Participation and Attainment in A level Mathematics & Further Mathematics
An analysis of NPD data for the 2014/15 KS4 student cohort in England of their participation and attainment in A level Mathematics and Further Mathematics in 2015/16 or 2016/17
March 2019
Sean Demack, Sarah Reaney-Wood, Gill Adams, Bernadette Stiell
and Martin Culliney
Centre for Development and Research in Education, Sheffield
Institute of Education, Sheffield Hallam University
2
Contents
Contents 2
List of Tables 3
List of Figures 4
Participation and attainment in A level Mathematics and Further Mathematics in 2016 & 2017 5
Overview 5
Participation and attainment in A level Mathematics and Further Mathematics in 2016 & 2017 8
1. Introduction 8
1.1 Research Questions 8
1.2 Measuring participation and attainment in A level Mathematics and Further Mathematics 8
2. Modelling participation and attainment in A level Mathematics and Further Mathematics 11
2.1 Attainment at Key Stage 4 and participation/attainment in A level Mathematics and Further
Mathematics 13
2.2 Gender and participation/attainment in A level Mathematics and Further Mathematics 14
2.3 Free School Meals status (FSM) and participation/attainment in A level Mathematics and
Further Mathematics. 16
2.4 Ethnicity and participation/attainment in A level Mathematics and Further Mathematics 17
2.5 Type of KS5 institution and participation/attainment in A level Mathematics and Further
Mathematics 22
3. Summary of participation and attainment analyses 23
4. Appendix 25
4.1 Overview of participation and attainment multilevel analyses 25
4.2 Assessing and interpreting the multilevel models 27
4.3 The need for caution when comparing these analyses with Boylan et al (2016). 28
4.4 Statistical Tables 29
5. References 45
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List of Tables
Table 1: Participation in KS5, 1+ A level, A level Mathematics and A level Further Mathematics in 2016 or
2017 9
Table 2: UCAS points score in A level Mathematics and Further Mathematics (2016 or 2017) 10
Table 3: Summary of A level Participation Models, 2015 KS4 cohort in England, KS5/A level in 2016 or
2017 11
Table 4: Summary of A level Attainment Models, 2015 KS4 cohort in England, KS5/A level in 2016 or 2017
12
Table 5: Variance Partition Coefficients for null models 27
4
List of Figures
Figure 1: Participation in A level Mathematics and Further Mathematics by student ethnicity 20
Figure 2: Attainment in A level Mathematics and Further Mathematics by student ethnicity 21
Participation and attainment in A level Mathematics and Further
Mathematics in 2016 & 2017
Overview With some caveats1, the findings from analyses of NPD data into participation and attainment in A level
Mathematics and Further Mathematics in 2016 and 2017 strongly reflected those found by Boylan et al.
(2016).
The analyses revealed a great deal of consistency in terms of differential attainment and patterns of
participation relating to the type of KS5 institution attended, KS4 attainment, gender and FSM status.
However, as found by Boylan et al. (ibid) the relationship between ethnicity and participation in A level
Mathematics was notably different to that seen with participation in A level Further Mathematics.
For A level Mathematics, participation rates were observed to be higher for most Black and Minoritised
Ethnic (BME) groups compared with White British students with two exceptions (Black Caribbean and
mixed Black Caribbean and White students). The pattern in A level Mathematics participation reflects A
level participation generally but a notably different pattern is observed with participation in A level
Further Mathematics. For A level Further Mathematics, participation rates were higher for the Chinese
(strikingly so), White Other and Indian compared with White British students. Descriptive analyses also
identified new detail on the relatively high participation rates in A level Further Mathematics amongst
students from Sri Lankan Tamil or mixed Asian and White ethnic groups. Other BME groups were found to
be less likely to take the A level.
The analyses suggest scope for increased participation in A level Further Mathematics for Bangladeshi,
Pakistani and Black African students. The analyses also suggest that increasing participation in A level
Mathematics and Further Mathematics amongst Black Caribbean and mixed Black Caribbean and White
students should concentrate on barriers to mathematics attainment for these groups at KS4 or earlier.
In terms of attainment, in A level Mathematics, higher attainment was observed for Chinese, Indian,
White other and Black African students compared with White British students. For A level Further
Mathematics, attainment was observed to be higher only for Chinese compared with White British
students2.
Attainment at Key Stage 4 in Mathematics and overall is a key determinant to participation and
attainment in A level Mathematics and Further Mathematics. The inclusion of KS4 attainment into the
multivariate multilevel analyses had an impact on model coefficients of other explanatory variables. In
some instances, this might be seen as KS4 attainment statistically 'accounting' for differential patterns of
participation and/or attainment. For example, the inclusion of KS4 attainment within the A level
Mathematics and A level Further Mathematics participation models results in reducing the differential
participation rates for students identified as FSM. This suggests that some of the differential
1 See Appendix for summary of reasons to be cautious when comparing these analyses with those undertaken by
Boylan et al. (2016). 2 The descriptive analyses found that Indian students had one of the highest mean attainment in A level Further
Mathematics (114 UCAS points compared with 110 for White British and 111 for Chinese students) but within the multivariate analyses this difference is statistically accounted for by differences across other explanatory variables (notably KS4 attainment).
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participation rates relating to FSM might be a result of the relatively lower levels of KS4 attainment for
FSM students compared with their peers not classed as FSM. Therefore, removing barriers to KS4
attainment for students3 seems likely to lead to increased participation in A level Mathematics and
Further Mathematics.
Controlling for KS4 attainment also resulted in some interesting changes in model coefficients that are
more complex. For example, taking account of the relatively higher KS4 attainment of females taking A
level Mathematics or Further Mathematics revealed a hidden gender attainment gap. When KS4
attainment was not taken into account, the attainment of females was observed to be fairly comparable
to males. However, once KS4 attainment was included into the model, a gender difference (higher
attainment of males) is observed.
One striking impact of KS4 attainment on model coefficients was seen with the A level participation
models and relates to the type of KS5 institution a student took the A level in. Prior to taking KS4
attainment into account, students located in independent/fee paying KS5 institutions were observed to
be around 1.5 times as likely to take A level Mathematics and Further Mathematics compared with their
peers located in state school sixth forms. However, once KS4 attainment was included, the pattern
changed to show that students located in independent/fee paying KS5 institutions were less likely to take
A level Mathematics (0.80 times as likely) compared with their state educated peers. This change was not
observed for A level Further Mathematics; once KS4 attainment was included, students in
independent/fee paying KS5 institutions were observed to be around 1.27 times as likely to take A level
Further Mathematics compared with their state educated peers.
An increasing proportion of young people are participating in A level Mathematics and Further
Mathematics in England. This increased participation will hopefully help to increase and widen access to
future Mathematical education and employment opportunities. The analyses presented here highlight
differences in participation rates across gender, ethnic and socioeconomic groups. These analyses
suggest that there are challenges to ensure that the expansion of A level Mathematics and Further
Mathematics and future opportunities in England are equitable. In some instances (students classed as
FSM in KS4 or earlier, Black Caribbean and mixed Black Caribbean and White students) it is apparent that
barriers to attainment at KS4 or earlier should be understood and removed to help begin to improve
participation. In other instances (females, Pakistani , Bangladeshi and Black African students), it seems
apparent that the focus should be more on encouraging/converting high attaining KS4 students to take
the A level (particularly Further Mathematics).
Amongst students who took A level Mathematics or Further Mathematics, the hidden male bias revealed
in the analyses suggests that the mathematical potential of female students is less likely to be realised in
attainment compared with their male peers. In other words, given that on average, females have higher
KS4 attainment compared with males overall and have comparable attainment in KS4 Mathematics, they
would be expected to have higher levels of attainment in A level Mathematics and Further Mathematics
than was observed. In terms of attainment, it seems that males mathematically progress more sharply
than females between KS4 and A level. The statistical analyses of administrative educational data will
always be limited in helping to explore reasons behind patterns that are observed. However, the
3 FSM students are students from households were parents/guardians are in receipt of specified welfare payments.
If a household qualifies and the parent/guardian registers this with the school, the pupil is classed as having FSM status. This is measured in two ways, FSM within KS4 (Y11) and FSM at any time between KS1 (Y2) and KS4 (Y11).
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statistical analyses presented here highlighted a hidden female disadvantage in terms of participation and
attainment in A level Mathematics and Further Mathematics. Whilst it is important to continue to
statistically monitor this pattern, other research approaches are needed to help understand it with the
aim of removing barriers of access and attainment to A level Mathematics and Further Mathematics for
females in England.
Participation and attainment in A level Mathematics and Further
Mathematics in 2016 & 2017
1. Introduction
This report presents key findings from multilevel analyses into influences on participation and attainment
in A level Mathematics and Further Mathematics in 2016 and 2017. The analyses presented examine
patterns of participation and attainment for the cohort of pupils in England who completed KS4 in Y11 in
summer 2015 (N=621,758). A level participation and attainment in 2015/16 and/or 2016/17 are
examined. These new analyses took a similar approach to Boylan et al. (2016) with an earlier cohort of
pupils who completed KS4 in 2011 and took A level Mathematics or Further Mathematics between 2012
and 2014. Some comparisons between these new analyses and those reported by Boylan et al. (2016) are
cautiously made. The reasons for caution are summarised in the appendix but one key issue is the
different KS5 timescale taken here (two years following KS4 in 2015, in 2016 or 2017) compared with
Boylan et al. (ibid; three years following KS4 in 2011, in 2012, 2013 or 2014).
The main body of this report focuses on key findings. Additional detail and statistical tables can be found
in the Appendix.
1.1 Research Questions The NPD analyses aimed to address the following four research questions:
1. Are patterns of differential participation in A level Mathematics and Further Mathematics
comparable?
2. Are patterns of differential attainment in A level Mathematics and Further Mathematics
comparable?
3. To what extent can these differential participation and attainment patterns be statistically
accounted for by differential patterns in KS4/GCSE attainment (in Mathematics and overall KS4
attainment)?
4. What are the independent effects of student and school characteristics on participation and
attainment in A level Mathematics and Further Mathematics?
The population analysed are the entire 2015 KS4 cohort in England and their A level participation and
attainment in 2016 and 2017. These analyses are compared with analyses of the 2011 KS4 cohort in
England and their participation and attainment between 2012 and 2014
1.2 Measuring participation and attainment in A level Mathematics and
Further Mathematics Multivariate, multilevel models of participation and attainment in A level Mathematics and Further
Mathematics were developed. The models were used to examine differences and similarities between
participation and attainment in A level Mathematics and Further Mathematics by considering the
following explanatory variables:
Prior attainment at KS4 (overall and in Mathematics)
Pupil background (gender; FSM status & ethnicity)
KS5 institution type
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Amongst the 2015 KS4 pupil cohort, models were constructed to examine patterns of participation in A
level Mathematics or Further Mathematics in 2016 or 2017.
A second perspective on participation in A level Further Mathematics was provided by examining the
likelihood of participating given that a student took A level Mathematics. This conditional participation
outcome captures variations in taking A level Further Mathematics for students known to have taken a
Mathematical A level trajectory.
For these analyses, an additional participation outcome variable was used that captured general patterns
of A level participation. These models provided a reference point from which to consider patterns of
participation in A level Mathematics and Further Mathematics. Specifically, this final participation
outcome variable measured whether a student took 1+ A level in any subject or not in 2016 or 2017.
As shown in Table 1 below and in the Appendix, of the 621,758 students who took KS4 in 2015, 77.9%
(n=484,255) took 1+ KS5 assessment and 38.5% (n=239,448) took 1+ A level in 2016 or 2017. 67,847
students took A level Mathematics; 10.9% of the 2015 KS4 cohort and 28.3% of students who took 1+ A
level. 12,354 students took A level Further Mathematics; 2.0% of the 2015 KS4 cohort and 5.2% of
students who took 1+ A level.
12,339 students took both A level Mathematics and Further Mathematics; 18.2% of students who took A
level Mathematics and 99.9% of students who took A level Further Mathematics.
Table 1: Participation in KS5, 1+ A level, A level Mathematics and A level Further Mathematics in 2016 or 2017
N= % took 1+ KS5 Exam
% took 1+ A level
% took Mathematics
A level
% took Further
Mathematics A level
…whole 2015 KS4 Pupil Cohort 621,758 77.9 38.5 10.9 2.0 …who took 1+ KS5 484,255 100.0 49.4 14.0 2.6
... took 1+ A level 239,448 - 100.0 28.3 5.2 ... took A level Mathematics 67,847 - - 100.0 18.2
... took A level Further Mathematics 12,354 - - 99.9 100.0
Source: NPD cohort of pupils who completed KS4 in Y11 in 2015 (N=621,758). The four A level participation outcome variables are highlighted in blue in Table 1.
Following descriptive statistical analyses, multilevel linear regression models were constructed to help to
examine variations in UCAS points score in A level Mathematics and Further Mathematics across
explanatory variables.
The pre-2018 UCAS scoring scheme was used to convert A level grades to UCAS points score4. As shown
in Table 2 below and in the Appendix, attainment in A level Further Mathematics (mean=111.9 points)
was higher on average than attainment in A level Mathematics (101.3 points). Further, the A level
Mathematics attainment for students who also took A level Further Mathematics (mean=130.3 points)
was notably higher than the attainment of students who did not take Further Mathematics (94.8 points).
4 UCAS points are calculated by attaching a value to an A or AS level grade. At A level, the following points are
applied: grade A* (140 points); A (120); B (100); C (80); D (60); E (40). See www.ucas.com/ucas/undergraduate/getting-started/entry-requirements/tariff/tariff-tables/946
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Table 2: UCAS points score in A level Mathematics and Further Mathematics (2016 or 2017)
Source: NPD cohort of pupils who completed KS4 in Y11 in 2015 (N=621,758) and took A level Mathematics or A level Further Mathematics
A level Mathematics
mean (s.d.)
A level Further Mathematics mean (s.d.)
All students who took A level in 2016 or 2017 101.3 (30.92) 111.9 (27.91)
…12,339 who took A level Mathematics and Further Mathematics
130.3 (15.39) …55,508 who just took A level Mathematics 94.8 (29.78) -
2. Modelling participation and attainment in A level Mathematics and
Further Mathematics
Details on the modelling approach and summary Tables can be found in the Appendix. Table 3 below
summarises the final multilevel logistic regression models for A level participation and Table 4 summarises
the final multilevel linear regression models for A level attainment. The analyses are summarised and
discussed below in sections 2.1 to 2.5.
Table 3: Summary of A level Participation Models, 2015 KS4 cohort in England, KS5/A level in 2016 or 2017
Participation Outcome: Any A level in 2016 or 2017
(1+ A level)
A level Mathematics
A level Further Mathematics
A level Further Mathematics
(amongst A level Mathematics
students)
KS4 Attainment
KS4 Mathematics Grade A* 0.36 (1.43)** 2.32 (10.20)** 2.87 (17.68)** 1.72 (5.57)** (Females*Grade A*) Interaction term -0.67 (0.51)** -0.07 (0.93)** 0.01 (1.01) -0.26 (0.77)**
Overall KS4 points per exam 0.31 (1.36)** 0.22 (1.24)** 0.16 (1.17)** 0.10 (1.10)** (Females*Overall KS4 point2) -0.02 (0.98)** -0.03 (0.98)** -0.01 (0.99) -0.02 (0.98)**
Type of KS5 institution (Reference = State School 6th
Form)
(6th
Form College) -0.41 (0.67)** -0.23 (0.79)** -0.15 (0.86)** -0.09 (0.91)* (FE College) -3.33 (0.04)** -1.57 (0.21)** -0.82 (0.44)** 0.06 (1.06)
(Independent / Fee Paying) 0.16 (1.17)** -0.23 (0.80)** 0.24 (1.27)** 0.30 (1.35)** (Other) -4.30 (0.01)** -1.98 (0.14)** -1.26 (0.28)** -0.06 (0.94)
Pupil Background
Gender (Female) 0.23 (1.26)** -1.04 (0.35)** -1.40 (0.25)** -0.65 (0.52)**
Poverty (FSM) -0.30 (0.74)** -0.14 (0.87)** 0.04 (1.04) 0.12 (1.13)** Ethnicity (White British as reference) (white other) 0.25 (1.28)** 0.27 (1.31)** 0.28 (1.32)** 0.23 (1.26)**
(Indian) 0.36 (1.44)** 0.97 (2.65)** 0.13 (1.14)* -0.11 (0.89)* (Pakistani) 0.13 (1.14)** 0.60 (1.82)** -0.42 (0.66)** -0.64 (0.53)**
(Bangladeshi) 0.30 (1.35)** 0.70 (2.02)** -0.19 (0.83) -0.40 (0.67)** (black Caribbean) 0.18 (1.20)** 0.02 (1.02) -0.35 (0.70) -0.33 (0.72)
(black African) 0.42 (1.53)** 0.71 (2.04)** -0.19 (0.83)* -0.45 (0.64)** (mixed black Carib & white) 0.04 (1.04)NS -0.08 (0.92)NS -0.53 (0.59)** -0.55 (0.58)**
(Chinese) 0.66 (1.94)** 1.66 (5.24)** 1.26 (3.53)** 0.90 (2.45)** (Other) 0.05 (1.05)** 0.47 (1.60)** 0.23 (1.26)** 0.09 (1.09)**
Constant 0.32 -2.93 -5.71 -3.53
VPC
Level 2 (KS5 institution) 19% 9% 15% 9% Level 1 (student) 81% 91% 85% 91%
McFadden's Pseudo R2 58.9% 43.4% 39.9% 13.0%
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Table 4: Summary of A level Attainment Models, 2015 KS4 cohort in England, KS5/A level in 2016 or 2017
Attainment in A level Mathematics
Model Stages:
Mathematics Further Mathematics
KS4 Attainment
KS4 Mathematics Grade A* 17.80 (+0.58)** 8.40 (+0.30)** (Females*Grade A*) Interaction -2.41 (-0.08)** -0.61 (-0.02)
Overall KS4 points per exam 3.06 (+0.10)** 3.41 (+0.12)** (Females*Overall KS4 points per exam) Interaction 0.26 (+0.01)** 0.39 (+0.01)**
Type of KS5 institution
(6th
Form College) 0.35 (0.01) -2.34 (-0.08)** (FE College) -1.48 (-0.05)** -1.30 (-0.05)
(Independent / Fee Paying) 3.99 (+0.13)** 5.03 (0.18)** (Other) -2.77 (-0.09)** -1.67 (-0.06)
Pupil Background
Gender (Female) -9.90 (-0.32)** -10.54 (-0.38)** Poverty (FSM) -1.19 (-0.04)** -1.81 (-0.07)** Ethnicity (White British as reference)
(white other) 2.33 (+0.08)** 0.06 (0.00) (Indian) 2.38 (+0.08)** 0.84 (+0.03)
(Pakistani) 1.11 (0.04) -1.06 (-0.04) (Bangladeshi) -1.91 (-0.06)* -4.10 (-0.15)*
(black Caribbean) -5.38 (-0.17)** 0.22 (+0.01) (black African) 1.39 (+0.05)* -5.28 (-0.19)**
(mixed black Carib & white) -1.45 (-0.05) 1.11 (+0.04) (Chinese) 8.93 (+0.29)** 2.97 (0.11)*
(Other) 2.17 (+0.07)** 0.75 (+0.03) Constant
59.1
61.3
Variance Partition Coefficient (VPC)
Level 2 (KS5 institution) 7.3 8.6 Level 1 (student) 92.7 91.4
Explanatory Power (R2)
Level 2 (KS5 institution) 0.56 0.64 Level 1 (student) 0.36 0.27
Total 0.38 0.33
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2.1 Attainment at Key Stage 4 and participation/attainment in A level
Mathematics and Further Mathematics As in previous research, KS4 attainment was found to be the main influence in determining participation
and attainment in A level Mathematics and Further Mathematics. As might be expected, the influence
of attainment in KS4 Mathematics on the likelihood of participation is stronger for A level Mathematics
and Further Mathematics compared with taking any A level (where general KS4 attainment in terms of
points score per exam is seen to be more influential).
attaining A* in KS4 Mathematics is important in determining participation in A level Mathematics
and Further Mathematics, but it is more important for Further Mathematics
o students with A* in GCSE Mathematics were found to be 10 times as likely to take A level
Mathematics and 18 times as likely to take A level Further Mathematics compared with
students who attained lower than A*.
attaining A* in GCSE Mathematics is important in determining attainment in A level Mathematics
and Further Mathematics, but it is more important for Mathematics. This reflects greater
variation in GCSE Mathematics attainment amongst students who took A level Mathematics (50%
attained grade A*; 33% grade A and 6% grade B at GCSE5) compared with students who took A
level Further Mathematics (77% attained grade A*; 9% grade A and 0.3% grade B at GCSE6 ). In
other words, in terms of KS4 Mathematics attainment, students taking A level Further
Mathematics were more 'similar' to each other compared with students taking A level
Mathematics.
o once other factors are controlled for, attaining A* in GCSE Mathematics is associated with a
+17.8 UCAS point advantage for A level Mathematics and +8.4 UCAS points advantage for A
level Further Mathematics.
Overall KS4 attainment7 is also positively correlated with participation and attainment in A level
Mathematics and Further Mathematics.
The association between KS4 attainment and participation and attainment in A level Mathematics, and
Further Mathematics observed with the 2015 KS4 cohort are remarkably consistent with those found by
Boylan et al. (2016) for the 2011 KS4 cohort. Perhaps understandably, the strong link between high
attainment at KS4 and A level participation and attainment remains clear.
Half of students who took A level Mathematics in 2016 or 2017 had attained an A* in KS4
Mathematics in 2015. At the same time, a large majority (74.8%) of students who attained A*
and half (48%) of students who attained A* or A in KS4 Mathematics in 2015 took A level
Mathematics in 2016 or 2017.
77% of students who took A level Further Mathematics in 2016 or 2017 had attained an A* in KS4
Mathematics in 2015. At the same time, just over a fifth (21%) of students who attained A* and
under a tenth (9%) of students who attained A*or A in KS4 Mathematics in 2015 took A level
Further Mathematics in 2016 or 2017.
5 For 7% of cases there was no KS4 maths attainment data, 29% of these took A level Mathematics. These cases
make up 11% of A level Mathematics students. 6 Of the 7% of cases there was no KS4 maths attainment data, 5% of these took A level Further Mathematics. These
cases make up 13% of A level Further Mathematics students. 7 Measured using GCSE points score per exam sat [Total GCSE Points / Number of GCSEs taken]
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Boylan et al. (2016) also found that around half (48%) of students who attained A* or A in KS4
Mathematics took an A level in Mathematics. In terms of A level Further Mathematics, Boylan et al. (2016)
reported that 8% of students who attained A* or A in KS4 Mathematics took the A level (compared with
the 9% we found).
2.2 Gender and participation/attainment in A level Mathematics and Further
Mathematics A male bias in A level Mathematics and Further Mathematics participation was found - and this was
stronger in A level Further Mathematics compared with Mathematics. This male bias increases when the
relatively higher KS4 attainment of females taking A level Mathematics or Further Mathematics is
controlled for in the model - i.e. females were observed to not participate in A level Mathematics or
Further Mathematics in the proportions that might be expected given their relatively high attainment at
GCSE. This 'hidden' strengthening male bias was a pattern also found by Boylan et al. (2016) with the
2011 KS4 cohort. Essentially, this is suggesting that the mathematical potential (in terms of A level
participation) is less likely to be realised for females compared with males in England.
In terms of odds-ratios, before controlling for KS4 attainment, females are seen to be 0.61 times
as likely to take A level Mathematics and 0.35 times as likely to take A level Further Mathematics
compared with males. When KS4 attainment is controlled for, females are seen to be 0.28 times
as likely to take A level Mathematics and 0.21 times as likely to take A level Further Mathematics
compared with males.
Amongst students who did take A level Mathematics, females were less likely to take A level Further
Mathematics compared with males.
In terms of odds-ratios, before controlling for KS4 attainment, females taking A level Mathematics
are seen to be 0.46 times as likely to also take A level Further Mathematics compared with males
taking A level Mathematics. When KS4 attainment is controlled for, females taking A level
Mathematics are seen to be 0.33 times as likely to also take A level Further Mathematics
compared with males taking A level Mathematics
This male bias does not reflect the pattern observed more widely with A level participation where a
female bias is observed; once other factors are controlled for, females are 1.26 times as likely to take 1+ A
level (in any subject) compared with males.
In summary, the analyses suggest that a clear male bias in participation in A level Mathematics and (even
more so) Further Mathematics persists with this cohort. This pattern is out of step with the female bias in
taking 1+ A level. Females who take A level Mathematics are also less likely to also take Further
Mathematics compared with males. The size of this male bias is seen to increase when KS4 attainment is
controlled for.
Gender was found to interact with KS4/GCSE Mathematics attainment in determining participation in A
level Mathematics. Attaining A* in GCSE Mathematics is important in determining participation for males
and females - but, for A level Mathematics, this was found to be less important for females. The
relationship between GCSE attainment and participation in A level Further Mathematics was found to be
consistent for males and females when looked at directly. However, amongst A level Mathematics
students, the association between GCSE attainment and participation in A level Further Mathematics was
15
weaker for females compared with males. One result is a slightly greater male propensity to take the A
level amongst students who attained A* at KS4 compared with students who did not attain this threshold.
For A level Mathematics, for A* KS4 maths students, males are 3.1 times as likely to take the A
level compared with females; for students who did not attain A*, males are 2.8 times as likely to
take the A level compared with females.
For A level Further Mathematics, regardless of whether a student attained A* KS4 maths students,
males are 4.0 times as likely to take the A level compared with females.
Amongst A level Mathematics students who also take A level Further Mathematics, for A* KS4
maths students, males are 2.5 times as likely to take the A level compared with females; for
students who did not attain A*, males are 1.9 times as likely to take the A level compared with
females.
A male bias in A level Mathematics and Further Mathematics attainment was also found - but this was
slightly stronger in A level Mathematics compared with Further Mathematics. This male A level
attainment advantage in both Mathematics and Further Mathematics only emerged after the relatively
higher KS4 attainment of females was controlled for in the models. This is another example of a gender
difference that is hidden within the descriptive analyses but becomes apparent within the multilevel
analyses when other factors (and importantly KS4 attainment) are controlled for.
Prior to controlling for KS4 attainment and other factors, males were observed to have a +0.9
UCAS points advantage in A level Mathematics and +0.4 UCAS points advantage in A level Further
Mathematics
Once KS4 attainment and other factors were controlled for, males were observed to have a +8.1
UCAS points advantage in A level Mathematics and +5.7 UCAS points advantage in A level Further
Mathematics
A significant interaction between gender and KS4 attainment was also observed for the 1+ A level models
which suggests that the positive correlation between KS4 attainment and the likelihood of taking an A
level is weaker for females compared with males.
Gender also was found to significantly interact with GCSE Mathematics attainment in determining
attainment in A level Mathematics but less so for A level Further Mathematics. A larger male bias is
observed amongst students who attained A* in KS4 Mathematics:
Amongst students who attained A* in KS4 Mathematics, males are observed to have a +12.3 UCAS
point advantage in A level Mathematics compared with females. Amongst students who did not
attain A* in KS4 Mathematics, males are observed to have a +9.9 UCAS point advantage in A level
Mathematics compared with females
Amongst students who attained A* in KS4 Mathematics, males are observed to have a +11.2 UCAS
point advantage in A level Further Mathematics compared with females. Amongst students who
did not attain A* in KS4 Mathematics, males are observed to have a +10.5 UCAS point advantage
in A level Mathematics compared with females.
Gendered patterns of participation and attainment in A level Mathematics and Further Mathematics
closely reflect those reported by Boylan et al. (2016). In terms of participation, once KS4 attainment and
other factors were controlled for Boylan et al. (ibid) reported that, between 2012 and 2014 females were
35% as likely to take A level Mathematics and 22% as likely to take A level Further Mathematics compared
16
with males. We found that in 2016 and 2017, females were 28% as likely to take A level Mathematics and
21% as likely to take A level Further Mathematics compared with males. In terms of attainment, once KS4
attainment and other factors were controlled for Boylan et al. (ibid) reported that, between 2012 and
2014 males had a +6.5 UCAS point advantage in A level Mathematics and +4.1 point advantage in A level
Further Mathematics compared with females. We found that in 2016 and 2017, males had a +8.1 UCAS
point advantage in A level Mathematics and +5.7 point advantage in A level Further Mathematics
compared with females. In summary, whilst male bias in participation seems to have remained
static/entrenched; male advantage in attainment seems to have increased slightly. Finally, the
relationship between KS4 attainment and A level participation (overall and in A level Mathematics and/or
Further Mathematics) differs for males and females.
2.3 Free School Meals status (FSM) and participation/attainment in A level
Mathematics and Further Mathematics. In terms of FSM, once KS4 attainment and other factors were controlled for, students who were identified
as ever eligible and claiming Free School Meals up to KS4 in 2015 were slightly less likely to take A level
Mathematics compared with their non-FSM peers. For A level Further Mathematics, once KS4
attainment and other factors were controlled for, participation was not significantly different for FSM and
non-FSM students. Amongst students taking A level Mathematics, FSM students are slightly more likely
to take A level Further Mathematics compared with non-FSM students.
For A level Mathematics, prior to controlling for KS4 attainment, FSM students are observed to be
0.36 times as likely to take the A level compared with non-FSM students; when prior attainment
and other factors are controlled for FSM students are observed to be 0.87 times as likely to take
the A level compared with non-FSM students.
For A level Further Mathematics, prior to controlling for KS4 attainment, FSM students are
observed to be 0.33 times as likely to take the A level compared with non-FSM students; when
prior attainment and other factors are controlled for FSM students are observed to be equally
likely to take the A level compared with non-FSM students.
Amongst A level Mathematics students who also take A level Further Mathematics, FSM students
are observed to be 0.89 times as likely to take the A level compared with non-FSM students;
when prior attainment and other factors are controlled for FSM students are observed to be 1.13
times as likely to take the A level compared with non-FSM students.
It is interesting to note that the FSM disadvantage observed with participation in A level
Mathematics and Further Mathematics is not as great as that seen with the general 1+ A level
participation models. When KS4 and other factors are controlled for, FSM students are observed
to be 0.74 times as likely to take 1+ A level compared with their not-FSM peers; this compares
with odds-ratios of 0.87 (A level Mathematics); 1.04 (Further Mathematics) and 1.13 (Further
Mathematics for students taking A level Mathematics).
Prior attainment at KS4 was seen to account for most of the differences in participation between FSM and
non-FSM students in A level Mathematics and nearly all of the difference in A level Further Mathematics.
Because of lower attainment in GCSE Mathematics, FSM students are less likely to participate in A level
Mathematics and Further Mathematics. Once KS4 attainment and other factors were controlled for, FSM
students attained slightly lower in A level Mathematics and Further Mathematics compared with their
non-FSM peers.
17
at KS4, in 2015 non-FSM students were over 4 times as likely to attain A* in GCSE Mathematics
compared with their FSM peers8:
Prior to controlling for KS4 attainment, non-FSM students had a +6.2 UCAS point advantage in A
level Mathematics and a +8.6 UCAS point advantage in A level Further Mathematics compared
with their FSM peers. Once KS4 attainment and other factors were controlled for, the non-FSM
student attainment advantages reduces to +1.2 UCAS point advantage in A level Mathematics.
For A level Further Mathematics, a small (+1.8 UCAS point) attainment advantage for FSM
students emerges.
These patterns largely echo those reported by Boylan et al. (2016). Lower rates of participation for FSM
students in A level Mathematics and Further Mathematics were accounted for statistically to a large
extent by differences in KS4 attainment between FSM and non-FSM pupils both here and by Boylan et al.
(2016). It seems that socioeconomic background is less influential in A level Mathematics and Further
Mathematics participation compared with observed patterns of general A level participation. In terms of
attainment, Boylan et al., (2016) reported that, between 2012 and 2014, once KS4 attainment and other
factors were controlled for, non-FSM students had a +1.1 UCAS point advantage in A level Mathematics
and a +2.5 point advantage in Further Mathematics compared with FSM students. We found that in 2016
or 2017, non-FSM students had a +1.2 UCAS point advantage in A level Mathematics and a +1.8 point
advantage in Further Mathematics compared with FSM students.
The FSM findings suggest that most/all of the issues of lower rates of participation and attainment in A
level Mathematics and Further Mathematics stem from KS4 or earlier. This leads to concluding that a
focus on identifying and removing socioeconomic barriers to Mathematics attainment within compulsory
education is required in order to address the observed inequalities at A level. The analyses show that
most/all of the differences between FSM and non-FSM pupils in A level participation and attainment can
be statistically accounted for by differences in KS4 attainment (overall and in Mathematics). Finally, it
needs to be noted that FSM is a very rough proxy for socioeconomic background that includes an
assumption that pupils not claiming or just not eligible can be considered as having similar socioeconomic
circumstances to pupils with two professionally employed parents. These analyses reveal a difference
between a relatively small group (13% are identified as FSM in KS4, 25% were identified as claiming FSM
at some point between KS1 and KS4) and the majority of pupils (that can largely be accounted for by
differences in KS4 attainment). However, these analyses were not able to examine socioeconomic
differences within the majority of non-FSM students. Socioeconomic analyses of the NPD will remain
limited in this way until a more finely grained measure of socioeconomic background is collected and
made available for analyses.
2.4 Ethnicity and participation/attainment in A level Mathematics and
Further Mathematics Whilst great consistency in the association between participation and attainment in A level Mathematics
and Further Mathematics was reported by Boylan et al. (2016) in relation to KS4 attainment, gender, free
school meal status and type of KS5 institution; when examining patterns across pupil ethnic groups,
notable differences between A level Mathematics and Further Mathematics participation and attainment
were reported. To look closer at this, these new analyses requested that the student ethnicity NPD
variable was provided in its most disaggregated form. This enabled some statistical insight into
8 As an odds-ratio, non-FSM (9.8%) are 4.42 times as likely as FSM (2.4%) students to attain A*
18
participation and attainment for student ethnic groups commonly hidden behind broader ethnicity
groupings. For consistency purposes, the main multilevel analyses used the same ethnicity classification
of ten student groups9 as Boylan et al. (2016). However, within the descriptive analyses shown in Tables
I.1 (participation) and I.2 (attainment) of the Appendix, additional details are shown for four different
'White other' groups (White Eastern European, White Western European, White Irish and White Turkish);
one additional Asian group (Sri Lankan Tamils); three different 'Black African' groups (Somalia, Nigeria and
Ghanaian); two additional mixed ethnic identities (Asian & White and Black African & White) and the
Middle Eastern/Arab student ethnic group.
Unpacking the ethnic groupings revealed interesting detail relating to participation and attainment in A
level Mathematics and Further Mathematics. For example, whilst the strikingly high participation rates in
A level Mathematics and Further Mathematics for Chinese students was something found by Boylan et al.
(201610) and remains clearly evident here (45.6% took Mathematics, 14.9% took Further Mathematics in
2017); the relatively high participation of Sri Lankan Tamils is not previously known (45.2% took
Mathematics, 7.6% took Further Mathematics in 2017). Relatively high participation was also observed
for Indian students (26.6% took Mathematics, 4.4% took Further Mathematics) and Mixed Asian & White
students (16.2% took Mathematics, 3.1% took Further Mathematics). It is interesting that the three
groups most likely to take 1+ A level in 2016 or 2017 were Chinese (69.8%), Sri Lankan Tamil (63.3%) and
Indian (57.2%) students; compared with 38.5% of all 2015 KS4 students.
Other ethnic groups that were more likely than White British students to take A level Mathematics but
less so in Further Mathematics including Middle Eastern/Arab (39.9% 1+ A level, 16.0% Mathematics,
1.6% Further Mathematics); Bangladeshi (42.6% 1+ A level, 13.7% Mathematics, 1.6% Further
Mathematics), Black Nigerian (50.4% 1+ A level, 13.5% Mathematics, 1.1% Further Mathematics) and
White Irish (50.2% 1+ A level, 13.0% Mathematics, 2.3% Further Mathematics).
The relatively high participation rates for Chinese students is accompanied by relatively higher attainment
in both A level Mathematics (mean=108.7 UCAS points compared with 99.8 points for White British
students) and, to a lesser extent, Further Mathematics (111.4 points compared with 109.9 points for
White British students). Similar attainment advantages are seen for Indian students in Mathematics
(102.2 points) and even more so in Further Mathematics (114.0 points) but not Sri Lankan Tamil students
(Mathematics 98.3 points; Further Mathematics 106.2 points).
Within the multilevel analyses, once KS4 attainment and other factors were controlled for, differential
patterns of participation and attainment in A level Mathematics were found to be notably different from
those seen with A level Further Mathematics. Low levels of participation and attainment amongst Black
Caribbean and mixed Black Caribbean and White students could be statistically accounted for by the
relatively low levels of attainment at KS4 for these ethnic groups. As with the FSM finding, this suggests
that increasing participation in A level Mathematics and Further Mathematics amongst Black Caribbean
and mixed Black Caribbean and White students should focus on addressing and removing structural
barriers to attainment in Mathematics at KS4 and earlier.
9 White British, White other, Indian, Pakistani, Bangladeshi, Black Caribbean, Black African, Chinese, mixed Black
Caribbean and White and other/missing 10
Amongst Chinese students who took KS4 in 2011, Boylan et al. (2016) found that 52.4% took A level Mathematics (compared with 16.7% overall) and 14.6% took A level Further Mathematics.
19
Figures 1 and 2 below summarise the differences in participation and attainment in A level Mathematics
and Further Mathematics across ethnic groups once KS4 attainment and other factors are controlled for.
Figure 1 presents student ethnic differences in participation in A level Mathematics and Further
Mathematics once KS4 attainment and other factors are controlled for. Additionally, in Figure 1, ethnic
differences in participation in any A level are shown alongside A level Mathematics and Further
Mathematics. The comparable figure for A level participation differences across student ethnic groups
from Boylan et al. (2016) is shown below Figure 1.
Compared with White British students, the relatively higher participation of Chinese, Indian, Bangladeshi,
Black African and Pakistani students in A level Mathematics reflects the general pattern of A level
participation. However, a very different pattern is seen with A level Further Mathematics with only
Chinese and Indian students having relatively higher participation compared with White British students.
This suggests that there is sizable scope for the expansion of participation in A level Further Mathematics
across Pakistani, Bangladeshi and Black African ethnic groups.
20
Figure 1: Participation in A level Mathematics and Further Mathematics by student ethnicity
Figure 2 presents attainment differences in A level Mathematics and Further Mathematics as Cohen's d
effect-size statistics. These statistics measure the relative difference in mean UCAS points score for each
ethnic group compared with the White British reference group in units of standard deviations. Figure 2
shows the figure drawn from these new analyses of the 2015 KS4 English pupil cohort and their
attainment in A level Mathematics and Further Mathematics in 2016 or 2017. Below this, the
comparable Figure from Boylan et al. (2016) is shown
Figure 2: Attainment in A level Mathematics and Further Mathematics by student ethnicity
The relative attainment advantage for Chinese and Indian students is seen in both charts. The relative
attainment disadvantage for Bangladeshi students is also consistent for both. A more mixed pattern is
seen for Pakistani, Black Caribbean, Black African and mixed Black Caribbean and White students.
22
2.5 Type of KS5 institution and participation/attainment in A level
Mathematics and Further Mathematics In terms of the type of KS5 institution a student attended, once KS4 attainment and other factors were
controlled for, students in state school sixth forms or sixth form colleges were the most likely to
participate in A level Mathematics and students in independent school sixth forms were the most likely to
participate in A level Further Mathematics. Students in FE colleges were the least likely to participate in
either A level. Table I.1 in the Appendix shows that whilst a greater proportion of students in
independent school sixth forms took A level Mathematics (35.8%) compared with students in state school
sixth forms (22.1%), this difference would be expected to be even greater given the different KS4
attainment for the two student groups. In other words, the proportion taking A level Mathematics in
independent school sixth forms would be expected to be higher than 35.8% given their relatively higher
levels of KS4 attainment. Once this is accounted for in the multilevel analyses, students in state school
sixth forms are found to be statistically more likely to take A level Mathematics.
Prior to controlling for KS4 attainment, state school pupils were 0.70 times as likely to take A level
Mathematics and 0.64 times as likely to take A level Further Mathematics compared with pupils in
independent schools. When KS4 attainment and other factors are controlled for, state school
pupils were 1.25 times as likely to take A level Mathematics and 0.79 times as likely to take A level
Further Mathematics compared with pupils in independent schools.
Once KS4 attainment and other factors were controlled for, students in independent / fee paying KS5
institutions were found to attain the highest in A level Mathematics and Further Mathematics, students in
FE colleges were found to attain the lowest.
Prior to controlling for KS4 attainment, students in independent / fee paying institutions attained
+8.6 UCAS point higher in A level Mathematics and +9.9 UCAS points higher in A level Further
Mathematics compared with students in state school sixth forms. Once KS4 attainment and other
factors are controlled for, students in independent / fee paying institutions attained +4.0 UCAS
point higher in A level Mathematics and +5.1 UCAS points higher in A level Further Mathematics
compared with students in state school sixth forms
The differences in A level Mathematics and Further Mathematics participation and attainment across
students from different types of school in KS4 closely reflect those found by Boylan et al. (2016).
3. Summary of participation and attainment analyses
This section is organised under the four research questions from section 1.1
Are patterns of differential participation in A level Mathematics and Further Mathematics
comparable?
The descriptive analyses and multivariate multilevel analyses reveal a great deal of consistency in terms of
differential patterns of participation relating to the type of KS5 institution attended, KS4 attainment
(overall and in GCSE Mathematics), gender and FSM status. However, as found by Boylan et al. (2016), the
relationship between ethnicity and participation in A level Mathematics was notably different to that seen
with participation in A level Further Mathematics. For A level Mathematics, participation rates were
observed to be higher for most BME groups compared with White British students with two exceptions
(Black Caribbean and mixed Black Caribbean and White students). The pattern in A level Mathematics
participation reflects A level participation generally but a notably different pattern is observed with
participation in A level Further Mathematics. For A level Further Mathematics, participation rates were
higher for Chinese, White Other and Indian students compared with White British students, with students
in other BME groups being less likely to take the A level. This suggests scope for increased participation
in A level Further Mathematics for Bangladeshi, Pakistani and Black African students. The analyses also
suggest that increasing participation in A level Mathematics and Further Mathematics amongst Black
Caribbean and mixed Black Caribbean and White students should focus on barriers to mathematics
attainment for these groups at KS4 or earlier.
Are patterns of differential attainment in A level Mathematics and Further Mathematics
comparable?
The descriptive analyses and multivariate multilevel analyses also reveal a great deal of consistency in
terms of differential patterns of attainment relating to the type of KS5 institution attended, KS4
attainment (overall and in GCSE Mathematics), gender and FSM status. However, again, the relationship
between ethnicity and attainment in A level Mathematics was notably different to that seen with
attainment in A level Further Mathematics. For A level Mathematics, attainment was observed to be
higher for Chinese, Indian, White other and Black African students compared with White British students.
For A level Further Mathematics, attainment was observed to be higher only for Chinese compared with
White British students.
To what extent can these differential participation and attainment patterns be statistically
accounted for by differential patterns in KS4/GCSE attainment (in Mathematics and overall KS4
attainment)?
Attainment at Key Stage 4 in Mathematics and overall is a key determinant to participation and
attainment in A level Mathematics and Further Mathematics. The inclusion of KS4 attainment into the
multivariate multilevel analyses had an impact on model coefficients of other explanatory variables (see
Appendix for details). In some instances, this might be seen as KS4 attainment statistically 'accounting' for
differential patterns of participation and/or attainment. For example, the inclusion of KS4 attainment
within the A level Mathematics and A level Further Mathematics participation models results in reducing
the differential participation rates for students identified as FSM. This suggests that some of the
differential participation rates relating to FSM might be a result of the relatively lower levels of KS4
24
attainment for FSM students compared with their peers not classed as FSM. Therefore, removing
barriers to KS4 attainment for FSM students seems likely to lead to increased participation in A level
Mathematics and Further Mathematics.
The inclusion of KS4 attainment also resulted in some interesting changes in model coefficients that are
more complex. For example, taking account of the relatively higher KS4 attainment of females taking A
level Mathematics or Further Mathematics revealed a hidden gender attainment gap. When KS4
attainment was not taken into account, the attainment of females was observed to be fairly comparable
to males. However, once KS4 attainment was included into the model, a gender difference (higher
attainment of males) is observed.
One striking impact of KS4 attainment on model coefficients was seen with the A level participation
models and relates to the type of KS5 institution a student took the A level in. Prior to taking KS4
attainment into account, students located in independent/fee paying KS5 institutions were observed to
be around 1.5 times as likely to take A level Mathematics and Further Mathematics compared with their
peers located in state school sixth forms. However, once KS4 attainment was included, the pattern
changed to show that students located in independent/fee paying KS5 institutions were less likely to take
A level Mathematics (0.80 times as likely) compared with their state educated peers. This change was not
observed for A level Further Mathematics; once KS4 attainment was included, students in
independent/fee paying KS5 institutions were observed to be around 1.27 times as likely to take the A
level compared with their state educated peers.
A similar pattern was reported by Boylan et al. (2016) but this was consistent for both A level
Mathematics and Further Mathematics. It seems that, for the 2015 KS4 cohort, the increased likelihood
of participating in A level Further Mathematics for students located in independent/fee paying schools
cannot be fully accounted for by differences in KS4 attainment and other explanatory variables.
What are the independent effects of student and school characteristics on participation and
attainment in A level Mathematics and Further Mathematics?
The type of KS5 institution, gender, ethnicity and (to a lesser extent) FSM status were all found to
independently influence differential patterns of participation and attainment in A level Mathematics and
Further Mathematics (see Appendix for details).
The patterns relating to KS5 institution, gender and FSM are largely consistent for both A level
Mathematics and Further Mathematics. Notable differences are seen in how student ethnicity is
associated with A level participation and attainment in Mathematics and Further Mathematics.
4. Appendix
4.1 Overview of participation and attainment multilevel analyses Participation in A level Mathematics and Further Mathematics was modelled using a series of multilevel,
multivariate binary logistic regression models. Attainment in A level Mathematics and Further
Mathematics was modelled using a series of multilevel, multivariate linear regression models.
This Appendix provides summary tables and additional details for the All England analyses into
participation and attainment in A level Mathematics and Further Mathematics.
Table I.1 presents percentage participation rates across the explanatory variables. Table I.2 presents
mean attainment in A level Mathematics and Further Mathematics across explanatory variables.
Tables I.1 and I.2 provide the first perspective on how participation and attainment in A level
Mathematics and Further Mathematics is associated with KS4 attainment, pupil background and the type
of KS5 institution a student attends. However, these analyses will not take any account of associations
amongst the explanatory variables. In order to do this, multilevel logistic and linear regression models
were constructed. The model analyses closely reflect those undertaken previously by Boylan et al. (2016)
to allow for some comparison.
Model Stages
1. The empty or 'null' model
2. Including KS4 attainment (overall and KS4 Mathematics) alone
3. Including KS5 location alone
4. Including pupil background (FSM, gender and ethnicity) alone
5. Complete main effects model (Pupil background, KS5 location and KS4 attainment all together)
Following this, an interaction between gender and KS4 attainment was included.
The summary tables for the models will focus on the complete main effect stage and including the gender
* KS4 attainment interaction with further support tables provided for detail on stages 1 to 4.
The complete main effects models will show how the explanatory variables are associated with the A level
participation and attainment outcome variables in multivariate space, once all other explanatory variables
are statistically controlled for. For example, the models will show the likelihood of females participating
in A level Mathematics compared with males after KS4 attainment, KS5 location, FSM status and ethnicity
have all been statistically controlled for.
The inclusion of an interaction between gender and KS4 attainment enables a view on whether the
relationship between KS4 attainment (in KS4 Mathematics and overall KS4 attainment) and the A level
participation and attainment outcome variables is consistent for males and females. Specifically, the
inclusion of the interaction will enable the following questions to be answered:
Is the relationship between KS4 attainment and A level participation the same for males and
females?
Is the relationship between KS4 attainment and A level attainment the same for males and
females?
For more detail on the theoretical specification of the models, please see Boylan et al., (2016).
The null model is used to examine the hierarchical structure of the data to help evaluate whether a
multilevel model is useful. A two-level hierarchical structure is examined (KS4 school and student). Table
26
5 summarises the school level Variance Partition Coefficients (VPC) for the A level participation and
attainment models. The VPC is the proportion of variance in an outcome that is clustered at the school
level.
In terms of A level participation, the proportion of variation found at the school level is very similar for
both Mathematics and Further Mathematics but smaller for the conditional models. In terms of A level
attainment, a slightly higher proportion of variation at the school level is seen with Further Mathematics
compared with Mathematics. This highlights that, in terms of A level participation, differences between
schools is greater for Further Mathematics compared with Mathematics. The VPC statistics shown in
Table 5 highlight the value in adopting a multilevel approach to the modelling. A notable proportion of
variation in A level participation and attainment is seen to lie between schools and acknowledging this
within the analyses will result in more accurate estimations of model coefficients (and hence
understanding of associations with A level participation and attainment).
27
Table 5: Variance Partition Coefficients for null models
School level VPC Statistics CURRENT 2015 KS4 Models
A level Participation Models Mathematics
Further Mathematics Further Mathematics given taking Mathematics
0.27 0.27 0.07
A level Attainment Models Mathematics
Further Mathematics
0.10 0.16
4.2 Assessing and interpreting the multilevel models Modelling participation in A level Mathematics and Further Mathematics
The A level participation models are multilevel logistic regression models that involve a logit link function
that converts the probabilities (of participation) into log-odds. This means that the model coefficients
within the participation models are not directly readable. To aid interpretation, the exponential of the
coefficients is taken to convert the coefficients into odds-ratios. These are the relative odds of one group
(as captured by a dummy variable) compared with a reference group. For example, for A level
Mathematics within the interaction model, the female coefficient is estimated as '-1.04' which equates to
an odds-ratio of 0.3511 - telling us that females are 0.35 times (or 35%) as likely to take A level
Mathematics compared with males. This gender difference is observed once all other explanatory
variables have been controlled for.
One way of estimating the overall statistical explanatory power of the models is McFadden's pseudo r-
square (Menard, 2001) which has some conceptual similarities to the coefficient of determination R-
square statistic commonly used within linear regression. In addition to McFadden's pseudo r-square, the
variance partition coefficient is calculated to show the structure of the variance in terms of the
percentage at levels 2 (KS4 school) and 1 (student).
For Mathematics A level participation, the empty model has a pseudo r-square of 0% (because it is the
null model) and the vpc shows that 27% of the variation lies at level 2 and (therefore) 73% will be at level
1. In the final (interaction) model, the model has a pseudo r-square value of 43.4% (nearly half of the
variation in participation in A level Mathematics has been accounted for by variation across the
explanatory variables) and the final VPC shows that 9% of the remaining variation lies at level 2 and the
remaining 91% at level 1.
Attainment in A level Mathematics and Further Mathematics
The attainment models are more standard multilevel linear regression models where the outcome (A
level attainment) is measured directly (UCAS points score) without the need for a logit link function.
The coefficients are presented in their original scale (UCAS points score) which is converted into a Cohen's
d effect- size statistic by dividing by the standard deviation of the A level attainment distribution12. For
example, in the summary table for the A level Mathematics attainment models, in the final interaction
11 𝑒(−1.04) = 0.35345
12 This is the square root of the total variance at levels 1 and 2 for the null model.
28
model, the female coefficient is seen as -8.11 ~ females attain around 8.1 UCAS points lower than males
in A level Mathematics once all other variables are controlled for. Alongside this coefficient is the Cohen's
d effect-size statistic of -0.26 ~ females attain around 0.26 standard deviations lower than males in A
level Mathematics UCAS points once all other variables are controlled for.
Assessing fit for the attainment models is a more straightforward process than with the A level
participation models. The variation can be partitioned and the explanatory power at each level can be
estimated using the standard coefficient of determination R2.
For the A level Mathematics attainment models, the null model found that 10% of variance in attainment
lay at level 2 and 90% at level 1. The final interaction model shows that the variation remaining had 7% at
level 2 and 93% at level 1. The overall explanatory power of the model was 38% with a greater proportion
of variance being accounted for at level 2 (56%) compared with level 1 (36%).
4.3 The need for caution when comparing these analyses with Boylan et al
(2016). There are three key reasons for the need for caution when comparing the models presented here and
those presented by Boylan et al (2016).
The analyses presented here relate to two KS5 years (2016 and 2017) for the 2015 KS4 pupil
cohort but the analyses presented by Boylan et al. (2016) covered three KS5 years (2012 to 2014)
for the 2011 KS4 pupil cohort.
Within these multilevel analyses, the level 2 (school/institution) identifier relates to the KS4
school that a pupil attended in 2015. In Boylan et al. (2016), the KS5 institution where the A level
was taken was used for the level 2 identifier.
Boylan et al. (2016) also included KS5 institution level variables around engagement with the
FMSP whilst the analyses presented here do not.
New restrictions and regulations around NPD data access and use meant that the KS5 institution unique
identifier (LAESTAB) was not provided for analyses and so the KS4 school was used for level 2. This means
that school-level clustering will be accounted for in the analyses but that this clustering relates back to
KS4 rather than KS5. For students who remain in the same school from KS4 into KS5, this would be
fine/accurate but for students who leave for other institutions, it would not be. In reality, a degree of
KS4 school clustering is likely to remain in the data and be accompanied by additional clustering post-KS4
in KS5. To examine this more completely, a complex 3-level cross-classified multilevel design would be
needed. This is beyond the scope of analyses presented here.
29
4.4 Statistical Tables Descriptive Statistical Analyses
Table I.1: Participation in KS5, 1+ A level, A level Mathematics and A level Further
Mathematics
Table I.2: Attainment in A level Mathematics and Further Mathematics
Modelling Participation in A levels generally, A level Mathematics and A level Further Mathematics
Table II.1: Modelling participation in A level (taking 1+ A level in any subject)
Table II.2: Modelling participation in A level Mathematics
Table II.3: Modelling participation in A level Further Mathematics
Table II.4: Modelling participation in A level Further Mathematics for students known to
have taken A level Mathematics
Modelling Attainment in A level Mathematics and Further Mathematics
Table III.1: Modelling attainment in A level Mathematics
Table III.2: Modelling attainment in A level Further Mathematics
30
Table I.1: Participation in KS5, 1+ A level, A level Mathematics and Further Mathematics
A level in 2016 or 2017 N= % took 1+ KS5 Exam
% took 1+ A level
% took Mathematics
A level
% took Further
Mathematics A level
All Pupils… …whole 2015 KS4 Cohort
621,758
77.9
38.5
10.9
2.0
…who took 1+ KS5 484,255 100.0 49.4 14.0 2.6 ... took 1+ A level 239,448 - 100.0 28.3 5.2
... took A level Mathematics 67,847 - - 100.0 18.2 ... took A level Further Mathematics 12,354 - - 99.9 100.0
KS4 Attainment
Overall (5+ A*-C GCSEs including English & Mathematics)
328,853 86.7 61.0 17.3 3.1
KS4 Mathematics Attainment: Attained grade A* 45,309 96.6 92.2 74.8 21.1
…grade A or A* 115,605 92.4 83.8 48.4 9.2 …grade B or higher 229,679 88.4 70.6 26.2 4.7 …grade C or higher 403,300 84.0 52.7 14.9 2.7
Pupil Background
FSM Status Classed as FSM in 2011 79,556 67.8 16.1 3.4 0.5
Ever Classed as FSM KS1-KS4 156,968 69.1 18.1 3.8 0.6 Never classed as FSM KS1-KS4 464,790 80.9 45.4 13.3 2.5
Gender Male 319,018 75.9 33.2 12.9 2.9
Female 302,740 79.9 44.1 8.8 1.1 Ethnicity
White (Total) 445,152 78.5 35.2 8.6 1.6 …White British 419,175 78.7 35.0 8.5 1.6
…White Eastern European 4,424 74.6 32.0 8.9 2.0 …White Western European 2,236 78.1 42.6 11.4 2.3
…White Irish 1,910 79.6 50.2 13.0 2.3 …White Turkish 1,404 67.8 35.9 9.4 1.3
Asian (Total) 49,864 76.4 44.9 17.5 2.5 …Indian 13,401 81.8 57.2 26.6 4.4
…Pakistani 20,142 72.8 35.4 10.1 0.9 …Bangladeshi 8,075 75.2 42.6 13.7 1.6
…Sri Lankan Tamil 723 80.8 63.3 45.2 7.6 Black (Total) 27,800 70.8 35.6 8.6 0.9
…Black Caribbean 7,562 69.9 26.8 4.3 0.4 …Black African (combined) 16,911 71.5 40.5 11.1 1.1
…Black African (Somali) 3,350 62.1 30.5 9.9 1.0 …Black African (Nigerian) 1,780 74.4 50.4 13.5 1.1
…Black African (Ghanaian) 874 75.5 43.4 10.2 1.4 Mixed Ethnicity (Total) 22,932 76.1 38.8 10.8 2.0 Mixed Black Caribbean & White 6,456 73.2 27.9 5.2 0.6
Mixed Asian & White 4,761 80.3 49.5 16.2 3.1 Mixed Black African & White 2,577 76.2 39.8 9.5 1.5
Chinese 2,074 87.8 69.8 45.6 14.9
Middle Eastern / Arab 1,984 70.7 39.9 16.0 1.6 Other / missing 100,895 77.7 51.8 19.0 3.6
31
Table I.1 continued: Participation in KS5, 1+ A level, A level Mathematics and Further Mathematics
A level in 2016 or 2017 N= % took 1+ KS5 Exam
% took 1+ A level
% took Mathematics
A level
% took Further
Mathematics A level
Type of School in KS4 in 2015 Mainstream State 543,872 78.1 37.5 10.0 1.8
Mainstream Private / Fee Paying 46,270 88.7 74.2 27.8 5.6 Other 31,616 59.1 4.3 1.3 0.3
Type of Institution in KS5 2016-2017 Mainstream State School 6
th Form 181,104 100.0 78.0 22.1 4.1
Mainstream Private School 6th
Form 32,807 100.0 90.0 35.8 7.5 FE - In Sixth Form College 65,890 100.0 69.8 16.2 2.6
FE - In FE College 165,256 100.0 7.6 1.4 0.2 Other 39,198 100.0 25.9 7.7 1.1
32
Table I.2: Attainment in A level Mathematics and Further Mathematics
A level in 2016 or 2017 A level Mathematics A level Further Mathematics
mean (sd) n= mean (sd) n=
All Students Mean UCAS Points (sd) 101.3 (30.92) 67,847
111.9 (27.91) 12,354 Took A level Further Mathematics 130.3 (15.39) 12,339 Did not take Further Mathematics 94.8 (29.78) 55,508 - - Across Explanatory Variables
KS4 Mathematics Attainment:
Attained Grade A* 114.2 (24.18) 33,909 113.5 (25.89) 9,567 Attained Grade A 84.3 (28.30) 22,025 83.1 (29.44) 1,115 Attained Grade B 66.6 (29.14) 4,139 71.4 (35.13) 37 Attained Grade C 48.9 (38.14) 99 SUPP <10
FSM Status:
Classed as FSM in KS4 91.5 (32.17) 2,711 100.4 (30.5) 384 Ever classed as FSM 91.3 (32.56) 5,967 100.5 (31.36) 881
Never classed as FSM 102.2 (30.59) 61,876 112.8 (27.11) 11,473 Gender
Male 101.8 (31.74) 41,105 111.9 (27.73) 9,148 Female 100.5 (29.61) 26,738 112.1 (27.27) 3,206
Ethnicity
…White British 99.8 (31.19) 35,660 109.9 (27.9) 6,632 …White Eastern European 96.5 (33.1) 392 105.2 (29.48) 88
…White Western European 103.6 (30.26) 256 116.2 (26.28) 52 …White Irish 105.4 (28.93) 249 113.0 (26.86) 43
…White Turkish 95.9 (30.04) 132 100.0 (31.44) 18 …Indian 102.2 (30.27) 3,565 114.0 (25.9) 589
…Pakistani 93.2 (30.28) 2,036 105.1 (29.46) 179 …Bangladeshi 91.3 (32.93) 1,104 100.2 (30.87) 129
…Sri Lankan Tamil 98.3 (31.58) 327 106.2 (29.53) 55 …Black Caribbean 85.3 (31.76) 325 101.8 (24.30) 34
…Black African (combined) 91.8 (30.81) 1,870 100.2 (32.94) 186 …Black African (Somali) 89.8 (30.21) 331 86.9 (35.78) 32
…Black African (Nigerian) 93.0 (30.42) 239 112.6 (22.32) 19 …Black African (Ghanaian) 96.0 (30.92) 89 101.7 (33.53) 12
Mixed Black Caribbean & White 95.4 (31.58) 389 109.5 (26.96) 42 Mixed Asian & White 103.2 (30.21) 770 117.1 (26.69) 147
Mixed Black African & White 97.8 (31.36) 245 108.7 (26.67) 39 Chinese 108.7 (30.64) 945 111.4 (28.00) 308
Middle Eastern / Arab 91.4 (33.9) 317 105.2 (32.24) 31 Type of School in KS4 in 2015
Mainstream State 99.4 (31.21) 54,557 109.8 (28.00) 9,695 Mainstream Private / Fee Paying 109.5 (28.21) 12.865 120.2 (24.08) 2,579
Other 96.2 (32.07) 421 107.8 (35.51) 80 Type of Institution in KS5 2016-2017
Mainstream State School 6th
Form 100.3 (30.85) 40,016 110.7 (27.63) 7,370 Mainstream Private School 6
th Form 111.0 (27.40) 11,760 121.5 (23.01) 2,453
FE - In Sixth Form College 98.5 (31.14) 10,705 107.0 (28.56) 1,704 FE - In FE College 93.6 (33.03) 2,350 105.2 (29.1) 391
Other 92.1 (33.46) 3,012 104.7 (32.49) 436
33
Table II.1: Modelling participation in 1+ A level Stages of the main effects 1+ A level participation models; 2015 KS4 English pupil cohort, KS5/A level in 2016 or 2017
Participation in A level Further Mathematics
Model Stages:
1. Null Model
2. KS4 Attain
Logit (OR)
3. KS5 Location
Logit (OR)
4. Pupil Backgrd
Logit (OR)
6. Full Main Effects
Logit (OR)
KS4 Attainment
KS4 Mathematics Grade A* - 0.10 (1.10)**
- - 0.10 (1.11)**
Overall (KS4 points per exam) - 0.32 (1.38)**
- - 0.29 (1.34)**
Type of KS5 Institution
(6th
Form College) - - -0.50 (0.62)** - -0.4 (0.67)** (FE College) - - -4.30 (0.01)** - -3.33 (0.04)**
(Independent / Fee Paying) - - 0.30 (1.36)** - 0.16 (1.17)** (Other) - - -4.70 (0.01)** - -4.31 (0.01)**
Pupil Background
Gender (Female) - - - 0.54 (1.71)** 0.14 (1.15)**
Poverty (FSM) - - - -1.02 (0.36)** -0.29 (0.74)**
Ethnicity (white other) - - - 0.13 (1.14)** 0.24 (1.28)** (Indian) - - - 0.78 (2.17)** 0.37 (1.44)**
(Pakistani) - - - 0.31 (1.37)** 0.13 (1.14)** (Bangladeshi) - - - 0.72 (2.06)** 0.30 (1.36)**
(black Caribbean) - - - -0.28 (0.75)** 0.18 (1.2)** (black African) - - - 0.50 (1.65)** 0.42 (1.53)**
(mixed black Carib & white) - - - -0.13 (0.87)** 0.04 (1.04)NS (Chinese) - - - 1.27 (3.57)** 0.66 (1.93)**
(Other) - - - 0.13 (1.13)** 0.05 (1.05)**
Constant -1.28 -1.24 -1.30 -1.33 0.36
VPC - - -
Level 2 (KS4 institution) 50% 15% 27% 45% 19% Level 1 (student) 50% 85% 73% 55% 81%
McFadden's Pseudo R2 - 39.4% 41.9% 3.7% 58.9%
Source: Data from the 2015 pupil-level cohort of all young people in England who took KS4 assessments at the end of Y11 in summer 2015 who took A level(s) between 2016 and 17.
34
Table II.1 continued: Modelling participation in 1+ A level Including the gender*KS4 attainment interaction; 2015 KS4 English pupil cohort, KS5/A level in 2016 or 2017
Participation in A level Further Mathematics
Model Stages:
Full Main Effects
Logit (odds-ratio)
Including gender*KS4 interaction terms
Logit (odds-ratio)
KS4 Attainment
KS4 Mathematics Grade A* 0.10 (1.11)** 0.36 (1.43)** (Females*Grade A*) Interaction term - -0.67 (0.51)**
Overall KS4 points per exam 0.29 (1.34)** 0.31 (1.36)** (Females*Overall KS4 points per exam) Interaction - -0.02 (0.98)**
Type of KS5 institution
(6th
Form College) -0.4 (0.67)** -0.41 (0.67)** (FE College) -3.33 (0.04)** -3.33 (0.04)**
(Independent / Fee Paying) 0.16 (1.17)** 0.16 (1.17)** (Other) -4.31 (0.01)** -4.30 (0.01)**
Pupil Background
Gender (Female) 0.14 (1.15)** 0.23 (1.26)**
Poverty (FSM) -0.29 (0.74)** -0.30 (0.74)** Ethnicity (white other) 0.24 (1.28)** 0.25 (1.28)**
(Indian) 0.37 (1.44)** 0.36 (1.44)** (Pakistani) 0.13 (1.14)** 0.13 (1.14)**
(Bangladeshi) 0.30 (1.36)** 0.30 (1.35)** (black Caribbean) 0.18 (1.2)** 0.18 (1.2)**
(black African) 0.42 (1.53)** 0.42 (1.53)** (mixed black Carib & white) 0.04 (1.04)NS 0.04 (1.04)NS
(Chinese) 0.66 (1.93)** 0.66 (1.94)** (Other) 0.05 (1.05)** 0.05 (1.05)**
Constant 0.36 0.32
VPC
Level 2 (KS4 institution) 19% 19% Level 1 (student) 81% 81%
McFadden's Pseudo R2 58.9% 58.9%
Source: Data from the 2015 pupil-level cohort of all young people in England who took KS4 assessments at the end of Y11 in summer 2015 who took A level(s) between 2016 and 17.
35
Table II.2: Modelling participation in A level Mathematics Stages of the main effects A level Mathematics participation models; 2015 KS4 English pupil cohort, KS5/A level in 2016 or
2017
Participation in A level Mathematics
Model Stages:
1. Null Model
2. KS4 Attain
Logit (OR)
3. KS5 Location
Logit (OR)
4. Pupil Backgrd
Logit (OR)
6. Full Main Effects
Logit (OR)
KS4 Attainment
KS4 Mathematics Grade A* - 2.33 (10.33)** - - 2.27 (9.67)**
Overall (KS4 points per exam) - 0.21 (1.23)** - - 0.20 (1.23)**
Type of KS5 Institution
(6th
Form College) - - -0.40 (0.67)** - -0.23 (0.79)** (FE College) - - -3.07 (0.05)** - -1.57 (0.21)**
(Independent / Fee Paying) - - 0.36 (1.43)** - -0.23 (0.80)** (Other) - - -2.94 (0.05)** - -1.98 (0.14)**
Pupil Background
Gender (Female) - - - -0.50 (0.61)** -1.28 (0.28)**
Poverty (FSM) - - - -1.01 (0.36)** -0.14 (0.87)**
Ethnicity (white other) - - - 0.24 (1.28)** 0.27 (1.31)** (Indian) - - - 1.07 (2.93)** 0.97 (2.65)**
(Pakistani) - - - 0.36 (1.44)** 0.60 (1.82)** (Bangladeshi) - - - 0.80 (2.24)** 0.71 (2.02)**
(black Caribbean) - - - -0.66 (0.52)** 0.02 (1.02) (black African) - - - 0.48 (1.62)** 0.71 (2.04)**
(mixed black Carib & white) - - - -0.36 (0.70)** -0.08 (0.92) (Chinese) - - - 1.99 (7.33)** 1.66 (5.24)**
(Other) - - - 0.45 (1.57)** 0.47 (1.60)**
Constant -2.67 -3.79 -1.43 -2.40 -2.85
VPC - - -
Level 2 (KS4 institution) 27% 9% 14% 22% 9% Level 1 (student) 73% 91% 86% 78% 91%
McFadden's Pseudo R2 - 37.8% 14.2% 3.1% 43.4%
Source: Data from the 2015 pupil-level cohort of all young people in England who took KS4 assessments at the end of Y11 in summer 2015 who took A level(s) between 2016 and 17.
36
Table II.2 continued: Modelling participation in A level Mathematics Including the gender*KS4 attainment interaction; 2015 KS4 English pupil cohort, KS5/A level in 2016 or 2017
Participation in A level Mathematics
Model Stages:
Full Main Effects
Logit (odds-ratio)
Including gender*KS4 interaction terms
Logit (odds-ratio)
KS4 Attainment
KS4 Mathematics Grade A* 2.27 (9.67)** 2.32 (10.20)** (Females*Grade A*) Interaction term - -0.07 (0.93)**
Overall KS4 points per exam 0.20 (1.23)** 0.22 (1.24)** (Females*Overall KS4 points per exam) Interaction - -0.03 (0.98)**
Type of KS5 institution
(6th
Form College) -0.23 (0.79)** -0.23 (0.79)** (FE College) -1.57 (0.21)** -1.57 (0.21)**
(Independent / Fee Paying) -0.23 (0.80)** -0.23 (0.80)** (Other) -1.98 (0.14)** -1.98 (0.14)**
Pupil Background
Gender (Female) -1.28 (0.28)** -1.04 (0.35)**
Poverty (FSM) -0.14 (0.87)** -0.14 (0.87)** Ethnicity (white other) 0.27 (1.31)** 0.27 (1.31)**
(Indian) 0.97 (2.65)** 0.97 (2.65)** (Pakistani) 0.60 (1.82)** 0.60 (1.82)**
(Bangladeshi) 0.71 (2.02)** 0.70 (2.02)** (black Caribbean) 0.02 (1.02) 0.02 (1.02)
(black African) 0.71 (2.04)** 0.71 (2.04)** (mixed black Carib & white) -0.08 (0.92) -0.08 (0.92)
(Chinese) 1.66 (5.24)** 1.66 (5.24)** (Other) 0.47 (1.60)** 0.47 (1.60)**
Constant -2.85 -2.93
VPC
Level 2 (KS4 institution) 9% 9% Level 1 (student) 91% 91%
McFadden's Pseudo R2 43.4% 43.4%
Source: Data from the 2015 pupil-level cohort of all young people in England who took KS4 assessments at the end of Y11 in summer 2015 who took A level(s) between 2016 and 17.
37
Table II.3: Modelling participation in A level Further Mathematics Stages of the main effects A level Further Mathematics participation models; 2015 KS4 English pupil cohort, KS5/A level in
2016 or 2017
Participation in A level Further Mathematics
Model Stages:
1. Null Model
2. KS4 Attain
Logit (OR)
3. KS5 Location
Logit (OR)
4. Pupil Backgrd
Logit (OR)
6. Full Main Effects
Logit (OR)
KS4 Attainment
KS4 Mathematics Grade A* - 3.15 (23.23)** - - 2.87 (17.65)**
Overall (KS4 points per exam) - 0.14 (1.16)** - - 0.16 (1.17)**
Type of KS5 Institution
(6th
Form College) - - -0.42 (0.66)** - -0.15 (0.86)** (FE College) - - -2.88 (0.06)** - -0.82 (0.44)**
(Independent / Fee Paying) - - 0.45 (1.57)** - 0.23 (1.26)** (Other) - - -2.84 (0.06)** - -1.26 (0.28)**
Pupil Background
Gender (Female) - - - -1.06 (0.35)** -1.55 (0.21)**
Poverty (FSM) - - - -1.12 (0.33)** 0.04 (1.04)
Ethnicity (white other) - - - 0.35 (1.41)** 0.28 (1.32)** (Indian) - - - 0.74 (2.10)** 0.13 (1.14)*
(Pakistani) - - - -0.38 (0.68)** -0.42 (0.66)** (Bangladeshi) - - - 0.25 (1.28)* -0.19 (0.83)
(black Caribbean) - - - -1.16 (0.31)** -0.35 (0.71) (black African) - - - -0.20 (0.82)* -0.19 (0.83)*
(mixed black Carib & white) - - - -0.83 (0.44)** -0.53 (0.59)** (Chinese) - - - 2.05 (7.80)** 1.26 (3.53)**
(Other) - - - 0.42 (1.52)** 0.23 (1.26)**
Constant -4.50 -6.43 -3.48 -3.97 -5.68
VPC - - -
Level 2 (KS4 institution) 27% 18% 17% 21% 15% Level 1 (student) 73% 82% 83% 79% 85%
McFadden's Pseudo R2 - 35.7% 9.0% 4.1% 39.9%
Source: Data from the 2015 pupil-level cohort of all young people in England who took KS4 assessments at the end of Y11 in summer 2015 who took A level(s) between 2016 and 17.
38
Table II.3 continued: Modelling participation in A level Further Mathematics Including the gender*KS4 attainment interaction; 2015 KS4 English pupil cohort, KS5/A level in 2016 or 2017
Participation in A level Further Mathematics
Model Stages:
Full Main Effects
Logit (odds-ratio)
Including gender*KS4 interaction terms
Logit (odds-ratio)
KS4 Attainment
KS4 Mathematics Grade A* 2.87 (17.65)** 2.87 (17.68)** (Females*Grade A*) Interaction term - 0.01 (1.01)
Overall KS4 points per exam 0.16 (1.17)** 0.16 (1.17)** (Females*Overall KS4 points per exam) Interaction - -0.01 (0.99)
Type of KS5 institution
(6th
Form College) -0.15 (0.86)** -0.15 (0.86)** (FE College) -0.82 (0.44)** -0.82 (0.44)**
(Independent / Fee Paying) 0.23 (1.26)** 0.24 (1.27)** (Other) -1.26 (0.28)** -1.26 (0.28)**
Pupil Background
Gender (Female) -1.55 (0.21)** -1.40 (0.25)**
Poverty (FSM) 0.04 (1.04) 0.04 (1.04) Ethnicity (white other) 0.28 (1.32)** 0.28 (1.32)**
(Indian) 0.13 (1.14)* 0.13 (1.14)* (Pakistani) -0.42 (0.66)** -0.42 (0.66)**
(Bangladeshi) -0.19 (0.83) -0.19 (0.83) (black Caribbean) -0.35 (0.71) -0.35 (0.70)
(black African) -0.19 (0.83)* -0.19 (0.83)* (mixed black Carib & white) -0.53 (0.59)** -0.53 (0.59)**
(Chinese) 1.26 (3.53)** 1.26 (3.53)** (Other) 0.23 (1.26)** 0.23 (1.26)**
Constant -5.68 -5.71
VPC
Level 2 (KS4 institution) 15% 15% Level 1 (student) 85% 85%
McFadden's Pseudo R2 39.9% 39.9%
Source: Data from the 2015 pupil-level cohort of all young people in England who took KS4 assessments at the end of Y11 in summer 2015 who took A level(s) between 2016 and 17.
39
Table II.4: Modelling participation in A level Further Mathematics given that student took A level Mathematics Stages of the main effects A level Further Mathematics conditional participation models; 2015 KS4 English pupil cohort, KS5/A
level in 2016 or 2017
Participation in A level Further Mathematics
Model Stages:
1. Null Model
2. KS4 Attain
Logit (OR)
3. KS5 Location
Logit (OR)
4. Pupil Backgrd
Logit (OR)
6. Full Main Effects
Logit (OR)
KS4 Attainment
KS4 Mathematics Grade A* - 1.67 (5.31)** - - 1.65 (5.18)**
Overall (KS4 points per exam) - 0.07 (1.07)** - - 0.09 (1.10)**
Type of KS5 Institution
(6th
Form College) - - -0.14 (0.87)** - -0.09 (0.91)* (FE College) - - -0.11 (0.89) - 0.06 (1.07)
(Independent / Fee Paying) - - 0.11 (1.12)** - 0.30 (1.35)** (Other) - - -0.30 (0.74)** - -0.06 (0.94)
Pupil Background
Gender (Female) - - - -0.77 (0.46)** -1.11 (0.33)**
Poverty (FSM) - - - -0.12 (0.89)** 0.12 (1.13)**
Ethnicity (white other) - - - 0.17 (1.19)** 0.23 (1.26)** (Indian) - - - -0.14 (0.87)** -0.11 (0.90)*
(Pakistani) - - - -0.83 (0.44)** -0.64 (0.53)** (Bangladeshi) - - - -0.52 (0.59)* -0.40 (0.67)**
(black Caribbean) - - - -0.65 (0.52)** -0.32 (0.72) (black African) - - - -0.69 (0.50)* -0.45 (0.64)**
(mixed black Carib & white) - - - -0.60 (0.55)** -0.55 (0.58)** (Chinese) - - - 0.83 (2.29)** 0.90 (2.45)**
(Other) - - - 0.00 (1.00) 0.09 (1.10)*
Constant -1.63 -3.49 -1.60 -1.30 -3.43
VPC
- - -
Level 2 (KS4 institution) 7% 11% 6% 6% 9% Level 1 (student) 93% 89% 94% 94% 91%
McFadden's Pseudo R2 - 9.7% 0.1% 2.3% 13.0%
Source: Data from the 2015 pupil-level cohort of all young people in England who took KS4 assessments at the end of Y11 in summer 2015 who took A level(s) between 2016 and 17.
40
Table II.4 continued: Modelling participation in A level Further Mathematics given that student took A level Mathematics
Including the gender*KS4 attainment interaction; 2015 KS4 English pupil cohort, KS5/A level in 2016 or 2017
Participation in A level Further Mathematics
Model Stages:
Full Main Effects
Logit (odds-ratio)
Including gender*KS4 interaction terms
Logit (odds-ratio)
KS4 Attainment
KS4 Mathematics Grade A* 1.65 (5.18)** 1.72 (5.57)** (Females*Grade A*) Interaction term - -0.26 (0.77)**
Overall KS4 points per exam 0.09 (1.10)** 0.10 (1.10)** (Females*Overall KS4 points per exam) Interaction - -0.02 (0.98)**
Type of KS5 institution
(6th
Form College) -0.09 (0.91)* -0.09 (0.91)* (FE College) 0.06 (1.07) 0.06 (1.06)
(Independent / Fee Paying) 0.30 (1.35)** 0.30 (1.35)** (Other) -0.06 (0.94) -0.06 (0.94)
Pupil Background
Gender (Female) -1.11 (0.33)** -0.65 (0.52)**
Poverty (FSM) 0.12 (1.13)** 0.12 (1.13)** Ethnicity (white other) 0.23 (1.26)** 0.23 (1.26)**
(Indian) -0.11 (0.90)* -0.11 (0.89)* (Pakistani) -0.64 (0.53)** -0.64 (0.53)**
(Bangladeshi) -0.40 (0.67)** -0.40 (0.67)** (black Caribbean) -0.32 (0.72) -0.33 (0.72)
(black African) -0.45 (0.64)** -0.45 (0.64)** (mixed black Carib & white) -0.55 (0.58)** -0.55 (0.58)**
(Chinese) 0.90 (2.45)** 0.90 (2.45)** (Other) 0.09 (1.10)** 0.09 (1.09)**
Constant -3.43 -3.53
VPC
Level 2 (KS4 institution) 9% 9% Level 1 (student) 91% 91%
McFadden's Pseudo R2 13.0% 13.0%
Source: Data from the 2015 pupil-level cohort of all young people in England who took KS4 assessments at the end of Y11 in summer 2015 who took A level(s) between 2016 and 17.
41
Table III.1: Modelling attainment in A level Mathematics Stages of the main effects A-level Attainment models; 2015 KS4 English pupil cohort, KS5/A level in 2016 or 2017
Attainment in A level Mathematics
Model Stages:
1. Null Model
2. KS4 Attain
(Cohen's d)
3. KS5 Location
(Cohen's d)
4. Pupil Backgrd
(Cohen's d)
6. Full Main Effects
(Cohen's d)
KS4 Attainment
KS4 Mathematics Grade A* - 17.41 (+0.56)** - - 16.89 (+0.55)** Overall (KS4 pts per exam) - 2.99 (+0.10)** - - 3.16 (+0.10)**
Type of KS5 Inst
(6th
Form College) - - -0.51 (-0.02) - -0.36 (-0.01) (FE College) - - -6.22 (-0.20)** - -1.51 (-0.05)**
(Independent) - - 8.56 (+0.28)** - 4.03 (+0.13)** (Other) - - -8.28 (-0.27)** - -2.74 (-0.09)**
Pupil Background
Gender (Female) - - - -0.88 (-0.03)** -8.11 (-0.26)** Poverty (FSM) - - - -6.22 (-0.2)** -1.20 (-0.04)** Ethnicity (white other) - - - 1.70 (+0.05)** 2.34 (+0.08)**
(Indian) - - - 1.70 (+0.05)** 2.38 (+0.08)** (Pakistani) - - - -3.67 (-0.12)** 1.11 (0.04)
(Bangladeshi) - - - -4.68 (-0.15)** -1.90 (-0.06)* (black Caribbean) - - - -12.02 (-0.39)** -5.40 (-0.17)**
(black African) - - - -4.22 (-0.14)** 1.40 (+0.05)* (mixed blk Carib & white) - - - -2.51 (-0.08) -1.46 (-0.05)
(Chinese) - - - 8.15 (+0.26)** 8.90 (+0.29)** (Other) - - - 2.46 (+0.08)** 2.17 (+0.07)**
Constant 98.0 58.0 97.7 98.6 58.6
VPC
Level 2 (KS4 institution) 10.3 9.0 8.8 8.9 7.4 Level 1 (student) 89.7 91.0 91.2 91.1 92.6
Explanatory Power (R
2)
Level 2 (KS4 institution) - 43.9% 16.8% 14.9% 55.7% Level 1 (student) - 34.6% 0.3% 0.3% 35.9%
Total - 35.5% 2.0% 1.8% 38.0%
Source: Data from the 2015 pupil-level cohort of all young people in England who took KS4 assessments at the end of Y11 in summer 2015 and took A level Mathematics between 2016 and 17.
42
Table III.1 Continued: Modelling attainment in A level Mathematics Including the gender*KS4 attainment interaction; 2015 KS4 English pupil cohort, KS5/A level in 2016 or 2017
Attainment in A level Mathematics
Model Stages:
Full Main Effects
(Cohen's d)
Including gender*KS4 interaction terms
(Cohen's d)
KS4 Attainment
KS4 Mathematics Grade A* 16.89 (+0.55)** 17.80 (+0.58)** (Females*Grade A*) Interaction -2.41 (-0.08)**
Overall KS4 points per exam 3.16 (+0.10)** 3.06 (+0.10)** (Females*Overall KS4 points per exam) Interaction 0.26 (+0.01)**
Type of KS5 institution
(6th
Form College) 0.36 (0.01) 0.35 (0.01) (FE College) -1.51 (-0.05)** -1.48 (-0.05)**
(Independent / Fee Paying) 4.03 (+0.13)** 3.99 (+0.13)** (Other) -2.74 (-0.09)** -2.77 (-0.09)**
Pupil Background
Gender (Female) -8.11 (-0.26)** -9.90 (-0.32)**
Poverty (FSM) -1.20 (-0.04)** -1.19 (-0.04)**
Ethnicity (white other) 2.34 (+0.08)** 2.33 (+0.08)** (Indian) 2.38 (+0.08)** 2.38 (+0.08)**
(Pakistani) 1.11 (0.04) 1.11 (0.04) (Bangladeshi) -1.90 (-0.06)* -1.91 (-0.06)*
(black Caribbean) -5.40 (-0.17)** -5.38 (-0.17)** (black African) 1.40 (+0.05)* 1.39 (+0.05)*
(mixed black Carib & white) -1.46 (-0.05) -1.45 (-0.05) (Chinese) 8.90 (+0.29)** 8.93 (+0.29)**
(Other) 2.17 (+0.07)** 2.17 (+0.07)**
Constant 58.6 59.1
Variance Partition Coefficient (VPC)
Level 2 (KS4 institution) 7.4 7.3 Level 1 (student) 92.6 92.7
Explanatory Power (R2)
Level 2 (KS4 institution) 55.7% 56.1% Level 1 (student) 35.9% 35.9%
Total 38.0% 38.0%
Source: Data from the 2015 pupil-level cohort of all young people in England who took KS4 assessments at the end of Y11 in summer 2015 and took A level Mathematics between 2016 and 17.
43
Table III.2: Modelling attainment in A level Further Mathematics Stages of the main effects A-level Attainment models; 2015 KS4 English pupil cohort, KS5/A level in 2016 or 2017
Attainment in A level Further Mathematics
Model Stages:
1. Null Model
2. KS4 Attain
(Cohen's d)
3. KS5 Location
(Cohen's d)
4. Pupil Backgrd
(Cohen's d)
6. Full Main Effects
(Cohen's d)
KS4 Attainment
KS4 Mathematics Grade A* - 6.18 (+0.22)** - - 8.22 (+0.30)**
Overall (KS4 pts per exam) - 3.55 (+0.13)** - - 3.49 (+0.13)**
Type of KS5 Inst
(6th
Form College) - - -2.87 (-0.10)** - -2.36 (-0.09)**
(FE College) - - -4.83 (-0.17)** - -1.33 (-0.05)
(Independent) - - 9.92 (+0.36)** - 5.06 (+0.18)**
(Other) - - -5.30 (-0.19)** - -1.69 (-0.06)**
Pupil Background
Gender (Female) - - - 0.42 (0.02) -5.73 (-0.21)** Poverty (FSM) - - - -8.62 (-0.31)** -1.82 (-0.07)** Ethnicity (white other) - - - 0.26 (0.01) 0.04 (0.00)
(Indian) - - - 2.57 (+0.09)* 0.81 (+0.03) (Pakistani) - - - -2.59 (-0.09) -1.03 (-0.04)
(Bangladeshi) - - - -6.56 (-0.24)** -3.97 (-0.14) (black Caribbean) - - - -6.06 (-0.22) 0.07 (0.00)
(black African) - - - -6.01 (-0.22)** -5.28 (-0.19)** (mixed blk Carib & white) - - 2.9 (0.1)* 0.76 (0.03) 1.22 (+0.04)
(Chinese) - - 1.05 (0.04) 1.05 (0.04) 2.9 (+0.10)* (Other) - - - 4.54 (+0.16)** 0.72 (0.03)
Constant 109.6 60.1 109.0 109.3 60.3
VPC
Level 2 (KS4 institution) 16.2 9.5 13.4 13.7 8.7 Level 1 (student) 83.8 90.5 86.6 86.3 91.3
Explanatory Power (R
2)
Level 2 (KS4 institution) - 59.8% 20.0% 18.0% 63.8% Level 1 (student) - 25.5% -0.2% -0.3% 26.6%
Total - 31.1% 3.1% 2.7% 32.7%
Source: Data from the 2015 pupil-level cohort of all young people in England who took KS4 assessments at the end of Y11 in summer 2015 and took A level Further Mathematics between 2016 and 17
44
Table III.2 Continued: Modelling attainment in A level Further Mathematics Including the gender*KS4 attainment interaction; 2015 KS4 English pupil cohort, KS5/A level in 2016 or 2017
Attainment in A level Further Mathematics
Model Stages:
Full Main Effects
(Cohen's d)
Including gender*KS4 interaction terms
(Cohen's d)
KS4 Attainment
KS4 Mathematics Grade A* 8.22 (+0.30)** 8.40 (+0.30)** (Females*Grade A*) Interaction -0.61 (-0.02)
Overall KS4 points per exam 3.49 (+0.13)** 3.41 (+0.12)** (Females*Overall KS4 points per exam) Interaction 0.39 (+0.01)**
Type of KS5 institution
(6th
Form College) -2.36 (-0.09)** -2.34 (-0.08)** (FE College) -1.33 (-0.05) -1.30 (-0.05)
(Independent / Fee Paying) 5.06 (+0.18)** 5.03 (0.18)** (Other) -1.69 (-0.06)** -1.67 (-0.06)
Pupil Background
Gender (Female) -5.73 (-0.21)** -10.54 (-0.38)**
Poverty (FSM) -1.82 (-0.07)** -1.81 (-0.07)**
Ethnicity (white other) 0.04 (0.00) 0.06 (0.00) (Indian) 0.81 (+0.03) 0.84 (+0.03)
(Pakistani) -1.03 (-0.04) -1.06 (-0.04) (Bangladeshi) -3.97 (-0.14) -4.10 (-0.15)*
(black Caribbean) 0.07 (0.00) 0.22 (+0.01) (black African) -5.28 (-0.19)** -5.28 (-0.19)**
(mixed black Carib & white) 1.22 (+0.04) 1.11 (+0.04) (Chinese) 2.90 (+0.10)* 2.97 (0.11)*
(Other) 0.72 (+0.03) 0.75 (+0.03)
Constant 60.3 61.3
Variance Partition Coefficient (VPC)
Level 2 (KS4 institution) 8.7 8.6 Level 1 (student) 91.3 91.4
Explanatory Power (R2)
Level 2 (KS4 institution) 63.8% 64.1% Level 1 (student) 26.6% 26.6%
Total 32.6% 32.7%
Source: Data from the 2015 pupil-level cohort of all young people in England who took KS4 assessments at the end of Y11 in summer 2015 and took A level Further Mathematics between 2016 and 17.
5. References
Boylan, M., Demack., S., Stevens, A., Coldwell, M. & Stiell, B. (2016) An Evaluation of the Further
Mathematics Support Programme Research Report Undertaken 2014-2016 and reported in May 2016.
http://shura.shu.ac.uk/14897/
Menard, S. (2001) Applied Logistic Regression Analysis. Sage Quantitative Applications in the Social Sciences Series, Volume 106.