Cover
Half Title
Title Page
Copyright Page
Table of Contents
Foreword by Professor Maggie Snowling
Chapter 1 Introduction: Dyscalculia and mathematical learning difficulties: The test protocol
Dyscalculia #10,0,-32767 What is mathematics? What is numeracy? #13,0,-32767 Mathematical learning difficulties #14,0,-32767 Tests and testing #18,0,-32767 A diagnostic protocol #19,0,-32767 Mathematical learning difficulties and individuals #20,0,-32767 Teaching and diagnosing #21,0,-32767 Co-occurring difficulties: Comorbidity #21,0,-32767 Further reading #22,0,-32767Chapter 2 Diagnosis, assessment and teaching: The benefits of linking
Assessment #24,0,-32767 Questionnaire for selecting a norm-referenced test (NRT) #25,0,-32767 Criterion-referenced tests #30,0,-32767 Skills for diagnosis #30,0,-32767 Ongoing diagnosis #30,0,-32767 Feeding back the results of the diagnosis #31,0,-32767Chapter 3 The Dyscalculia Checklist: Thirty-one characteristics that can contribute to maths failure
1. Finds it impossible to ‘see’ that four objects are four without counting (or three objects, if a young child) #32,0,-32767 2. Has difficulty counting objects accurately and lacks the ability to make ‘one-to-one correspondence’ #33,0,-32767 3. Finds it much harder to count backwards compared to counting forwards #33,0,-32767 4. Counts on for addition facts, for example, for 6 + 3, counts on ‘7, 8, 9’ to get the answer #33,0,-32767 5. Has difficulty with retrieving addition facts from memory #34,0,-32767 6. Counts all the numbers when adding, for example, for 5 + 3, counts ‘1, 2, 3, 4, 5 … 6, 7, 8’ #35,0,-32767 7. Finds it difficult to count fluently sequences that are less familiar, such as 1, 3, 5, 7 … or 4, 14, 24, 34 … #36,0,-32767 8. Uses tally marks for addition or subtraction problems #36,0,-32767 9. Has difficulty in progressing from the materials and images, for example, counters, blocks, tallies, to the symbols/numbers #36,0,-32767 10. Has poor skills with money, for example, unable to calculate change from a purchase #37,0,-32767 11. Thinks an item priced at £4.99 is ‘£4 and a bit’ rather than almost £5 #37,0,-32767 12. ‘Sees’ numbers literally and not inter-related, for example, counts up from 1 to get 9, rather than using 10 – 1 #37,0,-32767 13. Finds it difficult to write numbers which have zeros within them, such as, ‘three hundred and four’ or ‘four thousand and twenty-one’ #38,0,-32767 14. Finds estimating impossible #38,0,-32767 15. Finds it difficult to judge whether an answer is right, or nearly right (and do they even look at an answer?) #38,0,-32767 16. Organises written work poorly, for example does not line up columns of numbers properly #39,0,-32767 17. Doesn’t ‘see’ automatically that 7 + 5 is the same as 5 + 7 (or that 7 × 3 is the same as 3 × 7) #39,0,-32767 18. Writes 51 for fifteen or 61 for sixteen (and the same ‘reversal’ for all the teen numbers) #39,0,-32767 19. Forgets the question asked in mental arithmetic #39,0,-32767 20. Struggles with mental arithmetic #40,0,-32767 21. Learns multiplication facts, but then forgets them overnight #40,0,-32767 22. Only knows the 2x, 5x and 10x multiplication facts #41,0,-32767 23. Counts on to access the 2x and 5x facts #41,0,-32767 24. Makes ‘big’ errors for multiplication facts, such as 6 × 7 = 67 or 6 × 7 = 13 #41,0,-32767 25. Likes to use formulas, but uses them mechanically without any understanding of how they work #42,0,-32767 26. Forgets mathematical procedures, especially as they become more complex, such as decomposing, re-naming, re-grouping or borrowing for subtraction and, almost certainly, the ‘traditional’ method for division #42,0,-32767 27. Gets very anxious about doing any mathematics #42,0,-32767 28. Refuses to try any mathematics, especially unfamiliar topics #43,0,-32767 29. Becomes impulsive when doing mathematics, rather than being analytical. Rushes to get it over with #43,0,-32767 30. Shows an inability to ‘see’ patterns or generalisations, especially ones that are incompatible with previous patterns, for example that 1/2, 1/3, 1/4, 1/5 is a sequence that is getting smaller #43,0,-32767 31. Thinks that algebra is impossible to understand #43,0,-32767 Checklist for dyscalculia ©Steve Chinn 2016
Using the checklist
Chapter 4 Starting the assessment/diagnosis: Getting to know the person through informal activities
Some informal starter questions #47,0,-32767 Informal diagnostic activities #47,0,-32767 Finally, don’t forget the obvious #54,0,-32767 A record/observation sheet: Informal items
The cards #59,0,-32767Chapter 5 Short-term memory and working memory: Two key underlying skills that influence learning
Interactions #62,0,-32767 The tests #63,0,-32767 Giving the test #64,0,-32767 Short-term memory #64,0,-32767 Short-term memory test: Digits Forward (DF)
Working memory
Working memory test: Digits Reversed (DR)
Variations
Self-monitoring when teaching #68,0,-32767 Two final notes #68,0,-32767Chapter 6 Tests of basic facts - addition, subtraction, multiplication and division: Their role in mathematical learning difficulties and dyscalculia
What is a ‘basic fact’? #69,0,-32767 Research #70,0,-32767 The role of basic facts in maths and maths education #71,0,-32767 The basic fact tests #73,0,-32767 Using the basic fact tests: Test procedure #74,0,-32767 The 60-second test for addition Steve Chinn © 2011
The 60-second test for subtraction Steve Chinn © 2011
The 120-second test for multiplication Steve Chinn © 2011
The 120-second test for division Steve Chinn © 2011
The data
What the tests reveal #79,0,-32767Chapter 7 Mathematics anxiety: Which topics and activities create anxiety
The Mathematics Anxiety Questionnaire (MAQ) #86,0,-32767 Reflections on the scores from the questionnaire #88,0,-32767 How to administer the mathematics anxiety questionnaire #89,0,-32767 How I feel about mathematics © 2016 Steve Chinn Teacher’s sheet
How I feel about mathematics © 2016 Steve Chinn Student sheet
Chapter 8 The 15-Minute norm-referenced Mathematics Test: Basic computations and algebra designed to compare performances
It can be used with an individual or with a group #93,0,-32767 The test items #95,0,-32767 Instructions for administration #103,0,-32767 Mathematics Test 15 minutes (© 2015 Steve Chinn)
Answers
Norm-referenced data and interpreting the scores
Finally #116,0,-32767Chapter 9 Errors and the 15-Minute Mathematics Test: Recognising and understanding common error patterns
Errors and teaching #117,0,-32767 Classifying errors #118,0,-32767 Some favourite errors from the basic fact tests #121,0,-32767 Errors and the 15-Minute Mathematics Test #122,0,-32767 Summary #135,0,-32767 Finally #135,0,-32767Chapter 10 Cognitive (thinking) style: How learners think about and solve mathematics problems
The characteristics of the ‘inchworm’, the formula, sequential thinker #137,0,-32767 The characteristics of the grasshopper, the relational, holistic thinker #138,0,-32767 Behaviouristic #139,0,-32767 Constructivist #139,0,-32767 The cognitive (thinking) style test #139,0,-32767 Interpreting the test results #140,0,-32767 The Test of Cognitive Style in Mathematics (TCSM) #149,0,-32767 TCSM observation sheet © Steve Chinn 2017
TCSM worksheet © Steve Chinn 2017
The TCSM profile line © Steve Chinn 2017
Chapter 11 Estimation: A key life skill used to develop more confidence with mathematics
Dyscalculia and subitising #158,0,-32767 Coins/counters and dots tasks #158,0,-32767 Empty number lines #158,0,-32767 Estimation and checking an answer #159,0,-32767 Estimating and the test protocol #160,0,-32767Chapter 12 Mathematics vocabulary, symbols and word problems: Exploring how they contribute to mathematics learning difficulties
Symbol/vocabulary matching cards: The key words and symbols #162,0,-32767 Example of a structured word problem test sheet #163,0,-32767 Word problems
Word problems. Observation sheet
Basic information observation sheet
Word and symbol cards
Observation sheet. Matching words and symbols
Chapter 13 Criterion-referenced (formative) tests: Focusing on identified problems and showing how to build ongoing diagnosis into teaching
Criteria #171,0,-32767 Setting up CRTs #173,0,-32767 Criteria and objectives #174,0,-32767 Pre-requisite skills and knowledge #174,0,-32767 Focused CRTs #175,0,-32767 Pre-intervention and post-intervention CRTs #176,0,-32767 Overview CRTs #178,0,-32767 Remember, practice may not make perfect, but it should make for improvement #179,0,-32767Chapter 14 Speed of working: The implications of ‘doing mathematics’ quickly
Slow processing, speed of working and examinations #180,0,-32767 A previous study #181,0,-32767 The ‘no answer’ #181,0,-32767 Indirect evidence #182,0,-32767Chapter 15 Two sample reports
Previous assessments. The GL Dyscalculia Screener #183,0,-32767 Outline of the assessment #183,0,-32767 Main concerns from the pre-assessment pro-forma #184,0,-32767 Teacher/tutor observations. Mathematics #184,0,-32767 Student’s main concerns with maths #185,0,-32767 Checklist for dyscalculia and maths learning difficulties © Steve Chinn, 2016 #186,0,-32767 The assessment #188,0,-32767 Informal tasks #189,0,-32767 Counting forwards and backwards #189,0,-32767 Number bonds #190,0,-32767 Numbers and place value #190,0,-32767 Short-term memory. Working memory #191,0,-32767 Anxiety #191,0,-32767 Basic facts: 60-second/120-second worksheets #192,0,-32767 Symbols and vocabulary for the basic symbols, + – × ÷ and = #193,0,-32767 The 15-Minute Mathematics Test #193,0,-32767 Summary #194,0,-32767 S J Chinn. 2018 #195,0,-32767 The assessment #195,0,-32767 Main concerns #195,0,-32767 Child’s main concerns with maths #196,0,-32767 Teacher/tutor observations #197,0,-32767 Teacher/tutor observations. Mathematics ©Steve Chinn, 2015 #197,0,-32767 Please give examples where possible #197,0,-32767 Peter’s main concerns with maths #198,0,-32767 The Dyscalculia Checklist #198,0,-32767 The assessment session #201,0,-32767 Counting forwards and backwards #203,0,-32767 Basic number bonds #203,0,-32767 Place value #203,0,-32767 Multiplying by 2, 20 and 200 #204,0,-32767 Placing decimal numbers in order of value (biggest value first) #204,0,-32767 Word/symbol matching for the four operations #204,0,-32767 Basic facts: 60-second/120-second worksheets #204,0,-32767 Short-term memory (Stm). Working memory (WM) #206,0,-32767 Anxiety #207,0,-32767 The 15-Minute Mathematics Test #208,0,-32767 Cognitive style #209,0,-32767 Summary #210,0,-32767Appendix 1 A sample ‘teacher observations’ pro-forma
Teacher/tutor observations. Mathematics
Appendix 2 A pre-assessment pro-forma for parents/carers
CONFIDENTIAL #214,0,-32767Appendix 3 Schools, colleges, institutions and individuals who provided data for the norm-referenced tests in Chapters 6 and 8
References
Index
