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Mathematics Explained for Primary Teachers.

Sixth Edition
by Derek Haylock and Ralph Manning

Student Resources

  • Curriculum Links
  • Section Introduction Videos
    • Section A: Mathematical Understanding
    • Section B: Mathematical Reasoning and Problem Solving
    • Section C: Numbers and Calculations
    • Section D: Further Number Concepts and Skills
    • Section E: Algebra
    • Section F: Measurement
    • Section G: Geometry
    • Section H: Statistics and Probability
  • Problem Solved! Videos
    • Chapter 6: Numbers and Place Value
    • Chapter 8: Mental Strategies for Addition and Subtraction
    • Chapter 9: Written Methods for Addition and Subtraction
    • Chapter 11: Mental Strategies for Multiplication and Division
    • Chapter 12: Written Methods for Multiplication and Division
    • Chapter 13: Natural numbers: Some key concepts
    • Chapter 14: Integers: Positive and Negative
    • Chapter 15: Fractions and Ratios
    • Chapter 16: Decimal Numbers and Rounding
    • Chapter 17: Calculations with Decimals
    • Chapter 18: Proportionality and Percentages
    • Chapter 19: Algebraic Reasoning
    • Chapter 21: Concepts and Principles of Measurement
    • Chapter 23: Angle
    • Chapter 27: Comparing Sets of Data
  • Self-Assessment Questions
    • Chapter 3: Learning How to Learn Mathematics
    • Chapter 4: Key Processes in Mathematical Reasoning
    • Chapter 5: Modelling and Problem Solving
    • Chapter 6: Numbers and Place Value
    • Chapter 7: Addition and Subtraction Structures
    • Chapter 8: Mental Strategies for Addition and Subtraction
    • Chapter 9: Written Methods for Addition and Subtraction
    • Chapter 10: Multiplication and Division Structures
    • Chapter 11: Mental Strategies for Multiplication and Division
    • Chapter 12: Written Methods for Multiplication and Division
    • Chapter 13: Natural Numbers: Some Key Concepts
    • Chapter 14: Integers: Positive and Negative
    • Chapter 15: Fractions and Ratios
    • Chapter 16: Decimal Numbers and Rounding
    • Chapter 17: Calculations with Decimals
    • Chapter 18: Proportionality and Percentages
    • Chapter 19: Algebraic Reasoning
    • Chapter 20: Coordinates and Linear Relationships
    • Chapter 21: Concepts and Principles of Measurement
    • Chapter 22: Perimeter, Area and Volume
    • Chapter 23: Angle
    • Chapter 24: Transformations and Symmetry
    • Chapter 25: Classifying Shapes
    • Chapter 26: Handling Data
    • Chapter 27: Comparing Sets of Data
    • Chapter 28: Probability
  • Lesson Plans & Worksheets
    • Chapter 6: Numbers and Place Value
    • Chapter 7: Addition and Subtraction Structures
    • Chapter 8: Mental Strategies for Addition and Subtraction
    • Chapter 9: Written Methods for Addition and Subtraction
    • Chapter 10: Multiplication and Division Structures
    • Chapter 11: Mental Strategies for Multiplication and Division
    • Chapter 12: Written Methods for Multiplication and Division
    • Chapter 13: Natural numbers: Some key concepts
    • Chapter 14: Integers: Positive and Negative
    • Chapter 15: Fractions and Ratios
    • Chapter 16: Decimal Numbers and Rounding
    • Chapter 17: Calculations with Decimals
    • Chapter 18: Proportionality and Percentages
    • Chapter 19: Algebraic Reasoning
    • Chapter 20: Coordinates and Linear Relationships
    • Chapter 21: Concepts and Principles of Measurement
    • Chapter 22: Perimeter, Area and Volume
    • Chapter 23: Angle
    • Chapter 23: Angle
    • Chapter 24: Transformations and Symmetry
    • Chapter 25: Classifying Shapes
    • Chapter 26: Handling Data
    • Chapter 27: Comparing Sets of Data
    • Chapter 28: Probability
  • Knowledge Checks
  • SAGE Journal Articles
    • Section A: Mathematical Understanding
    • Section B: Mathematical Reasoning and Problem Solving
    • Section C: Numbers and Calculations
    • Section D: Further Number Concepts and Skills
    • Section E: Algebra
    • Section F: Measurement
    • Section G: Geometry
    • Section H: Statistics and Probability
  • Study Skills

Section B: Mathematical Reasoning and Problem Solving

Click on the following links. Please note these will open in a new window.

  • Dimitriadis, C. (2012) ‘How are schools in England addressing the needs of mathematically gifted children in primary classrooms? A review of practice’, Gifted Child Quarterly, 56(2): 59–76. April 2012. [not directly related to this section but interesting!]
  • Gallagher Landi, M. (2001) ‘Helping students with learning disabilities make sense of word problems’, Intervention in School and Clinic, 37(1): 13–18. September 2001. 
  • Harding, S.E. et al. (2017) ‘Measuring collaborative problem solving using mathematics-based tasks’, AERA Open, 3(3). Article first published online: August 29, 2017. Issue published July 1, 2017. 
  • Herbst, P. (2003) ‘Using novel tasks in teaching mathematics: three tensions affecting the work of the teacher’, American Educational Research Journal, 40(1): 197–238. March 20, 2003.
  • Mann, E. (2006) ‘Creativity: the essence of mathematics’, Journal for the Education of the Gifted, 30(2): 236–260. December 21, 2006.
  • Xin, P., Wiles, B. and Lin, Y. (2008) ‘Teaching conceptual model-based word problem story grammar to enhance mathematics problem solving’, Journal of Special Education, 42(3): 163–178. November 2008. 

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