This paper addresses the continuing need for mathematics teachers to enrich their mathematical knowledge beyond the school curriculum, in order to effectively engage students in creative and imaginative thinking, particularly, but not exclusively, students who show exceptional promise. The author, a retired university professor, works staff and…

A robust understanding of place value is essential. Using a problem-based approach set within meaningful contexts, students' attention may be drawn to the multiplicative structure of place value. By using quotitive division problems through a concrete-representational-abstract lesson structure, this study showed a powerful strengthening of Year 3…

Professional bodies expect engineers to show competence in both mathematics and engineering topics such as mechanics, using their abilities in both of these to solve problems. Yet within engineering programmes there is a phenomenon known as "The Mathematics Problem", with students not demonstrating understanding of the subject. This…

This paper is premised on the fact that math can be an important tool in helping people make sense of the world. Math offers a unique and particular lens, helping people to focus on a range of characteristics from shape and amount to the relationship between the general and the particular. To promote math as a tool for making sense, early…

Concern about children's mathematics performance in Ireland and elsewhere has prompted a range of responses from researchers, policymakers, educators and the media. While policy-level responses in Ireland include revising curricula and implementing a numeracy strategy that calls for increased tuition hours, teachers have also drawn on a wide array…

The backdrop of this research is among others (1) the content of article 8 legislation national education system 20/2003 that the society takes the participation in planning and evaluating education, (2) the criterion of curriculum 2013 that is integrated and has a theme of natural environment, (3) the reality in the field showing that mathematics…

This exploratory study examined how pre-service teachers (PSTs) pose mathematical problems for free and structured mathematical problem-posing conditions. It was hypothesized that PSTs would pose more complex mathematical problems under structured posing conditions, with increasing levels of complexity, than PSTs would pose under free posing…

Spatial abilities are used in many aspects of everyday life, thus developing these abilities should be one of the most important goal of Mathematics Education. These abilities should be developed starting with early school years, thus pre-school and primary school teachers have an important role in setting the foundation of these abilities. A…

An understanding of partitive division is foundational for numerous other mathematics topics, including unit rate, slope, and probability. However, research has shown that learners tend to have a limited understanding of partitive division when the divisor is a proper fraction. To extend research on conceptions of partitive division in this study,…

The Interactive Whiteboard (IWB) is now a common technological artefact in Swedish preschools and schools. This study examines preschool teachers' thinking behind the embedding of IWB in the early years' mathematics classroom and how preschool teachers structure their mathematical activities when using IWB. Two complementary empirical studies,…

This study investigates Spanish and Chinese students' performance on both addition problems and proportion problems considering a cross-national perspective. The effect of number structure and nature of quantities was also considered. Nine hundred twenty-five 4th to 8th graders (453 Chinese, 472 Spanish) took a test which is composed of addition…

Integrating literature in mathematics is a powerful strategy used by many teachers to meet the reformative goals outlined by the National Council of Teachers of Mathematics. This article reports a teacher education study in which 15 elementary preservice teachers engaged in a task that challenged them to link the pedagogical strategy of…

Students regularly struggle with mathematical tasks, particularly those concerning non-routine problems in geometry. Although educators would like for their learners to transfer their knowledge to non-routine and real-life situations, students run into a number of difficulties. The goal of this exploratory study was to analyze three participants'…

Launching a problem is critical in a problem-based lesson. We investigated teachers' perspectives on the use of a problem that was analogous to the one provided during a launch. Our goal was to identify teachers' underlying assumptions regarding what should constitute a launch as elements of the "practical rationality of mathematics…

The purpose of this paper is to examine trainee primary school teachers' confidence in their mathematical content knowledge (MCK) and confidence to teach specific primary mathematics concepts (mathematics pedagogical content knowledge --MPCK) which was correlated to their actual MCK on specific tasks. For this correlational study survey and test…