How to teach maths : understanding learners' needs / Steve Chinn.

Format:

Book

Author/Creator:

Chinn, Stephen J., author.

Language:

English

Subjects (All):

Mathematics--Study and teaching.

Mathematics.

Physical Description:

1 online resource (164 pages)

Edition:

1st ed.

Place of Publication:

London ; New York, New York : Routledge, [2021]

Summary:

How to Teach Maths challenges everything you thought you knew about how maths is taught in classrooms. Award-winning author Steve Chinn overviews many of the long-established methods, the beliefs and the culture of maths teaching with a critical eye.

Contents:

Cover

Half Title

Title Page

Copyright Page

Table of Contents

Introduction

Chapter 1: Where we are with maths education

Data on performance in maths

Some detailed data

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Initiatives in general

Initiatives then and now

Parents

Final thoughts

An overview from a research paper

Chapter 2: Key identifiers of future and current maths difficulties

Factors that influence learning maths

Some behaviours that might reveal difficulties in learning maths

Foundations of number sense

The list

The basics

Counting

Number facts

Place value

Estimation

Math memories

Speed of working

Poor organisation of work on the page

Anxiety

Noticing, monitoring and diagnosing these problem behaviours

Who started long before me?

Sequencing, classifying and understanding number

Generalising and patterns

Chapter 3: The core curriculum for arithmetic

Some observations

Number: Addition and subtraction

Number: Multiplication and division

Observations

Fractions

Chapter 4: The developmental nature of maths

A mention of 'being almost right'

What students do when they don't know the right answer: An interesting lesson for teachers and parents

Where does ab = y go?

Summing up

Chapter 5: Topics which cause the most difficulty

Basic facts

Addition and subtraction facts

Multiplication and division facts

Strategies for the troublesome 16

Self-voice echo

Exams and times table facts

Final note on times tables

Division

Long(ish) division

Chapter 6: Learner characteristics and key skills

Key factors

An ability to work with symbols

Maths vocabulary

Short-term memory

Working memory

Long-term maths memory

Speed of processing.

Sequencing (forwards and backwards)

Cognitive style

Generalising, seriation and classifying

Anxiety, fear and risk avoidance

Chapter 7: Metacognition

Some background

Does it matter how you think in maths?

Grasshoppers and Inchworms

Cognitive style and teachers

The curriculum and cognitive style

Mind maps

Interactions between cognitive style and other learning factors

Implications for teaching and learning

Footnote

Chapter 8: Linking facts and concepts

Students must understand facts and ideas in the context of a conceptual framework

Students organise knowledge in ways that facilitate retrieval and application

Facts: Right, wrong and inferior

Fractions, decimals and percentages

Chapter 9: The role of language, vocabulary and symbols: Communication and perspectives on communication

Inconsistencies and too much information (also see Chapter 10)

Where to go? Food or maths? Do I need to do a subtraction before I can order my food?

Homophones

Hidden symbols

Confusing symbols

Confusing, misleading and quick-fix instructions

Chapter 10: The inconsistencies of maths and their impact on learning

Some examples of inconsistencies and potential confusions

Teen numbers

Sounds like

Sequences

Fractions and ordinal numbers

Patterns for 6

The commutative property

Coins

Words for operations

Decimal numbers

Algebra and symbols

Time

Chapter 11: How to use materials and visual images

A quick overview and critique of those 'old ideas'

Maths apparatus: Initial thoughts

Some useful kit (not exhaustive) and examples of their use

Cuisenaire rods

Empty, full and sloping number lines

Base-ten Dienes blocks

Fingers and tallies

The balance

Chapter 12: Two visual methods

An introduction.

What are fractions? The big picture (of a small part)

How can this be demonstrated?

More on symbols and inconsistencies (see also Chapter 10)

Paper modelling and fractions

Word problems

The Singapore bar model method

The Singapore model method and the four operations

Last comments

Chapter 13: Anxiety and withdrawal

The many facets of maths anxiety

What creates maths anxiety?

The 'no answer'

Addressing maths anxiety, self-esteem, self-efficacy and self-concept

Transactional analysis

Keeping the student in a break-times

Chapter 14: Assessment and diagnosis of mathematical difficulties

Assessment and diagnosis

Dyscalculia

What are you testing?

What to assess

Factors to consider and address when testing and when setting homework

Evidence

Chapter 15: Classroom management

Writing

Instructions

Presenting information

Worksheets and homework

Working and short-term memories

Classroom ethos and student well-being (see also Chapter 13)

What hinders learning

What helps learning

Chapter 16: Bringing it all together

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Chapter 15

Appendix 1 What an 11-year-old is expected to know

Number: Number and place value

Number: Addition, subtraction, multiplication and division

Number: Fractions (including decimals and percentages)

Ratio and proportion

Measurement

Statistics

Appendix 2 Books and resources

Books, resources and papers from Steve Chinn

Books

Resources

Papers

Other books and reading

Index.

Notes:

Description based on print version record.

ISBN:

1-00-301807-6

1-003-01807-6

1-000-21705-1

9781003018070

OCLC:

1198989942