DIFFICULTIES WITH NUMERACY
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- Adelia Carson
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1 Catch Up Numeracy: an Intervention for Dr Ann Dowker Department of Experimental Psychology University of Oxford Wayne Holmes Head of Research and Communications Catch Up DIFFICULTIES WITH NUMERACY Around 6% of children in the UK have severe difficulties with numeracy (Gross 2007) Equates to 180,000 primary school children (DfE 2010) Difficulties with numeracy 2
2 180,000 would fill Wembley stadium twice Difficulties with numeracy 3 180,000 is about as many people who auditioned for X-Factor 2010 Difficulties with numeracy 4
3 If we were to count 180,000 children, at one child every second, we d still be counting in two days time Difficulties with numeracy 5 The consequences are profound Around 20% of the UK have difficulties with mathematics which cause significant practical, educational or functional difficulties (Parsons & Bynner 2005) People with poor numeracy skills are more likely to be unemployed, more likely to be depressed, more likely to be ill and more likely to be arrested (Butterworth & Yeo 2004) Two thirds of young prisoners have numeracy skills at or below the level of an 11-year-old child (Social Exclusion Unit 2002) Costs the UK exchequer as much as 2.4 billion every year (Gross et al. 2009) Difficulties with numeracy 6
4 Mathematics anxiety Many people, especially those with poor numeracy skills, become very anxious about maths. This sometimes reaches the level of a true phobia. Mathematics anxiety can impair performance, both by overloading working memory during mathematics tasks (Ashcraft et al, 2007), and by causing people to avoid opportunities to learn or practice mathematics. Thus a vicious circle develops. This makes it even more important to intervene, preferably as early as possible. Difficulties with numeracy 7 What do these children find difficult? Counting higher than 20 Counting more than 10 objects Reading numbers and number words Which is larger, 18 or 22? What is 18 9? Kim has 3 toys. Donna gives her 1 more. How many toys does Kim have now? If I tell you that = 17, can you quickly tell me what =? Difficulties with numeracy 8
5 Intervention Until recently, there were few research-based interventions to support children with numeracy difficulties. It was to address this gap that Catch Up, a not-for-profit charity, developed the Catch Up Numeracy intervention 9 Catch Up Numeracy To date, Catch Up Numeracy has been implemented in clusters of schools by more than 45 local authorities across England and Wales, and has been used to support more than 20,000 learners 10
6 Conceptual framework componential view of arithmetic exemplified in the Numeracy Recovery intervention devised by Ann Dowker (Department of Experimental Psychology, University of Oxford) Pragmatic framework the approach and methods used in the Catch Up Literacy intervention 11 Conceptual framework: Componential view of arithmetic Arithmetic is made up of multiple abilities, not one It comprises many content areas, and many cognitive processes and forms of understanding (Dowker, 2001, 2005, 2007) 12
7 Arithmetical knowledge may be divided into three broad categories factual knowledge (for example, addition facts, multiplication facts, names given to numbers and operations) procedural knowledge (which guides the execution of written, oral and concrete arithmetical procedures and algorithms) conceptual knowledge (the understanding of arithmetic operations and principles, such as that of commutativity, that allows one to make inferences or to relate the different aspects of arithmetic knowledge) 13 Arithmetical categories may be subdivided into a multitude of components although independently developing, these components are inter-related; weakness in any one component can impact on performance in other components a child might perform well at what might seem to be a rather more difficult task (such as solving word problems) while performing poorly at what might seem to be an easier component (such as counting verbally) 14
8 How many marbles do they each finish up with? 1. Between them, Daniel, Fatima, Thomas and Tracy finish up with 30 marbles. 2. Daniel starts with two marbles, Fatima with 1, Thomas five and Tracy has Fatima wins 1 marble from Thomas and then wins one more from him. 4. They each get more. 5. Daniel wins three marbles from Fatima and Tracy wins two marbles from Thomas. 6. If this were a competition, who would have come first, 2nd, 3rd and last? 15 Pragmatic framework: Catch Up Literacy Designed for learners who are struggling to learn to read (not beginning readers) they have lots of experience and some knowledge of letters, phonics, high frequency words, but are well below the expected NC Level for their age Intervention addresses all aspects of the reading process, including systematic phonics, word recognition, language comprehension Delivered by classroom assistants who have attended a 3 half-day training course 16
9 Pragmatic framework: Catch Up Literacy Evidence from schools is that Catch Up Literacy is effective for struggling readers aged between 6 and 14 years, enabling them to achieve on average more than twice as many months progress in Reading Age as the period of intervention (Brooks 2007, Holmes et al. submitted) 17 Catch Up Numeracy Researched in schools Developed for learners who are struggling to learn numeracy rather than for those who are beginning numeracy they have some knowledge of number, but are well below the expected NC Level for their age Catch Up Numeracy 18
10 2 dimensions of Catch Up Numeracy Components and sub-components of numeracy Catch Up Numeracy Levels Catch Up Numeracy 19 How many marbles do they each finish up with? 1. Between them, Daniel, Fatima, Thomas and Tracy finish up with 30 marbles. Word problems Estimation 2. Daniel starts with two marbles, Fatima with 1, Thomas five and Tracy has Fatima wins 1 marble from Thomas and then wins one more from him. 4. They each get more. 5. Daniel wins three marbles from Fatima and Tracy wins two marbles from Thomas. 6. If this were a competition, who would have come first, 2nd, 3rd and last? Reading and writing Counting verbally Remembered facts Counting objects Translation Derived facts Hundreds, tens and units Ordinal numbers Catch Up Numeracy 20
11 The 10 components of Catch Up Numeracy Counting verbally Counting objects Reading and writing Hundreds, tens and units Ordinal numbers Word problems Translation Derived facts Estimation Remembered facts Catch Up Numeracy 21 The Catch Up Numeracy Levels The Levels aim to help make the intervention practical to administer by school staff and provide a proxy indicator of achievement and progress Catch Up Numeracy 22
12 4 Stages of Catch Up Numeracy Stage 1: formative assessments Stage 2: identifying an appropriate focus for intervention Stage 3: individual sessions Stage 4: ongoing monitoring Catch Up Numeracy 23 Quantitative outcomes primary school children from 15 local authorities (England and Wales) At start of intervention Catch Up Numeracy Matched time No intervention n Mean age (in months) (SD = 14.5) (SD = 13.4) (SD = 12.79). Mean mathematic age (in months)* (SD = 14.58) (SD = 14.11) (SD = 15.96) * Derived from the results of Gillham and Hesse s 2008 Number Screening Test Outcomes 24
13 Quantitative outcomes primary school children from 15 local authorities (England and Wales) Catch Up Numeracy Matched time No intervention n Mean duration of intervention (in months) 4.94 (SD = 1.99) 4.56 (SD = 0.8) 4.57 (SD = 0.82). Mean gain in mathematic age (in months)* (SD = 9.14) (SD = 8.25) (SD = 8.79) * Derived from the results of Gillham and Hesse s 2008 Number Screening Test Outcomes 25 Quantitative outcomes primary school children from 15 local authorities (England and Wales) Catch Up Numeracy Matched time No intervention n Mean ratio gain* (SD = 1.9) (SD = 1.78) (SD = 1.8) * Mean ratio gain = mean of (months gained in mathematical age divided by duration of intervention in months) (Topping 1987), where a gain of 2 is good impact (Brooks 2007). An ANOVA, with group as the factor and ratio gain as the dependent variable, showed that there was a difference between the three groups (F(2, 437) = 8.92, p <.001). Tamhane s T2 post hoc tests showed that the Catch Up Numeracy group made higher ratio gains than either of the other groups (which did not differ significantly from one another). Outcomes 26
14 Quantitative outcomes primary school children from 15 local authorities (England and Wales) Catch Up Numeracy group compared with matched time group d (effect size) = 0.54 Catch Up Numeracy group compared with no intervention group d (effect size) = 0.60 Outcomes 27 Quantitative outcomes primary school children receiving Catch Up Numeracy (Vale of Glamorgan) At start of intervention Cohort 1 Cohort 2 n Mean age (in months) (SD = 11.67) (SD = 16.74). Mean mathematic age (in months)* (SD = 13.53) (SD = 14.44) * Derived from standardised assessments administered by school staff. Outcomes 28
15 Quantitative outcomes primary school children receiving Catch Up Numeracy (Vale of Glamorgan) Cohort 1 Cohort 2 n Mean duration of intervention (in months) 7.22 (SD = 1.91) 4.54 (SD = 0.77). Mean number of 15 minute sessions per week 0.89 (SD = 0.40) 1.51 (SD = 0.48) Mean gain in mathematic age (in months)* (SD = 8.99) (SD = 6.87) * Derived from standardised assessments administered by school staff. Outcomes 29 Quantitative outcomes primary school children receiving Catch Up Numeracy (Vale of Glamorgan) Cohort 1 Cohort 2 n Mean ratio gain 1.75 (SD = 1.3) 3.69 (SD = 1.93) Mean gain in months per hour of intervention (SD = 1.81) (SD = 1.48) Paired t-test analyses of the mean mathematical ages at the start and end of the intervention showed that the children in both cohorts had increased their mathematical age (Cohort 1: t = 12.63, df = 84, p <.001; Cohort 2: t = 12.22, df = 55, p < 0.01). Outcomes 30
16 Quantitative outcomes primary school children receiving Catch Up Numeracy (Vale of Glamorgan) Cohort 1 (average of 0.89 fifteen minute sessions per week): Effect size (difference between the mean gain in Maths Age and the mean duration of intervention) d = 0.78 Cohort 2 (average of 1.51 fifteen minute sessions per week): Effect size (difference between the mean gain in Maths Age and the mean duration of intervention) d = 2.34 Outcomes 31 Qualitative outcomes Feedback from schools suggests that classroom staff believe that Catch Up Numeracy is of considerable benefit to learners who struggle with numeracy It improves the learners understanding of maths ( it tunes them into maths, teacher quoted in Evans 2008) It gives them a wider range of strategies on which to draw ( they begin to see a pattern that they hadn t even thought of before, teacher at Review and Next Steps session); It allows them to begin to enjoy maths ( it was very cool today because we did it against the clock and now I think it s easier with bigger numbers, learner quoted in OCN submission); It puts them in control of their learning ( maths is power!, learner quoted in OCN submission) It raises their self-confidence both with maths and across other areas of the curriculum ( the impact has been amazing..., their confidence has grown in the classroom, they re putting their hands up to answer questions..., where normally they wouldn t even have attempted it, classroom assistant) Outcomes 32
17 Discussion Catch Up Numeracy, an intervention targeted to children s specific strengths and weaknesses in arithmetic, can lead to very significant improvements in arithmetic. Children who received Catch Up Numeracy intervention made two and a half times as much gain over time as would be expected on the basis of the passage of time alone. The targeted nature of Catch Up Numeracy is a crucial factor in its success Effective intervention doesn t have to be intensive, expensive or delivered by highly trained teachers Discussion 33 Discussion The data lends further support to the view that arithmetical ability is made up of multiple components, and that there is no such thing as arithmetical ability, only arithmetical abilities (Dowker, 2005) Discussion 34
18 Discussion Further research: are the particular components used the crucial cial ones, or are others as important? to what extent does the amount of time (overall duration and time spent per week) affect the level of progress? how does the effectiveness of Catch Up Numeracy compare with other interventions? how might Catch Up Numeracy be made appropriate for an extended age range (for children in secondary school or adults with numeracy difficulties)? (Research is now beginning on its use in secondary schools.) Discussion 35 Discussion Further research: could numeracy difficulties be diagnosed and interventions assembled at the time of school entry? There is evidence (Dowker, 2008) that by age 4, there are basic numerical abilities are already made up of many components which can show marked discrepancies; and that there are considerable individual differences in numerical abilities as a whole and in specific components. Discussion 36
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