DIFFICULTIES WITH NUMERACY

3rd National Conference Dyscalculia & Maths LD Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Hol...
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3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

Catch Up Numeracy: an Intervention for Learners who Struggle with Numeracy Dr Ann Dowker Department of Experimental Psychology University of Oxford [email protected] Wayne Holmes Head of Research and Communications Catch Up [email protected]

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

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

180,000 would fill Wembley stadium twice

Difficulties with numeracy

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180,000 is about as many people who auditioned for X-Factor 2010

Difficulties with numeracy

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

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

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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 q as much as £2.4 billion every y yyear (Gross et al. 2009)

Difficulties with numeracy

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

Mathematics anxiety ●

Many people, especially those with poor numeracy skills, become very anxious about maths.

● ●

This sometimes reaches the level of a true phobia.

● ●

Thus a vicious circle develops.

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. This makes it even more important p to intervene,, p preferably y as early y as possible.

Difficulties with numeracy

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What do these children find difficult? ● ● ● ● ● ●

Counting higher than 20



If I tell you that 12 + 5 = 17, can you quickly tell me what 5 + 12 = ?

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?

Difficulties with numeracy

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

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

Developing Catch Up Numeracy

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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

Developing Catch Up Numeracy

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

Developing Catch Up Numeracy 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

Developing Catch Up Numeracy

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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))

Developing Catch Up Numeracy

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

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)

Developing Catch Up Numeracy

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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 p ((such as counting g verbally) y)

Developing Catch Up Numeracy

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

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 2. 3. 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?

Developing Catch Up Numeracy

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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

Developing Catch Up Numeracy

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

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)

Developing Catch Up Numeracy

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Catch Up Numeracy ● ●

Researched in schools 2007-2008 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

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

2 dimensions of Catch Up Numeracy

● Components and sub-components of numeracy ● Catch Up Numeracy Levels

Catch Up Numeracy

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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 2.

Reading and writing Counting verbally

3.

Fatima wins 1 marble from Thomas and then wins one more from him.

Remembered facts

4.

They each get

Counting objects Translation Derived facts

5.

Daniel wins three marbles from Fatima and Tracy wins two marbles from Thomas.

Hundreds, tens and units

6.

If this were a competition, who would have come first, 2nd, 3rd and last?

Ordinal numbers

Catch Up Numeracy

more.

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

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 E ti ti ● Remembered facts Catch Up Numeracy

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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

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

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

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Quantitative outcomes 1 ●

440 primary school children from 15 local authorities (England and Wales)

At start of intervention

Catch Up Numeracy

Matched time

No intervention

n

348

50

42

Mean age (in months)

103.85 (SD = 14.5)

106.45 (SD = 13.4)

105.78 (SD = 12.79).

Mean mathematic age 96.25 94.39 97.39 (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

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

Quantitative outcomes 1 ●

440 primary school children from 15 local authorities (England and Wales) Catch Up Numeracy

Matched time

No intervention

n

348

50

42

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 11.27 7.00 6.29 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

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Quantitative outcomes 1 ●

440 primary school children from 15 local authorities (England and Wales) Catch Up Numeracy

Matched time

No intervention

n

348

50

42

Mean ratio gain*

2.51 (SD = 1.9)

1.49 (SD = 1.78)

1.37 (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

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

Quantitative outcomes 1 ● ●

440 primary school children from 15 local authorities (England and Wales)



Catch Up Numeracy group compared with ‘no intervention’ group d (effect size) = 0.60

Catch Up Numeracy group compared with ‘matched matched time time’ group d (effect size) = 0.54

Outcomes

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Quantitative outcomes 2 ●

141 primary school children receiving Catch Up Numeracy (Vale of Glamorgan)

At start of intervention

Cohort 1

Cohort 2

n

85

56

Mean age (in months)

103.73 (SD = 11.67)

108.07 (SD = 16.74).

Mean mathematic age (in months)*

99.46 (SD = 13.53)

97.07 (SD = 14.44)

* Derived from standardised assessments administered by school staff.

Outcomes

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

Quantitative outcomes 2 ●

141 primary school children receiving Catch Up Numeracy (Vale of Glamorgan) Cohort 1

Cohort 2

n

85

56

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)*

12.32 (SD = 8.99)

15.96 (SD = 6.87)

* Derived from standardised assessments administered by school staff.

Outcomes

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Quantitative outcomes 2 ●

141 primary school children receiving Catch Up Numeracy (Vale of Glamorgan) Cohort 1

Cohort 2

n

85

56

Mean ratio gain

1.75 (SD = 1.3)

3.69 (SD = 1.93)

Mean gain in months per hour of intervention

2.14 (SD = 1 1.81) 81)

2.93 (SD = 1 1.48) 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

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

Quantitative outcomes 2 ● ●

141 primary school children receiving Catch Up Numeracy (Vale of Glamorgan)



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

Cohort 1 (average of 0.89 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

Outcomes

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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

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

Discussion ●

Catch Up Numeracy, an intervention targeted to children’s specific p strengths g 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

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Discussion ●

The data lends further support to the view that arithmetical abilityy is made up p of multiple p components, p , and that ‘there is no such thing as arithmetical ability, only arithmetical abilities’ (Dowker, 2005)

Discussion

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk

3rd National Conference Dyscalculia & Maths LD

Catch Up Numeracy: an Intervention for  Learners who Struggle with Numeracy  Dr Ann Dowker & Wayne Holmes

Discussion ●

Further research:



are the partic particular lar components used sed the cr crucial cial ones 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

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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

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© Dr Ann Dowker & Wayne Holmes www.learning–works.org.uk      T. +44 (0)1672 512914       info@learning‐works.org.uk