Over the years, the author has learned that illustrated books can help dispel the myth that math is dull, unimaginative, and inaccessible. They can spark children's mathematical imaginations in ways that textbooks and workbooks often don't. Picture books can also help students who love to read--but think math isn't their thing--experience the…

We consider here the plethora of mathematical ideas arising from something as apparently banal as an association logo. This example is used to illustrate the fact that a potentially rich task may also have the capacity to appeal, in a powerful way, to learners' aesthetic sensibilities. It is to be hoped that both teachers and lecturers will find…

In this article, the authors investigate how the difficulty of a "set shot" at goal varies with position on the field. By "set shot" they mean a player kicking for goal following a mark or free kick. The analysis begins by defining the "angle of opportunity" as a measure of difficulty for kicks at a given distance and…

The article discusses using differentiated instruction in mathematics education for pre-service teachers, including background information and details on a differentiated unit on fractions and integers. In addition, a study was conducted on this lesson and results are included which suggest that students who received the differentiated lesson did…

In this article, we propose to introduce the differential of a function through a non-classical way, lying on hyperreals and infinite microscopes. This approach is based on the developments of nonstandard analysis, wants to be more intuitive than the classical one and tries to emphasize the functional and geometric aspects of the differential. In…

In Germany during the past few years the nursery school (for ages three-six) is increasingly regarded as an educational institution rather than a childcare centre. This is reflected in the increasing number of curricula for young children, which include mathematics as a domain of learning skills. In the past mathematics has not been part of the…

Autograph is a two- and three-dimensional dynamic statistics and graphing utility, developed in England, that has grown out of direct classroom experience. A simple select-and-right-click interface, together with tools such as Autograph's unique Slow Plot, Scribble Tool, and dynamic Constant Controller help make the classroom experience…

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process--1) use of physical manipulatives, 2) interactive exploration of computer…

Since most elementary school teachers do not hold a degree in mathematics, teaching math may be a daunting task for some. Following are a few techniques to help make teaching and learning math easier and less stressful. First, know that math is a difficult subject to teach--even for math teachers. The subject matter itself is challenging. Second,…

Every year the Institute of Mathematics Pedagogy meet for a residential conference in July working together to focus on particular aspects of teaching and learning mathematics. The conference is open to all, and includes all sorts of people involved in mathematics and education. This year the focus was on proof and narrative. This article looks at…

More important than infusing courses and curricula with modern content is to give students the tools to use and understand mathematics--including some that does not yet exist. A curriculum organized around habits of mind tries to close the gap between what users and makers of mathematics do and what they say. These cross-journal articles are…

In this article we show how the Sudoku puzzle and the three simple rules determining its solution can be used as an introduction to proof-based mathematics. In the completion of the puzzle, students can construct multi-step solutions that involve sequencing of steps, use methods such as backtracking and proof by cases, and proof by contradiction…

Before instruction, children solve many arithmetic word problems with informal strategies based on the situation described in the problem. A Situation Strategy First framework is introduced that posits that initial representation of the problem activates a situation-based strategy even after instruction: only when it is not efficient for providing…

The aim of the study was to exemplify pupils' mastering of mathematical literacy. The study is a comparative multiple case study. In pupils' talk of mathematical activities aspects of mathematical literacy are discerned. A distinction is made between pupils: (1) pupils in mathematical difficulties, (2) pupils with another mother tongue than…

The aim of this study was to examine the self-efficacy beliefs about mathematical literacy among teachers of primary school mathematics and the relationship between the self-efficacy beliefs and attitudes towards mathematics. To that end, a descriptive research study was conducted with 550 prospective teachers studying primary school mathematics…