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Making Sense of Maths is the only series that develops conceptual understanding. This series will motivate, engage and develop the conceptual understanding of students at KS3 and KS4. Students build their own problem solving strategies based on their understanding of the world around them which then support them to tackle functional questions. The Teacher's Book provides support for the activities in the student book which develop the student's understanding of area, Pythagoras and volume. It also contains answers for the workbook questions which consolidate learning. Making Sense of Maths has been based on Realistic Maths Education (RME) and extensively trialled in KS3 and KS4 classrooms in the UK by a team from Manchester Metropolitan University. - Use alongside existing resources or on its own - Ideal for Year 10s heading for the C/D borderline - Ideal for intervention groups - Supports the move from modular to linear specifications by improving knowledge retention - Provides support for good teaching and learning under the current Ofsted criteria
Reproducible worksheets cover the concepts and skills identified by the National Council of Teachers of Mathematics as curriculum focal points for grades four through eight.
"Through investigations of real-life contexts, students develope a rich understanding of important mathematics that makes sense to them and which, in turn, enables them to make sense out of new situations and problems."--Page 1.
Research on teaching and learning proof and proving has expanded in recent decades. This reflects the growth of mathematics education research in general, but also an increased emphasis on proof in mathematics education. This development is a welcome one for those interested in the topic, but also poses a challenge, especially to teachers and new scholars. It has become more and more difficult to get an overview of the field and to identify the key concepts used in research on proof and proving. This book is intended to help teachers, researchers and graduate students to overcome the difficulty of getting an overview of research on proof and proving. It reviews the key findings and concepts in research on proof and proving, and embeds them in a contextual frame that allows the reader to make sense of the sometimes contradictory statements found in the literature. It also provides examples from current research that explore how larger patterns in reasoning and argumentation provide insight into teaching and learning.
This second volume of Greek Musical Writings contains important texts on harmonic and acoustic theory, illustrating the progress of these sciences from their beginnings in the sixth century BC over the subsequent thousand years. Writers represented include Philolaus, Plato, Aristotle, Theophrastus, Aristoxenus, Ptolemy, Aristides, Archytas, and Quintilianus. All the Greek texts are newly translated by the editor. Some replace inadequate existing translations; other significant portions of the book include much that is essential for an understanding of medieval and Renaissance musicology. Dr Barker provides detailed and authoritative commentary and annotations to all the texts. Each section is prefaced by an introductory essay and some of the more complex issues are discussed further in appendices.

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