THE KEY STAGE 3 NATIONAL STRATEGY FOR MATHEMATICS:
its affects on pupils’ attitudes to mathematics and their classroom experiences.
Paul J. Wilson
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Submitted by Paul John Wilson to the University of Exeter as a dissertation for the degree of Doctor of Education in Mathematics Education, January 2003.
This dissertation is available for Library use on the understanding that it is copyright material and that no quotation from the dissertation may be published without proper acknowledgement.
I certify that all material in this dissertation which is not my own work has been identified and that no material has previously been submitted and approved for the award of a degree by this or any other University.
ABSTRACT
This account explores how, for Year 8 pupils from a large comprehensive school, the introduction of the Key Stage 3 National Strategy for Mathematics has affected both
1. their attitudes to mathematics and
2. their experiences of mathematics teaching.
Data were collected from two groups of pupils using a questionnaire. The first (Year 8: 2001-2002) had not been formally affected by the implementation of the Strategy. The second group (Year 8: 2002-2003) had been taught in line with the Key Stage 3 Strategy for mathematics from Year 7. Comparisons were made between the two sets of results.
The questionnaire consisted of two sections, corresponding to the two areas of investigation:
1. ‘what you think about mathematics’ and
2. ‘maths lessons’.
The first section consisted of eighteen items concerning pupils’ beliefs and feelings about mathematics from the Third International Mathematics and Science Study (Keys et al, 1997). This enabled comparisons to be made between both samples and the TIMSS’ English results from 1996. The second section concerned the teaching approaches recommended by the Framework (DfES, 2001). Four items were from TIMSS, the remaining 23 items were devised to cover all of the approaches to teaching recommended for the Strategy.
There is no evidence from this project that the implementation of the Strategy has had a negative affect on pupils’ attitudes, as had been suggested by some commentators. In fact, there is some indication that pupils’ attitudes may have improved. There is evidence from the pupils’ responses that their teachers have started to adopt the teaching approaches recommended for the Strategy, though this varies between the teachers and between teaching approaches. The attitudes results from this project are more negative than those from TIMSS. This may
· be a characteristic of the two sample populations, or
· indicate that the TIMSS attitude results have limited relevance to these populations.
These results will contribute to the department’s review of the implementation of the Key Stage 3 Strategy. INSET will continue to focus on developing effective approaches to teaching, in line with the recommendations of the Framework. However, in order to avoid overtly mechanistic approaches, departmental members will be encouraged to be flexible and creative in their teaching.
List of Contents
1 Title Page
2 Abstract
4 List of Contents
8 List of Tables
10 Introduction
14 Chapter 1 The Introduction of The Key Stage 3 Strategy for Mathematics
14 1.1 The Historical Background
15 1.2 Contemporary Concerns about Standards
18 1.3 The National Numeracy Strategy
19 1.4 The Key Stage Three Strategy for Mathematics
23 Chapter 2 The Framework and the Aims and Pedagogy of the Key Stage
Three Strategy for Mathematics
23 2.1 The Framework
27 2.1.1 Expectations
28 2.1.2 Progression
29 2.1.3 Engagement
30 2.1.4 Transformation
31 2.2 The Aims of the Strategy
33 2.2.1 Raising Standards
35 2.2.2 Greater Central Control of the Curriculum and Pedagogy
35 2.2.3 Summary: the Aims of the Strategy
37 2.3 The Curricular Implications of the Strategy
37 2.3.1 Curriculum Organisation
40 2.3.2 Curriculum Content
40 2.3.3 Numeracy
42 2.3.4 The National Curriculum Attainment Targets
44 2.3.5 Summary: the Curricular Implications of the Key Stage Three
Strategy
45 2.4 The Pedagogy of the Strategy
45 2.4.1 Direct Interactive Teaching
47 2.4.2 The Three Part Lesson
48 2.4.3 A Typical Mathematics Lesson
50 2.4.4 Special Needs in Mathematics
51 2.4.5 Summary: the Pedagogy of the Strategy
53 Chapter 3 A Critical Review of the Strategy
53 3.1 Theoretical and Empirical Evidence Underpinning the Strategy
57 3.2 The Introduction of the Strategy
58 3.3 Levelness
62 3.4 Special Needs and Differentiation
64 3.5 Direct Interactive Whole-Class Teaching
67 3.6 Attitudes and Affective Responses to Mathematics
72 3.7 Summary
73 Chapter 4 Methodology
73 4.1 Research Paradigms
76 4.2 Principles Underlying the Strategy and TIMMS
78 4.3 Summary
80 Chapter 5 Methods
80 5.1 Overview
81 5.2 The School
82 5.3 The Year Eight Sample
83 5.4 Sample Size
84 5.5 Using a Questionnaire
85 5.6 TIMSS Items
86 5.7 Clusters
87 5.8 Section 1 Items
89 5.9 Section 2 Items
90 5.10 Section 2 Clusters
95 5.11 Methods of Analysis
98 5.12 The Pilot
99 5.13 Validity and Reliability
103 5.14 Ethics
106 Chapter 6 Analysis of the 2001 Research Data
106 6.1 Measures
107 6.2 2001 Data
109 6.3 Section 1 2001
110 6.4 Section 1 Clusters
117 6.5 Section 2 2001
118 6.6 Section 2 Clusters
128 6.7 Teachers’ Results
132 6.8 Summary of the 2001 Data
135 Chapter 7 Analysis of the 2002 Research Data
135 7.1 2002 Data
138 7.2 Section 1 2002
139 7.3 Section 1 Clusters
144 7.4 Section 2 2002
145 7.5 Section 2 Clusters
155 7.6 Teachers’ Results
160 7.7 Summary of the 2002 Data
163 Chapter 8 Comparison of the 2001 and the 2002 Research Data
163 8.1 Section 1 Data – Pupils
164 8.2 Differences in the Whole Sample Results Between 2001
and 2002
165 8.3 Differences Between the Genders
166 8.4 Section 1 Clusters
168 8.5 Section 2
170 8.6 Section 2 clusters
181 8.7 The Pupils’ Additional Comments
183 8.8 Teachers’ Results
186 8.9 Summary
191 Chapter 9 Conclusions and Evaluation
191 9.1 The Results of the Project
194 9.2 The School Context
197 9.3 The Wider Significance of the Results
200 9.4 Areas for Further Research
202 9.5 Consequences of the Project
203 9.6 Evaluation
208 Chapter 10 Postscript
209 10.1 My Role as Head of Department and Researcher
211 10.2 Classroom Observations
212 10.3 The Numeracy Consultant’s View
214 10.4 The Pupils’ Attainment in National Testing
216 10.4.1 Key Stage 2 Results
217 10.4.2 NFER CAT Screening Tests
219 10.5 A Personal View of the Introduction of the Key
Stage 3 Strategy in the School
221 10.6 A Contextual Review of the Research Findings
Appendices (omitted from this document. Contact author for details)
223 Appendix 5: Student Questionnaire: Final Version
227 Appendix 5:1 Questionnaire Framework Grid
15 Appendix 5.2: List of Clusters
16 Appendix 5.14: Note To Pupils
17 Appendix 6.2: 2001 Overall Analysis
18 Appendix 6.3: 2001 Section 1 and TIMSS
19 Appendix 6.4: Section 1 Clusters
20 Appendix 6.4d1: Individual Questions in Cluster D
234 Appendix 6.4e1: Individual Questions in Cluster E
235 Appendix 6.7a: Comparison Teacher and Pupil 2001
241 Appendix 6.7b: Teacher and Pupil 2001 Agreements
242 Appendix 7.1 2002 Overall Analysis
243 Appendix 7.2: 2002 Section 1 and TIMSS
244 Appendix 7.3: Section 1 Clusters
245 Appendix 7.3c1: Individual Questions in Cluster C
246 Appendix 7.3d1: Individual Questions in Cluster D
247 Appendix 7.3e1: Individual Questions in Cluster E
248 Appendix 7.6a: Comparison: Teacher and Pupil 2002
254 Appendix 7.6b: Teacher and Pupil 2002 Agreements.
255 Appendix 8.1: Section 1 Analysis of Individual Questions
258 Appendix 8.4: Section 1 Clusters
259 Appendix 8.5: Section 2 Analysis of Individual Questions
263 Appendix 8.6: Section 2 Clusters Revised
264 Appendix 8.7 Section 2 Analysis of Teachers' Responses to Individual Questions
267 Appendix 10.3 The Numeracy Consultant’s View
268 Appendix 10.4 Comparison of Y8 Teacher Assessments
269 Appendix 10.4.1: Comparison of KS2 Results
270 Appendix 10.4.2a: NFER Predictions
271 Appendix 10.4.2b: Comparison of NFER Forecasts
272 Bibliography
List of Tables
29 Table 2.1.2 School Year and National Curriculum Level
107 Table 6.2 2001 Pupil Data
109 Table 6.3 2001 Data: Comparison with TIMSS
111 Table 6.4a 2001 Section 1 Cluster A
112 Table 6.4b 2001 Section 1 Cluster B
113 Table 6.4c 2001 Section 1 Cluster C
114 Table 6.4d 2001 Section 1 Cluster D
114 Table 6.4d1 2001 Section 1 Cluster D (by gender)
115 Table 6.4e 2001 Section 1 Cluster E
116 Table 6.4e1 2001 Section 1 Cluster E (by gender)
118 Table 6.6a 2001 Section 2 Cluster A
119 Table 6.6b 2001 Section 2 Cluster B
121 Table 6.6c 2001 Section 2 Cluster C
122 Table 6.6d 2001 Section 2 Cluster D
123 Table 6.6e 2001 Section 2 Cluster E
123 Table 6.6f 2001 Section 2 Cluster F
124 Table 6.6g 2001 Section 2 Cluster G
125 Table 6.6h 2001 Section 2 Cluster H
125 Table 6.6i 2001 Section 2 Cluster I
126 Table 6.6j 2001 Section 2 Cluster J
127 Table 6.6k 2001 Section 2 Cluster K
129 Table 6.7 2001 Teachers’ Results
136 Table 7.1 2001 Pupil Data
138 Table 7.2 2002 Data: Comparison with TIMSS
140 Table 7.3a 2002 Section 1 Cluster A
140 Table 7.3b 2002 Section 1 Cluster B
141 Table 7.3c 2002 Section 1 Cluster C
142 Table 7.3d 2002 Section 1 Cluster D
143 Table 7.3e 2002 Section 1 Cluster E
145 Table 7.5a 2002 Section 2 Cluster A
146 Table 7.5b 2002 Section 2 Cluster B
148 Table 7.5c 2002 Section 2 Cluster C
149 Table 7.5d 2002 Section 2 Cluster D
150 Table 7.5e 2002 Section 2 Cluster E
150 Table 7.5f 2002 Section 2 Cluster F
151 Table 7.5g 2002 Section 2 Cluster G
152 Table 7.5h 2002 Section 2 Cluster H
153 Table 7.5i 2002 Section 2 Cluster I
154 Table 7.5j 2002 Section 2 Cluster J
155 Table 7.5k 2002 Section 2 Cluster K
156 Table 7.6 2002 Teachers’ Results
163 Table 8.1 Section 1: Comparison of Pupil Data
168 Table 8.5 Section 2: Comparison of Pupil Data
170 Table 8.6a Section 2: Comparison of Cluster A
171 Table 8.6b Section 2: Comparison of Cluster B
173 Table 8.6c Section 2: Comparison of Cluster C
174 Table 8.6d Section 2: Comparison of Cluster D
175 Table 8.6e Section 2: Comparison of Cluster E
176 Table 8.6f Section 2: Comparison of Cluster F
177 Table 8.6g Section 2: Comparison of Cluster G
177 Table 8.6h Section 2: Comparison of Cluster H
178 Table 8.6i Section 2: Comparison of Cluster I
179 Table 8.6j Section 2: Comparison of Cluster J
180 Table 8.6k Section 2: Comparison of Cluster K
183 Table 8.8 Comparison of Teachers’ Results
215 Table 10.4 Year 8 Teacher Assessments
216 Table 10.4.1 Key Stage 2 Results
217 Table 10.4.2 NFER CAT Forecasts
INTRODUCTION
The Key Stage 3 National Strategy was implemented in September 2001 with the intention of building on the results of the Literacy and Numeracy Strategies in primary schools. This was to be achieved by “…drawing on the best practice in secondary schools, experience in the 205 schools that have piloted developments in Key Stage 3, and findings from inspection and research about what helps to raise standards.” (DfEE, 2001: 2). In the review of the pilot which preceded the introduction of the Strategy (Ofsted, 2002), it is stated that “the aim of the Strategy is to raise standards by strengthening teaching and learning, developing cross-curricular skills such as literacy and helping pupils who come into Year 7 below level 4 to make faster progress” (ibid: 1). These aims may be summarised as raising standards of attainment in mathematics through the following mechanisms:
1. promoting progression and continuity in the curriculum
2. developing effective and engaging teaching approaches
3. setting challenging expectations
4. training and supporting teachers in developing effective teaching approaches.
Although the implementation of the Strategy is not mandatory, there is an expectation that schools should use the Framework “or be able to justify not doing so by reference to what they are doing.” (ibid: 2).
The Framework describes ‘ambitious targets’ (ibid: p2) for attainment in the Key Stage 3 National Curriculum tests (75% at level 5 or above by 2004 (TES, 2001d: 8)). The first target is set for 2004, so there is a three-year delay between the implementation of the Strategy and an evaluation of performance outcomes. (It will take three years for the first cohort of students to follow the programme of the Framework throughout Key Stage 3.) Since the results of these tests will be in the public domain, it will be obvious whether or not the targets have been met. However, it may prove more difficult to evaluate how the Strategy has affected the performance in the tests. Meeting the targets for the tests will not necessarily imply that standards have been raised for all pupils, it will not even imply that they have been met for the majority. In its ‘booster materials’ (DfES, 2002b), designed to help pupils prepare for the tests, schools are required to concentrate on those pupils whose attainment can realistically be boosted to level 5. Thus, it may be possible to achieve the targets by raising the attainment of a minority of pupils.
As described above, developing effective and engaging teaching approaches is one of the mechanisms offered for raising standards of attainment. As I describe in the following chapter, the Framework identifies and recommends specific teaching approaches. Significant sums of money have been provided by the DfEE (and later DfES) to promote these approaches through INSET programmes (overall the Government has planned to spend more than £420 million over three years on implementing the Strategy (TES, 2001b: 19)). My aim in this research project is to explore how the introduction of the Key Stage 3 Strategy and its associated pedagogy has affected the teaching approaches that pupils experience in a large comprehensive school. I will also explore how pupils’ perceptions of mathematics and mathematics lessons have been affected by the introduction of the Strategy. To do this I have investigated pupils’ attitudes and responses to mathematics and their perceptions of the mathematics teaching they experience.
In order to collect the data I devised a pupils’ questionnaire comprising two sections. The first section, ‘What you think about mathematics’, consisted of 18 questions concerning the respondents’ attitudes to mathematics. The second section, ‘Maths lessons’ concerned how the pupils perceived the classroom approaches they had experienced. The questions in the first section were taken from a major international survey, the Third International Mathematics and Science Study, or TIMSS (Keys et al, 1997). The second section was more specific, focussing on the particular teaching approaches promoted within the documentation of the Strategy (in particular the Framework). Only four of the TIMSS items addressed the teaching approaches that I had identified for the questionnaire. I included these items in the second section and devised another 23 items to address the other teaching approaches that I had identified. There were two reasons for using the TIMSS items. First, TIMSS items were tried and tested and should help to ensure the reliability and validity of my methods. Secondly, my results could be compared with national and international results.
I chose to focus on Year 8 pupils for this project. In the academic year 2000-2001 the Strategy was in its pilot stage and Year 8 pupils from the sample school were not involved in its implementation. Pupils from the next Year 8 cohort (in academic year 2001-2002) were subject to the full implementation of the Strategy. I collected data from most of the members of both Year 8 populations. This allowed me to compare data from before and after the introduction of the Strategy, drawn from comparable samples. Although this sample cannot be treated as a representative sample of Key Stage 3 students nationally, I hope that the results of the investigation may offer illumination and evaluative insights into the implementation of the Strategy.