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The Open University

Teaching mathematics

The Open University via OpenLearn

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Overview

This free course, Teaching mathematics, has been designed for non-specialist mathematics teachers of 8 to 14 year olds, teaching assistants, home schoolers and parents and draws on the established provision of mathematics education at The Open University. It can also be used as Continuing Professional Development by individuals or groups of teachers. The authors have many years’ experience of teaching mathematics in the classroom and in Initial and Continuing Teacher Education.This course aims to develop your understanding of the mathematical content covered in the middle school years and effective strategies and approaches to the teaching and learning of this content. Through your studies you will begin to understand how children in this age group learn mathematics and the common misconceptions which they may experience.Clearly it is not possible to cover all aspects of teaching mathematics in 24 hours of study. So, while we hope the course will be valuable for those groups mentioned above, it is not a substitute for formal initial teacher education courses such as Bachelor of Education degrees or the PGCE. TranscriptEnrolling on the course will give you the opportunity to earn an Open University digital badge. Badges are not accredited by The Open University but they're a great way to demonstrate your interest in the subject and commitment to your career, and to provide evidence of continuing professional development.Once you are signed in, you can manage your digital badges online from My OpenLearn. In addition, you can download and print your OpenLearn statement of participation – which also displays your Open University badge.The Open University would really appreciate a few minutes of your time to tell us about yourself and your expectations for the course before you begin, in our start-of-course survey. Once you complete the course we would also value your feedback and suggestions for future improvement, in our end-of-course survey. Participation will be completely confidential and we will not pass on your details to others. This course is accredited by the CPD Standards Office. It can be used to provide evidence of continuing professional development and on successful completion of the course you will be awarded 24 CPD points. Evidence of your CPD achievement is provided on the free Statement of Participation awarded on completion.Anyone wishing to provide evidence of their enrolment on this course is able to do so by sharing their Activity Record on their OpenLearn Profile, which is available before completion of the course and earning of the Statement of Participation.  

Syllabus

  • Introduction and guidance
  • Introduction and guidance
  • What is a badged open course?
  • How to get a badge
  • Acknowledgements
  • Week1Week 1: Teaching and learning: whole numbers and decimals
  • Introduction
  • Learning outcomes
  • 1 How children develop number sense
  • 1.1 Learning to count and counting effectively
  • 1.2 Making the connection between quantity and number
  • 1.3 Part-whole relationships and number bonds
  • 1.4 Understanding that addition and subtraction are inverses of each other
  • 1.5 Moving on from counting and working out relationships between quantities
  • 2 Developing mental methods
  • 2.1 Using number bonds to 10, 20, 100
  • 2.2 Mental addition and subtraction strategies
  • 2.3 Mental multiplication and division strategies
  • Understanding division problems
  • Division by partitioning can be a useful strategy
  • Multiplication tables
  • Developing mental arithmetic with your learners
  • 3 Developing formal written calculation methods
  • 3.1 Formal written methods of addition
  • 3.2 Formal written methods for subtraction
  • 3.3 Multiplication and division
  • 4 The concept of place value and decimals
  • 4.1 The decimal point and calculations with decimals
  • 4.2 Becoming familiar with decimals
  • 5 This week’s quiz
  • 6 Summary of Week 1
  • Further reading
  • Acknowledgements
  • Week2Week 2: Teaching and learning: percentages and fractions
  • Introduction
  • Learning outcomes
  • 1 Equivalence as a concept applied to fractions, decimals and percentages
  • 1.1 Diagrammatic representations of equivalence
  • The fraction wall
  • 1.2 Challenges to understanding the equivalence between fractions
  • 2 Approaches to teaching fractions
  • 2.1 What are fractions?
  • 2.2 Ordering fractions
  • 2.3 Adding and subtracting fractions
  • 2.4 Multiplying fractions
  • 2.5 Dividing fractions
  • 3 Approaches to teaching percentages
  • 3.1 Calculating percentages of amounts
  • 3.2 Percentage change: using multiplying factors
  • 3.3 Finding the original amount when given the result of a percentage change
  • 3.4 Using multiplying factors to find an original amount given the result of a percentage change
  • 4 This week’s quiz
  • 5 Summary of Week 2
  • Acknowledgements
  • Week3Week 3: Developing understanding of proportion and ratio
  • Introduction
  • Learning outcomes
  • 1 Developing proportional reasoning and an appreciation of multiplicative structure
  • 1.1 Additive versus multiplicative thinking
  • 1.2 When to use multiplicative thinking
  • 1.3 Developing learners’ proportional reasoning
  • 1.4 Using concrete resources
  • Teaching idea: Cooking with ratios
  • 1.5 Moving to abstract thinking and using pictorial representations
  • 2 Problem solving using proportional reasoning, including common misconceptions
  • 2.1 Problem solving using proportional reasoning
  • Teaching idea: School or home map
  • Best buys
  • Exchange rates
  • Mixtures and solutions
  • Teaching idea: A giant’s hand investigation
  • 2.2 Common misconceptions with proportional reasoning problems
  • Proportional problem 1: Soup
  • Proportional problem 2: Sharing the workload
  • Proportional problem 3: Paint
  • Proportional problem 4: Printing press
  • Proportional problem 5: Bookshop
  • 2.3 Teaching to address common misconceptions
  • 3 Connecting ratio and proportional reasoning
  • 3.1 Using simple ratios to make comparisons
  • Using manipulatives
  • 3.2 Connecting ratio and proportion
  • 3.3 Using ratio tables
  • 3.4 Continuing to develop learners’ proportional reasoning
  • 4 This week’s quiz
  • 5 Summary of Week 3
  • Further reading
  • Acknowledgements
  • Week4Week 4: Introducing algebra
  • Introduction
  • Learning outcomes
  • 1 Mathematical sentences and algebraic expressions
  • 1.1 Writing algebraic expressions
  • 1.2 Expressions and terms
  • 2 Finding the general in the particular
  • 2.1 Representations
  • 2.2 Indeterminacy: moving from specific unknowns to variables
  • 2.3 Comparing algebraic expressions
  • 3 The equals sign
  • 3.1 Relational understandings
  • 3.2 Always, sometimes, never true?
  • 4 This week’s quiz
  • 5 Summary of Week 4
  • Further reading
  • Acknowledgements
  • Week5Week 5: Introducing functions and graphs
  • Introduction
  • Learning outcomes
  • 1 Function machines
  • 2 Sequences as functions
  • 2.1 Term-to-term and position-to-term rules
  • 2.2 Generalising with sequences
  • Changing shapes
  • 2.3 Changing numbers
  • 2.4 Looking at structure in a sequence
  • 2.5 Summary
  • 3 Extending functions: variables and graphs
  • 3.1 Variables
  • 3.2 Increasing and decreasing graphs
  • Linear graphs
  • 3.3 The exponential function
  • 4 This week’s quiz
  • 5 Summary of Week 5
  • Further reading
  • Acknowledgements
  • Week6Week 6: Teaching and learning about geometry
  • Introduction
  • Learning outcomes
  • 1 How children think and reason about geometric shapes
  • 1.1 Progression in geometric thinking
  • Thinking holistically
  • Moving on to description
  • 1.2 Defining shapes using flexible definitions
  • 1.3 The visual or physical representation of shapes
  • 2 Investigating the properties of triangles and quadrilaterals
  • 2.1 Triangles
  • 2.2 Quadrilaterals
  • 3 Developing problem-solving skills in geometry
  • 3.1 Polyominoes
  • Pentominoes as an activity with learners
  • 3.2 Ideas for tasks using four cubes
  • 3.3 Enlarging shapes using repeating tiles
  • 4 This week’s quiz
  • 5 Summary of Week 6
  • References
  • Acknowledgements
  • Week7Week 7: Developing understanding about using measures
  • Introduction
  • Learning outcomes
  • 1 Measures and measuring
  • 1.1 Measuring scales
  • 1.2 The historic development of measures
  • Imperial measures of length
  • Imperial measures of weight
  • Imperial measures of volume (liquid capacity)
  • 1.3 The metric system
  • 1.4 Useful ‘rough’ metric to imperial equivalences
  • 1.5 Everyday measures
  • 1.6 Extending measures to compound measures
  • 2 Reading measures and accuracy
  • 2.1 Measuring scales
  • 2.2 Degrees of accuracy in measurement
  • 3 Teaching angle measures and angle facts
  • 3.1 Using a protractor to measure angles
  • 3.2 Angle sum of triangles
  • 4 Teaching about area and volume
  • 4.1 Area
  • Using the area formula for a rectangle to derive other area formulas
  • 4.2 Converting square metres into square centimetres
  • 4.3 Volume
  • 4.4 Converting cubic centimetres into cubic metres
  • 5 This week’s quiz
  • 6 Summary of Week 7
  • Further reading
  • Acknowledgements
  • Week8Week 8: Working with data and uncertainty
  • Introduction
  • Learning outcomes
  • 1 Collecting data and illustrating it in charts
  • 1.1 Collecting data
  • 1.2 Population and sampling
  • 1.3 Questionnaires
  • 1.4 Tally charts and frequency charts
  • 1.5 Grouping data
  • 1.6 Two-way tables
  • 1.7 Discrete and continuous data
  • 1.8 Grouping continuous data
  • 1.9 Stem and leaf diagrams
  • 2 Developing data sense and forming sensible conclusions
  • 2.1 Statistical thinking and the PCAI cycle
  • 2.2 Analysing data using measures of central tendency and spread
  • Teaching idea: People maths
  • 2.3 Comparing distributions and making sensible conclusions
  • 3 Charts and graphs as visual representations of data
  • 3.1 Basic charts and graphs
  • Pictograms
  • Bar charts
  • Other types of bar chart
  • 3.2 Pie charts
  • Teaching idea: Do Smarties® have the answer?
  • 3.3 Scatter graphs
  • Interpreting correlation
  • 3.4 Misleading correlation
  • 4 Addressing common misconceptions with probability
  • 4.1 Equal likelihood
  • 4.2 Gambler’s fallacy
  • 4.3 Sample space considerations
  • 4.4 Spinners
  • 4.5 Building misconceptions into your teaching
  • 5 Making the connections between theoretical and experimental probability
  • 5.1 Experimental probability
  • 5.2 Relative frequency
  • 5.3 Calculating theoretical probability
  • 5.4 Comparing experimental probability with theoretical probability
  • 5.5 Estimating probability
  • 6 This week’s quiz
  • 7 Summary of Week 8
  • 8 Conclusion
  • Tell us what you think
  • Further reading
  • Acknowledgements

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Reviews

5.0 rating, based on 1 Class Central review

4.6 rating at OpenLearn based on 44 ratings

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  • Profile image for Darkhan Zhanibekuly
    Darkhan Zhanibekuly @nicekhan
    The course was wonderful. It gave me a view about the thinking process that takes place in children's heads, hence it increased an understanding of their problems. Consequenlty, I have developed vital skills required for teaching children math. And the free certificate is a pleasant bonus. Regarding the approach, everything was great: it is easy to understand, all section are connected well, and my favourite part is it doesn't require much of your time to complete the course. I will rate it 10/10.
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