The author provides an account of launching a new branch at the Institute of Education at Reading University, a joint branch with the Mathematics Association. In the inaugural meeting, teachers had gathered to explore the theme of creativity in learning mathematics. The workshop provides some indication of the creative spirit these teachers…

The field of mathematics is complex, areas such as arithmetic, and geometry each consist of several sub-domains and encompass many cognitive processes. Achievement tests for elementary pupils assess a wide range of arithmetic skills such as number sense, procedural knowledge, and using problem solving strategies. Although mathematical tests often…

Understanding the equivalence in relation to fractions is centrally important. Students need many experiences of flexibly combining simple fractions in ways that reinforce equivalences among them. This article presents several ideas that are contributed by a range of people. They are designed to help students to develop understandings of…

Contemporary teachers need instructional practices that are (a) powerful enough to meet the needs of a rapidly diversifying student population, (b) feasible to implement on a classwide basis, and (c) socially acceptable to them and their pupils. Classwide peer tutoring (CWPT) is one such instructional practice. In addition to describing CWPT, its…

Using the structure of a metacognitive journal, this article describes the author's discovery of an unusual method for adding fractions after carefully considering a student's response. (Contains 3 figures.)

The design and empirical validation of a computer-based learning environment for acquiring long division skills, called the long division machine (LDM), are described. The construction of the LDM is primarily based on the didactic method of progressive schematisation. It offers the student a game-like environment for solving division problems by…

In the final article of a series of four, the author deconstructs the primary national strategy's approach to written division. The approach to division is divided into five stages: (1) mental division using partition; (2) short division of TU / U; (3) "expanded" method for HTU / U; (4) short division of HTU / U; and (5) long division.…

A derivative is the limit of a quotient. It is an abstraction of division. Since division is harder to understand than multiplication, teachers teach it later, hopefully only after a sound understanding of multiplication has been attained. For the same reason, it may make sense to teach integration first, and move on to differential calculus only…

How do composing and decomposing numbers connect with the properties of addition? Focus on the ideas that you need to thoroughly understand in order to teach with confidence. The mathematical content of this book focuses on essential knowledge for teachers about numbers and number systems. It is organized around one big idea and supported by…

Now in a second edition, the award-winning "The Trouble with Maths" offers important insights into the often confusing world of numeracy. By looking at learning difficulties in maths from several perspectives, including the language of mathematics, thinking styles and the demands of individual topics, this book offers a complete overview of the…

Useful for small groups or one-on-one instruction, this book offers successful math interventions and response to intervention (RTI) connections. Teachers will learn to target math instruction to struggling students by: (1) Diagnosing weaknesses; (2) Providing specific, differentiated instruction; (3) Using formative assessments; (4) Offering…

Children's thinking follows natural developmental paths in learning math. When teachers understand those paths and offer activities based on children's progress along them, they build developmentally appropriate math environments. The authors explain math learning trajectories and why teaching math using the trajectories approach is effective. A…

This quasi-experimental study aims to streamline cognitive models on fraction multiplication and division that contain the most worthwhile features of other existing models. Its exploratory nature and its approach to proof elicitation can be used to help establish its effectiveness in building students' understanding of fractions as compared to…

In the late seventies, Guy Brousseau set himself the goal of verifying experimentally a theory he had been building up for a number of years. The theory, consistent with what was later named (non-radical) constructivism, was that children, in suitable carefully arranged circumstances, can build their own knowledge of mathematics. The experiment,…

Past research has documented that the effectiveness of three different math strategies delivered to students via one-on-one instruction (i.e., cover-copy-compare (CCC); e.g., Skinner, Turco, Beatty, & Rasavage, 1989, traditional drill and practice (TDP); e.g., Cybriwsky & Schuster, 1990, and constant time delay (CTD); Kulik, 1994). This study…