Part I: How children learn primary mathematics -- 1. Constructing mathematical knowledge -- The neurological story -- Is there an innate ability to learn mathematics? -- Effecitve learning of mathematics -- 2. Recalling and transferring mathematical knowledge -- How we can help children recall and apply knowledge in new situations? -- Transfer (and generalization) -- 3. Desirable outcomes and motivations -- External pressures -- Motivation -- Engaging children in mathematics -- 4. Independent mathematicans -- What do we mean by independence? -- 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 -- 6. Young children learning mathematics -- Do babies have an innate ability to understand mathematics? -- Significant aspects of early mathematics learning -- 7. The role of mental mathematics and its relationship to calculation -- Confidence, rehearsal and flexibility -- Transition to written calculations -- 8. Approaches to numerical calculation --- Early number -- The numbers in-between -- 9. Mathematics in context -- Measures -- Data handling -- Ratio and proportion -- Part III: Four key issues in learning primary mathematics -- 10. The role of the calculator -- Questions often arising from calculator use -- 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 -- 12. Difficult and easy -- Learning, unlearning and relearning -- The nature of misconception -- Difficult mathematics -- Mathematically high attaining children? -- 13. Relationships, patterns and generalization -- Relationships -- Patterns -- Pattern-seeking skills -- Generalizing -- 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 -- 15. Creating a good learning environment -- Teacher input -- Resources and displays -- Other environments -- Task type -- Working with others -- 16. Teaching style -- School structures -- Structure of the lesson -- Ways of teaching -- Task type -- 17. The role of questioning in enhancing mathematical learning -- Applying questioning strategies to stages of a lesson -- 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 -- 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 -- 20. A Teacher's voice.