25. Assessment
• Emerson & Babtie, 2010,The Dyscalculia Assessment,
London: Continuum
• Chinn, 2012, More Trouble with Maths, Abingdon:
Routledge
• DIMP
• WRAT 4, WIAT III
• Hodder Tests & GL Assessment have variety of maths
tests
26. Apps
• Calculators e.g. • Count on it (Slavonic
Soulver, digits, talkin abacus)
g calculators • Math bingo
• Numberbonds • Wings
• I say you say • King of math
(number bonds) • Telling time
• Hungry fish • Fishy numbers
• Zoom
Editor's Notes
Does maths matter?Yes! Only 22% adults have numeracy skills equivalent to Grade A*-C GCSE60% of new jobs in 21st century will require maths skills possessed by only 20% of current workforcePoor numeracy skills are associated with:Unemployment/ poor job prospectsLow payDepression/illnessCrime – 65% adult prisoners have maths skills of 11 year old (or lower)
What makes maths difficult?Maths is abstractUses abstract and precise languageUses complicated system of written symbolsNeed secure foundations to progressOften taught as set of procedures
Typical dyslexic difficulties that may affect maths:LanguageMany everyday words have specific meanings in maths e.g. square, meanTeen numbersWord problemsAuditory discrimination: -teen/-ty; ten/tenth; hundred/hundredth; thousand/thousandthTricky words e.g. isosceles, rhombus, perpendicularMemory weaknesses – LTM, STM, WM:Difficulty in learning facts in the form of pure verbal associations e.g. multiplication tablesPoor working memoryMost aspects of working with numbers are step-by-step processes which involve holding several pieces of information in working memory at the same timeLose track of what they are doing, forget initial task or instructionsMay not be able to hold sum in visual or auditory memory while searching for number factFor information to enter long term memory the input (question) and output (answer) need to be close together for information to enter LTM – need efficientworking memory processes Poor fact and procedure retrieval from LTM contribute to WM problems, as LTM weaknesses drain processing resources of central executiveOver-reliant on counting – places very big demands on WMProcessing speedSlow to process incoming informationTake longer to access stored informationEmphasis on speedy responses undermines child’s ability to thinkComplete less work than peers, so get less practiceLeft-right orientation/ directional confusionMuddle written digitsDecoding and encoding two-digit numbersHorizontal methods work from L R, column based methods work from R L, but standard division algorithm is worked L R36 ÷ 4 or 364 or 4)36Sequencing difficulties:Counting and number systemMay learn to count laterFail to understand structure of number systemManaging counting sequences, especially backwardsSequences of instructions, many calculations involve a sequence of stepsEntering data into calculator in correct sequenceOrder:Teen numbers – say unit first, but write it second – leads to errors in ‘carrying’ numbersLearner hears ‘ten past seven’ and writes 10:7Reads ‘take 8 away from 18’ and writes 8 – 18Visual & spatial awarenessLiteracy skills Word problemsTypical dyslexic difficulties that may affect maths:LanguageMany everyday words have specific meanings in maths e.g. square, meanTeen numbersWord problemsAuditory discrimination: -teen/-ty; ten/tenth; hundred/hundredth; thousand/thousandthTricky words e.g. isosceles, rhombus, perpendicularMemory weaknesses – LTM, STM, WM:Difficulty in learning facts in the form of pure verbal associations e.g. multiplication tablesPoor working memoryMost aspects of working with numbers are step-by-step processes which involve holding several pieces of information in working memory at the same timeLose track of what they are doing, forget initial task or instructionsMay not be able to hold sum in visual or auditory memory while searching for number factFor information to enter long term memory the input (question) and output (answer) need to be close together for information to enter LTM – need efficientworking memory processes Poor fact and procedure retrieval from LTM contribute to WM problems, as LTM weaknesses drain processing resources of central executiveOver-reliant on counting – places very big demands on WMProcessing speedSlow to process incoming informationTake longer to access stored informationEmphasis on speedy responses undermines child’s ability to thinkComplete less work than peers, so get less practiceLeft-right orientation/ directional confusionMuddle written digitsDecoding and encoding two-digit numbersHorizontal methods work from L R, column based methods work from R L, but standard division algorithm is worked L R36 ÷ 4 or 36/4 or 4)36Sequencing difficulties:Counting and number systemMay learn to count laterFail to understand structure of number systemManaging counting sequences, especially backwardsSequences of instructions, many calculations involve a sequence of stepsEntering data into calculator in correct sequenceOrder:Teen numbers – say unit first, but write it second – leads to errors in ‘carrying’ numbersLearner hears ‘ten past seven’ and writes 10:7Reads ‘take 8 away from 18’ and writes 8 – 18Visual & spatial awarenessLiteracy skills Word problems
Co-occurring differencesDCD/ DyspraxiaFine motor skillsMotor planning – setting work outVisual perceptionOrganisational skillsBody awareness/ finger agnosia – lack of awareness of how many fingers they have or where they are in spaceSensory integration problems – difficulty processing feedback from different sensesOften ‘rigid’ maths thinkersADD/ADHDHyperactivity and distractibilityInability to focus on most relevant information Irrelevant information may crowd WM capacity Slower and less accurate in calculation – WM overload Difficulty representing a task mentally, poor cognitive flexibility and deductionAsperger’s SyndromeMay excel at maths – maths has standard procedures and rules and can be predictable and ‘safe’. May do mathsproblems in their head, but can’t tell or show how they got answer.May have difficulty selecting the important information and appropriate strategies May have difficulty monitoring the steps in their thinking; Can be disorganized or not know where to begin May have difficulty in relating to a ‘deep’ understanding of mathematical concepts, prefer rote learning and repetitionSpeech, language and communication difficultiesSpeech difficulties confusion (-teen/-ty, multisyllabic words)Expressive language – being able to describe what they’re doingUnderstanding language – abstract vocabulary, instructions, variety of terms (e.g. for +)Memory difficulties
Maths anxietyPanic stops the mind workingAnxiety causes intrusive thoughts and worry to drain WM resourcesMay not be confident enough to have a go – more likely not to attempt questions
Contrasts in maths learningGood at maths:Use derived facts most of the time (Derived facts – decompose and recompose numbers to make them more familiar)Seldom use countingWork in flexible ways with numbers – decomposing and recomposing themCompress and automatize conceptsUnderstand concepts so reduce memory loadFinds maths difficultCount most of the timeDon’t use derived factsUse difficult techniques e.g. counting backwards for subtractionDon’t think about bigger conceptsTry to rely on poorly memorized proceduresJo Boaler quotes William Thurnston (p. 141) ‘ Mathematics is amazing compressible: you may struggle a long time, step by step, to work through the same process or idea from several approaches. But once you really understand it and have the mental perspective to see it as a whole, there is often a tremendous mental compression. You can file it away, recall it quickly and completely when you need it, and use it as just one step in some other mental process. The insight that goes with this compression is one of the real joys of mathematics.’
Maths learning styleGrasshopper v inchworm
Concrete tools need to:Be used to foster thinking, not just as mechanical supportsBe used by learners to build models of problemsBe appropriate to learner’s level of understanding and cognitive styleBe linked to abstract work by recording alongside concrete workBe used purposefully
Slavonic abacus & number string - http://www.autopresseducation.co.uk
Counting:One-to-one correspondence – helps if move objects in ordered way. Objects can be counted in any order.Understand relationship between numbers in sequence (e.g. staircase activities)Cardinal/ordinalVocabulary: -teen/-tyForwards and backwardsStep-countingKnowing where to start, different starting points
Avoid the ‘counting trap’Counting seen as solution to every problemLiable to errorBurden on memory system – may have to start from beginning, not sure which number to start withDifficulty in synchronising count with objects persistent miscounting don’t see patterns and connections within and between numbers poor sense of numberPrevents development of more efficient techniques
SubitisingUse number patterns visual images of numbers
EstimatingNeed to recognise when an answer is reasonableWe use estimation all the time in daily life – most useful mathematical activity in workplaceEssential part of mathematical problem-solving
Place valueUse Base 10 material on HTU grid, Cuisenaire rods, moneyZero Bridging through 10 – need to know number bonds of ten and of numbers up to tenPrinciple of exchange
Number bonds and componentsNumber bonds of 10Doubles and near doubles (key facts)Components of numbers to ten Use number patterns, Cuisenaire rods, number bond ‘pack’, games
AdditionMove from counting all counting on known facts derived facts6 + 2 is the same as 2 + 6Use number bonds/componentsRecognise that + and - are opposites
SubtractionStages: Count out all numbers, count out number to be taken away, count remainderCount backCount upUse known facts and patterns – use componentsNeed to be able to work flexibly to deal with missing number questions: 5 - = 2
Learn key tables : 2x, 10x, 5x then 3x, 4x, 9x
TimeNeed to be able to deal with fractions: ¼,½, ¾Need to be able to count in fives up to 60Need to be able to understand clockwise movement, times ‘past’ and ‘to’12 on clock face, but 60 minutes and seconds12 on clock face, but 24 hours in day.24 hour clockDigital
Adult maths learners May be very anxious and lacking in confidenceWill probably have developed some strategies of their own for day-to-day mathsWill probably remember/half remember some procedures from schoolMay need to improve their maths for a specific purpose – tailor their programme to meet their needs
ActivitiesGames, visual-spatial puzzles,– e.g. Geoboard, tangrams, Think Fun games (like Rush Hour and Top This), Sudoku, board games, Shut the Box, dice games, card games, dominoes, word puzzles e.g. Boaler (p174) “ Given a 5 litre jar and a 3 litre jar and an unlimited supply of water, how do you measure out 4 litres exactly?”
AssessmentEmerson & Babtie, 2010,The Dyscalculia Assessment, London: ContinuumChinn, 2012, More Trouble with Maths, Abingdon: RoutledgeDIMPWRAT 4, WIAT IIIHodder Tests & GL Assessment have variety of maths tests
AppsCalculators e.g. Soulver, digits, talking calculatorsNumberbondsI say you say (number bonds)Hungry fishZoomCount on it (Slavonic abacus)Math bingoWingsKing of mathTelling timeFishy numbers
