How Many Paths Can a Child Go Down?
Children’s Progress in Numbers Count
Nick Dowrick, Victoria Jackson and Sylvia Dunn
Edge Hill University
correspondence address:Vicktoria Jackson, Faulty of Education, Edge Hill University, St Helens Road, Ormskirk, L39 4QP
Paper presented at the British Educational Research Association Annual Conference, University of Manchester, 2-5 September 2009
Abstract
This paper reports on a study of Numbers Count, a new numeracy intervention programme for low-attaining 6-7 year-old children in England that has been devised for the Every Child Counts initiative. Entry and exit data was collected on 1,607 children who took part in the first two terms of Numbers Count, between September 2008 and April 2009; teachers provided more detailed accounts of the progress made by 597 of the children.
This study aimed to assess the effectiveness of Numbers Count and to investigate the pathways that children followed as they progressed from the start to the end of their programmes. It found that the intervention was effective for all children and particularly for the very lowest-attaining children. Most children made steady progress from start to finish, but the greatest overall gains were achieved by a large group of children who started slowly before making fast progress later. The programme was long enough to allow this to happen.
Implications for practitioners are suggested.
Background
The Every Child Counts initiative is run by a partnership of the Every Child a Chance Trust, a university, the National Strategies, and the Department for Children, Schools and Families. It addresses a growing awareness that some children need early and intensive support in order to maximise their progress and close attainment gaps, and a growing understanding of the nature of effective mathematics intervention. It aims to enable the lowest-attaining Year 2 (6-7 years of age) children in mathematics to make greater progress towards expected levels of attainment and to achieve National Curriculum Level 2 or better by the end of Key Stage 1.
To achieve its aim of enabling progress for the lowest-attaining children in mathematics, a new numeracy intervention, Numbers Count, was developed specifically for Every Child Counts and based upon the recommendations of the Williams Review (2008). 210 specially-trained teachers began to give Numbers Count support to 4 of the lowest attaining Year 2 pupils in each of their schools in September 2008. Each child received 30 minutes of individual, daily support for approximately 12 weeks in the autumn term, and the teachers then taught another 4 children each in the spring term. The project will continue until 2011 but this paper reports only on the first two terms, September 2008 to April 2009.
Research on interventions
Dowker (2004: v) surveyed the international research on mathematics interventions and reported that:
Children's arithmetical difficulties are highly susceptible to intervention. Individualized work with children who are falling behind in arithmetic has a significant impact on their performance.
The most widely used mathematics intervention programme, both in this country and abroad, has been Mathematics Recovery. It was developed in the 1990’s and is aimed at children who are not meeting age-related attainments for numeracy. It encompasses four main elements that are shared by Numbers Count: early intervention, assessment, teaching, and professional development. Analysis of the Count Me In Too numeracy program in Australia (Bobis et al., 2005), which was based upon the learning framework of Mathematics Recovery, showed that it was successful in improving not only children's number skills but also their wider mathematics achievement. Wright, Martland and Stafford (2006) reported that children’s self-esteem and general attitudes to learning were improved as a result of taking part in Mathematics Recovery, as well as their mathematical abilities.
A study of Mathematics Recovery in England has also shown that it is highly effective in developing children's basic numeracy skills (Wiley, Holliday and Martland, 2007). Its effectiveness was endorsed by the Williams Review (Williams, 2008), which also reported high rates of progress for children supported by the London-based Numeracy Recovery programme that has a wide-ranging diagnostic assessment element also shared by Numbers Count. Haseler (2008)has commented that a strength of individualised intervention programmes as a whole is that they can be specifically targeted to address individual children's difficulties, and Dowker (2007) has reported that they can be very successful when they do so.
However, although the existing research clearly shows that mathematics interventions can be and are effective, it lacks the detail of the available literature on literacy intervention. Dowker (2007) recommends further investigation to ascertain how exactly mathematics interventions lead to children’s progress.
Research questions
This study is one of a number based upon Numbers Count as the intervention programme at the heart of the Every Child Counts project. Because it is a new intervention, theinitial aim was to find out whether it is effective:
Research Question 1Do low-attaining children make progress when they take part in Numbers Count?
If the answerto this was positive, a further aim was to find out more detail about how mathematics interventions lead to children’s progress. The specific questions for this project were:
Research Question 2What effect does Numbers Count have on children’s mathematical attainment and on their attitudes towards mathematics?
Research Question 3Is Numbers Countmoreeffective for the very lowest-attaining children or for children who are just below national norms?
Research Question 4Do most children follow identifiable pathways as they progress?
For example, do they make steady progress throughout the intervention or do they start slowly and accelerate later?
Research Question 5Do children’s attitudes towards mathematics and their mathematical attainment progress on similar pathways?
Research Question 6How do children’s pathways relate to the standard length of 12 weeks for the Numbers Count programme?
Methods
This study took place in the first year of Numbers Count, so there was no available information on which to base predictions about the children’s progress and pathways. Dowker (2004, 2007) has shown that little is yet known or published about the ways in which children make progress. A grounded theory approach (Goulding, 2002) was therefore taken to this project, whereby research findings would be grounded in the data collected rather than foregrounded in the findings of previous projects.
Answers to Research Question 1 were partially available through national data collected on Numbers Count for the Every Child Counts project, relating to 1,607 children taught between September 2008 and April 2009 by 216 teachers. A standardised test (the Sandwell Early Numeracy Test) was administered to each child on entry to the programme by their Numbers Count Teacher and on exit by an independent teacher. It yielded standard scores and number age scores and therefore allowed measures of gain between entry and exit for each child.
To answer Research Question 2, a measure of children’s attitudes towards mathematics was needed. Investigating the attitudes of 6- and 7-year-old children is problematic. Mostresearchhas investigated teachers’ perceptions of children’s attitudes, rather than children’s own reports or demonstrations of their attitudes, justified by doubts about children’s self-awareness(Smith, Duncan & Marshall, 2005) or their cognitive ability to process and respond to structured questions (Christensen & James 2008).
However, some studies have found that children can successfully report on their own attitudes, particularly when the researcher is well know to them (Smith, Duncan & Marshall 2005) and talks to them in their own homes (Maddock, 2006). While these advantages are not available to Numbers Count Teachers, a more practicable approach was suggested by the work of Cunningham (2008), who researched 5 and 6 year old children’s attitudes towards reading and writing. 201 pupils were questioned by their kindergarten teachers during the first week of school. The teacher showed them faces on a scale ranging from a very happy face depicting‘very good’ to a frowning face depicting‘not good’), and asked them to point to the relevant face in response to questions such as, ‘How do you feel when someone reads to you?’
An attitude survey with a mixed methodology was devised for Numbers Count. Children, their teachers and their parents separately answered questions about the child’s attitude to and confidence in mathematics; the children pointed at one of five faces to indicate their response while the adults used a five-point scale. The responses of all participants were scored (from 5 as ‘very positive’ to ‘1’ as very negative) and totalled to give an overall Numbers Count Attitude Survey score for each child on entry to and exit from the programme.
To answer Research Question 3, correlations between children’s entry scores and exit gains on the mathematics test and attitude survey were analysed.
For Research Questions 4 and 5, it was unrealistic to attempt to measure children’s attainment at short intervals along their journeys, which would anyway have been bedevilled by the difficulty of defining when learning has taken place (Houssart, 2004). Numbers Count Teachers were therefore asked to complete a questionnaire in April 2009, at the end of their second term of teaching, about the four children who had recently completed a Numbers Count programme with them. For each child, the teacher was asked to indicate which of six diagrams best described the pathway of the child’s progress over the course of the intervention (Figure 1). Teachers identified two pathways for each child:
- one to represent the child’s progress in confidence and attitude towards mathematics;
- one to represent the child’s progress in mathematical skills and knowledge.
Figure 1Children’s Pathways
152 out of 216 teachers responded to the questionnaire, reporting on 597 children. They also wrote a brief of explanation of the reasons why they though children had followed particular pathways.
In addition, 5 teachers agreed to keep a weekly log for one child each, recording their judgements of how much progress each child had made during the week.
Research Question 6 could partly be answered by an analysis of the questionnaires – if teachers reported that most children only began to make progress at the end of the intervention or that had completed their progress well before the end, questions could be raised about whether a different length of programme would be more suitable. An analysis was also carried out of the amount of progress children made in relation to the number of days that they had been taught, as reported by their teachers in a separate data-collection exercise.
Results
Table 1Entry Scores and Gains for All Children and for the Sample Children
AllChildren / Sample Children
Number of children / 1,607 / 597
Mean number of lessons / 40.6 / 41.5
Attitude Survey
mean entry score (points)
mean gain / 50.0
10.5 / 50.1
11.0
Number Test
mean entry standard score
mean gain
mean entry number age (months)
mean gain / 85.2
15.3
69.0
13.5 / 84.3
16.6
69.2
14.5
Table 1 reports on all of the 1,607 children who took part in Numbers Count between September 2008 and April 2009, and on the sample of 597 children whose teachers reported on their pathways in April 2009. It indicates that, after receiving an average of 41 lessons in 12 weeks, children’s attitude survey scores improved by about 20%. Their number test standard scores rose from a mean of 85 to 101, equalling the national norm, and their number ages progressed by a mean of 14 months, approximately 4.5 times the expected rate of progress in 12 weeks.
The entry scores and gains made by the sample children were similar to those of all children, indicating that the sample was an acceptable representation of the whole population of Numbers Counts children.
Table 2 indicates that children’s attitude survey entry scores were positively correlated to their number test entry scores: the more confident children tended to be the more competent children. There was also a negative correlation between entry scores and gain on both the attitude survey and the number test: children with the lowest entry scores made the most progress, as shown in Figures 2 and 3. Attitude gain was positively correlated with number test gain: children who made the most progress on one also made the most progress on the other.
Table 2 Relationships between attitude survey and number test entry scores and gains
Attitude survey entry score / Attitude survey gain / Number test entry standard score / Number test standard score gainAttitude survey entry score / Pearson Correlation / -.548** / .255** / .010
Sig. (2-tailed) / .000 / .000 / .814
Attitude survey gain / Pearson Correlation / -.548** / .013 / .244**
Sig. (2-tailed) / .000 / .778 / .000
Number test entry standard score / Pearson Correlation / .255** / .013 / 1.000 / -.133**
Sig. (2-tailed) / .000 / .778 / .001
Number test standard score gain / Pearson Correlation / .010 / .244** / -.133**
Sig. (2-tailed) / .814 / .000 / .001
**. Correlation is significant at the 0.01 level (2-tailed).n = 1607
Figure 2 Number test standard score gain and entry standard score
Figure 2 indicates that children across the lower band of entry standard scores (65 – 84) made broadly similar progress. Children whose entry scores were closer to the national norm (85 – 104) made less progress.
Figure 3 indicates that there was a fairly constant relationship between attitude entry scores and gains: the lower children’s entry scores, the more they gained.
Figure 3 Attitude Survey Score Gain and Entry Attitude Score
Table 3Numbers of Children identified by Teachers as having followed each Pathway
Pathway / Confidence and Attitude / Mathematicsn / % / n / %
1 no progress / 12 / 2.0% / 11 / 1.9%
2 steady progress / 276 / 46.3% / 217 / 36.5%
3 fast then slowing down / 38 / 6.4% / 50 / 8.4%
4 slow then getting faster / 155 / 26.0% / 148 / 24.9%
5 slow – fast – slow / 56 / 9.4% / 64 / 10.8%
6 stop – start – stop - start / 59 / 9.9% / 104 / 17.5%
all / 596 / 100% / 594 / 100%
Table 3 summarises teachers’ choices of the pathway diagram (see Figure 1, above) that best represented their children’s progress during their Numbers Count programmes. Teachers also had the option of describing or drawing another pathway if none of the offered diagrams was suitable: as only 4 teachers chose to do so (to describe 0.3% of the sample children), these results were not analysed.
Table 3 indicates that the majority of children took either Pathway 2 (steady progress) or Pathway 4 (slow then getting faster) in their confidence and attitude towards mathematics. These two pathways were followed by72% of all children, and no other pathway was taken by more than 10% of children. Pathway 1 (no progress) was typical of only 2% of children.
For progress in mathematical skills and understanding, Pathways 2 and 4 were also the most common. While Pathway 2 was again the most frequent, fewer children (37%) took this pathway for mathematics than did so for confidence and attitude (46%). Pathway 6 (stop – start – stop – start) was taken by almost twice as many children (18%) for mathematics as it was for confidence and attitude (10%). Pathway 1 was again typical of only 2% of children.
Table 4Confidence and Attitude Pathways and Attitude Survey Gains
Confidence and AttitudePathway / no. of children / Mean Attitude Survey Gain
1 no progress / 12 / 8.7
2 steady progress / 268 / 10.7
3 fast then slowing down / 35 / 11.0
4 slow then getting faster / 146 / 11.8
5 slow – fast – slow / 53 / 11.2
6 stop – start – stop - start / 56 / 10.7
Table 4 analyses the attitude survey gains of children who were identified by their teachers as following each pathway for confidence and attitude. It indicates that children who were identified as making no progress (Pathway 1) did in fact make significant progress, albeit considerably less than other children, Children identified by their teachers as having followed all the other pathways made broadly similar progress to each other. Children on Pathway 2 (steady progress) did not gain more than other children, while those on Pathway 4 (slow then getting faster) gained slightly more than others.
Table 5Mathematics Pathways and Number Test Gains
MathematicsPathway / no. of children / Mean Standard Score Gain
1 no progress / 11 / 4.5
2 steady progress / 217 / 17.8
3 fast then slowing down / 50 / 14.4
4 slow then getting faster / 148 / 19.6
5 slow – fast – slow / 64 / 15.0
6 stop – start – stop - start / 104 / 13.0
Table 5 analyses the number test gains of children who were identified by their teachers as following each pathway for mathematical skills and knowledge. Here, children identified as being on Pathway 1 (no progress) made much less progress than the other children. The greatest progress was made by children who had take Pathway 4 (slow then getting faster), followed by children on Pathway 2 (steady progress). Progress on the other three pathways was broadly similar.
Table 6Children who followed the same Pathways for Confidence and Attitudes and for Mathematics
Pathway / Confidence & Attitude / Mathematicschildren on this confidence and attitudes pathway,
as a % of all sample children / children on this confidence and attitudes pathway,
as a % of all children on this pathway for mathematics / children on this mathematics pathway,
as a % of all sample children / children on this mathematics pathway,
as a % of all children on this pathway for confidence and attitudes
1 no progress / 2.0% / 36.4% / 1.9% / 33%
2 steady progress / 46.3% / 68.7% / 36.5% / 54.0%
3 fast then slowing down / 6.4% / 30.0% / 8.4% / 39.5%
4 slow then getting faster / 26.0% / 45.3% / 24.9% / 43.8%
5 slow – fast – slow / 9.4% / 23.4% / 10.8% / 26.8%
6 stop – start – stop - start / 9.9% / 29.8% / 17.5% / 52.5%
Table 6 reports the percentage of children who followed the same pathways for each aspect of their measured progress – confidence and attitudes, and mathematical skills and knowledge. It shows that, in every case, children who took a particular pathway for one element were considerably more likely to take the same pathway for the other element than were other children not on that pathway. For example, 36% of children who took Pathway 1 for mathematics also took Pathway 1 for confidence and attitude, whereas only 2% of all children took Pathway 1 for confidence and attitude. 53% of children on Pathway 6 for confidence and attitude also took Pathway 6 for mathematics, three times as many as the proportion of all children (18%) who took Pathway 6 for mathematics.