Teaching mathematics to children can be difficult, especially with the current climate of failing mathematics grades, due to candidates being "required now have to exhibit a degree of familiarity with a much wider but shallower curriculum" (Reform 2006).![]()
Thinking Through Mathematics (published in September 2008) provides teachers of mathematics with 21 thinking skills activities which develop both generic thinking strategies and more specialised mathematical thinking. The activities included in Thinking Through Mathematics will help you to:
The structure of the book:
Part One Part One is aimed to provide you with a general introduction as to why and how the book was written. It consists of the following chapters: Introduction outlines the purpose of the book and underpinning principles.
Part Two Part Two contains 21 exemplars, grouped under eight thinking skills strategies. Each of the strategies is demonstrated with at least one activity which was developed for use in the mathematics classroom and trialled with different age and attainment groups. Below is a summary of the strategies and activities: Strategy 1 - Odd one out Odd one out is a powerful strategy that supports classification and understanding of the properties and defining attributes of things. Exemplars in strategy 1 include activities linking to:
Strategy 2 - Collective memory Collective memory begins to make pupils think harder about how they see and make sense of visual information - maps, sketches, photographs and diagrams. Exemplars in strategy 2 include activities linking to:
Strategy 3 - Classfication Classifying data or objects is a fundamental cognitive skill. It encourages pupils to identify key characteristics and justify their choice. Exemplars in strategy 3 include activities linking to:
Strategy 4 - Living graphs Living graphs give the figures and the lines of a graph real context and allow students to make connections between the abstraction of the graph on the page and the people and events that lie behind it. Exemplars in strategy 4 include activities linking to:
Strategy 5 - Mysteries The strategy is designed to encourage pupils to deal with ambiguity through addressing a question which has no single correct answer and where they are not sure what information is relevant - like in real life. Exemplars in strategy 5 include activities linking to:
Strategy 6 - Relational diagrams The use of relational diagrams in this strategy gives a visual representation of the relationships between the data being discussed in the diagrams. This is a good tool for clarifying understanding or clearing up misunderstandings. Exemplars in strategy 6 include activities linking to:
Strategy 7 - Taboo theory This strategy is based on the board game whereby the explainer in each team has got to get across a keyword to the rest of their team without using any of the taboo words. Using cards produced by The Association of Teachers of Mathematics (ATM) entitled 'Fourbidden', you and your students play a version of this game. Exemplars in strategy 7 include activities linking to:
Strategy 8 - Sequencing Sequencing is a strategy that promotes reasoning. In this context reasoning includes:
Exemplars in strategy 8 include activities linking to:
Part Three This section of the book is intended to elaborate and expand on points made in the exemplars. These points draw your attention to why the teachers did things is a particular way, and to how you might adapt that to your own teaching and learning contexts. Chapters included in Part Three are: Chapter 4 describes principles which underpin teaching thinking and the generic features of thinking skills lessons. This includes consideration of the close correlation between principles of teaching thinking and those promoted in Teaching and Learning in the Foundation Subjects (DfES, 2003). Chapter 5 looks at implications of teaching thinking for the roles of teacher and learner. Chapter 6 provides a few rules of thumb and some practical suggestions for you to get started. Chapter 7 is to a refl ect upon what we think now about thinking skills and mathematics. It summarises strengths of infusing thinking skills into mathematics lessons and points out challenges facing mathematics educators. Chapter 8 concentrates on the development that is made for us as teachers using these strategies in our classrooms.
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