on proof, PSTs often perceive it as disconnected from their future classroom practice. Our design research…

The application of mathematical skills is essential to our daily routine and is foundational for numerous disciplines. Among various computer-supported learning methods, Digital Game-Based Learning (DGBL) has been perceived as a promising method in teaching mathematics, promoting students' interest, and motivation. Therefore, the aim of this…

In this paper, we report on changes to teachers' knowledge and practices as a result of their participation in a professional learning initiative focused on cognitively challenging tasks and the pedagogies for enhancing student reasoning as such tasks unfold. Data from 239 primary teachers who responded to an online pre- and post-professional…

The goal of this paper is to present a framework of researcher knowledge development in conducting a study in mathematics education. The key components of the framework are: knowledge germane to conducting a particular study, processes of knowledge accumulation, and catalyzing filters that influence a researcher's decision making. The components…

Recent research in problem solving has shifted its focus to actual classroom implementation and what is really going on during problem solving when it is used regularly in classroom. This book seeks to stay on top of that trend by approaching diverse aspects of current problem solving research, covering three broad themes. Firstly, it explores the…

The phenomenon of wheel spinning refers to students attempting to solve problems on a particular skill, but becoming stuck due to an inability to learn the skill. Past research has found that students who do not master a skill quickly tend not to master it at all. One question is why do students wheel spin? A plausible hypothesis is that students…

New Zealand and Australian curricula require students to learn about weight/mass for at least six years. However, little research identifies what should be taught. This study reports cognitive interviews with 17 Year 9 students who were asked "how heavy is my rock?" Only one student demonstrated some understanding of how to use analogue…

The purpose of the study was to meta-synthesize research findings on the effectiveness of problem posing and to investigate the factors that might affect the incorporation of problem posing in the teaching and learning of mathematics. The eligibility criteria for inclusion of literature in the meta-analysis was: published between 1989 and 2011,…

Background: Robot-math is a term used to describe mathematics instruction centered on engineering, particularly robotics. This type of instruction seeks first to make the mathematics skills useful for robotics-centered challenges, and then to help students extend (transfer) those skills. A robot-math intervention was designed to target the…

This study examined 100 beginning teachers' transfer of learning when utilising Information Communication Technology-enhanced activity-based learning activities. The beginning teachers had participated in a professional development program that was characterised by "learning technology by collaborative design" in their final year of…

The two research questions that guided this study were: (1) How do preservice teachers develop mathematical knowledge for teaching during a coordinated math methods course and field experience? and (2) What types of portfolio tasks lend themselves to documenting mathematical knowledge in teaching? Six, female, elementary (K-8) teacher candidates…