More trouble with maths : a complete manual to identifying and diagnosing mathematical difficulties

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