This study examined whether practice with arithmetic problems presented in a nontraditional problem format improves understanding of mathematical equivalence. Children (M age = 8;0; N = 90) were randomly assigned to practice addition in one of three conditions: (a) traditional, in which problems were presented in the traditional "operations…

The emphasis on problem solving and problem solving courses has become a standard staple of most teacher preparation programs in mathematics. While opinions differ on whether problem solving should be integrated throughout the preparatory courses or teachers should also have a dedicated course for it, everybody agrees that problem solving skills…

Student mastery of rational number and proportional reasoning is a recognized challenge, yet supporting mastery is central within mathematics and science. This paper focuses on a 4-lesson teaching programme which was designed to foster mastery in the context of intensive quantities. Intensive quantities such as density, speed and temperature…

The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Here we argue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to…

The papers in the monograph address different topics related to mathematics teaching and learning processes which are of great interest to both students and prospective teachers. Some papers open new research questions, some show examples of good practice and others provide more information about earlier findings. The monograph consists of six…

This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…

This article describes a project inspired by Liping Ma's "Exploring New Knowledge" in which future 7-12 grade mathematics teachers enrolled in a fall 2013 capstone course at a typical regional state university were assigned fictitious student conjectures. These future teachers (all current high school mathematics teachers) were…

The teaching and learning of mathematics cannot be understood without considering the resolution of word problems. These kinds of problems not only connect mathematical concepts with language (and therefore with reality) but also promote the learning related to other scientific areas. In primary school, problems are solved by using basic…

This study aims to explore the influence of outdoor teaching among students, aged 13, on arithmetic performance and self-regulation skills as previous research concerning outdoor mathematics learning is limited. This study had a quasi-experimental design. An outdoor and a traditional group answered a test and a self-regulation skills questionnaire…

In this paper we discuss perceptions of the benefits of learner-generated podcasts for supporting postgraduate engineering students in a mathematics-intensive course. The course under study had previously been highlighted as one in which students had struggled to attain knowledge that formed an essential underpinning to their degree programme.…

The activity of posing and solving problems can enrich learners' mathematical experiences because it fosters a spirit of inquisitiveness, cultivates their mathematical curiosity, and deepens their views of what it means to do mathematics. To achieve these goals, a mathematical problem needs to be at the appropriate level of difficulty,…

If teachers are to adequately support development of their students' numeracy capabilities then they need to have an identity as a teacher of numeracy. A preliminary evaluation of a conceptual framework (Bennison & Goos, 2013) developed for use in a two-year study that seeks to understand this construct is presented. Initial findings about an…

Students explored variation and expectation in a probability activity at the end of the first year of a 3-year longitudinal study across grades 4-6. The activity involved experiments in tossing coins both manually and with simulation using the graphing software, "TinkerPlots." Initial responses indicated that the students were aware of…

This paper explores the physics of intelligence and provides an overview of what happens in the brain when a person is engaged in mental activity that we classify under thought or intelligence. It traces the formation of a concept starting with reception of visible or detectable signals from the real world by and external to the sense organs,…

The aim of this paper is to present a research on Hungarian 3th grade primary school textbooks from Romania. These textbooks are analyzed using two classifications. The first classification is based on how much creativity and problem solving skills pupils need to solve a given task. In this classification problems are gouped in three categories:…