Engaging Primary Children in Mathematics

Description

Primary school mathematics learning and teaching is reviewed in the light of current neurological findings. Developing neural pathways through experience, practice and application will build more neural memories and assist in more effective recall as well as promoting stronger understanding. Learning can be aided by the teacher drawing out and clarifying the underlying mathematical principles and relationships. Mathematical examples are used to illustrate this approach to teaching primary mathematics. Cover page Halftitle page Series page Title page Copyright page Contents Preface Introduction References Part I How Children Learn Primary Mathematics 1 Constructing Mathematical Knowledge The neurological story Is there an innate ability to learn mathematics? Effective learning of mathematics References 2 Recalling and Transferring Mathematical Knowledge How can we help children recall and apply knowledge in new situations? Transfer (and generalization) References 3 Desirable Outcomes and Motivations External pressures Motivation Engaging children in mathematics References 4 Independent Mathematicians What do we mean by independence? References Part II The Development of the Primary Mathematics Curriculum 5 The Map of Mathematics Progression through topics A lack of progression Connections across mathematical topics The curriculum is the content – the maths to be taught References 6 Young Children Learning Mathematics Do babies have an innate ability to understand mathematics? Significant aspects of early mathematics learning References 7 The Role of Mental Mathematics and Its Relationship to Calculation Confidence, rehearsal and flexibility Transition to written calculations References 8 Approaches to Numerical Calculation Early number The numbers in-between References 9 Mathematics in Context Measures Data handling Ratio and proportion References Part III Four Key Issues in Learning Primary Mathematics 10 The Role of the Calculator Questions often arising from calculator use References 11 Children Solving Mathematical Problems Simple word problems – calculations with words Why is problem solving generally so difficult? Possible ways forward Prompts to assist solving problems References 12 Difficult and Easy Learning, unlearning and relearning The nature of misconception Difficult mathematics Mathematically high attaining children? References 13 Relationships, Patterns and Generalization Relationships Patterns Pattern-seeking skills Generalizing References Part IV The Teacher’s Influence on Children Learning Primary Mathematics 14 The Nature of Mathematical Knowledge for Teaching Teacher beliefs Self-concept and confidence References 15 Creating a Good Learning Environment Teacher input Resources and displays Other environments Task type Working with others References 16 Teaching Style School structures Structure of the lesson Ways of teaching Task type References 17 The Role of Questioning in Enhancing Mathematical Learning Applying questioning strategies to stages of a lesson References 18 Planning for Progress Children’s progress and achievement Long-, medium- and short- term planning The shape of the lesson Measuring progress Creating a classroom where formative assessment can take place References 19 Other Factors Influencing the Teaching of Mathematics National and international league tables The role of government in promoting primary school mathematics Teacher training Cultural and societal expectation The curriculum Social factors References 20 A Teacher’s Voice Reference Index