participation and attainment in a level mathematics...

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

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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

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Table 5: Variance Partition Coefficients for null models 27

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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

http://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)


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

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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

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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


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)**


(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%


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)


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)**


(6th


(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 - - -




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)


Logit (odds-ratio)

KS4 Attainment




(6th


(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




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


Model Stages:

1. Null Model

2. KS4 Attain

Logit (OR)

3. KS5 Location

Logit (OR)

4. Pupil Backgrd

Logit (OR)


Logit (OR)

KS4 Attainment




(6th


(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 - - -




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


Model Stages:

Full Main Effects

Logit (odds-ratio)


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)


(6th


(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)**


VPC




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


Model Stages:

1. Null Model

2. KS4 Attain

Logit (OR)

3. KS5 Location

Logit (OR)

4. Pupil Backgrd

Logit (OR)


Logit (OR)

KS4 Attainment




(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

- - -




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


Model Stages:

Full Main Effects

Logit (odds-ratio)


Logit (odds-ratio)

KS4 Attainment




(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)**


VPC




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


Model Stages:

1. Null Model

2. KS4 Attain

(Cohen's d)

3. KS5 Location

(Cohen's d)

4. Pupil Backgrd

(Cohen's d)


(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


Model Stages:

Full Main Effects

(Cohen's d)


(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)**


(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




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)


(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)


(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)**


(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




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.

http://shura.shu.ac.uk/14897/

participation and attainment in a level mathematics...

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