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Maths attitudes, school affect and teacher characteristics as predictors of maths attainment trajectories in primary and secondary education

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Maths attainment is essential for a wide range of outcomes relating to further education, careers, health and the wider economy. Research suggests a significant proportion of adults and adolescents are underachieving in maths within the UK, making this a key area for research. This study investigates the role of children's perceptions of the school climate (children's affect towards school and student–teacher relationships), their attitudes towards maths and teacher characteristics as predictors of maths attainment trajectories, taking the transition from primary to secondary education into consideration. Two growth models were fit using secondary data analysis of the Avon Longitudinal Study of Parents and Children (ALSPAC). The first model, which looked at predictors of maths attainment in primary education, found significant associations only between positive maths attitudes and increased maths attainment. The second model, which looked at predictors of maths attainment in secondary education, found significant associations between increased maths attainment and positive maths attitudes, decreased school belonging, positive student–teacher relationships and increased teacher fairness. The findings suggest that the secondary education school environment is particularly important for maths attainment.
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royalsocietypublishing.org/journal/rsos
Research
Cite this article: Evans D, Field AP. 2020 Maths
attitudes, school affect and teacher characteristics
as predictors of maths attainment trajectories
in primary and secondary education. R. Soc. Open
Sci. 7: 200975.
http://dx.doi.org/10.1098/rsos.200975
Received: 1 June 2020
Accepted: 9 September 2020
Subject Category:
Psychology and cognitive neuroscience
Subject Areas:
psychology
Keywords:
maths attainment, school transition, maths
attitudes, school affect, studentteacher
relationships, Avon Longitudinal Study of Parents
and Children
Author for correspondence:
Danielle Evans
e-mail: de84@sussex.ac.uk
Electronic supplementary material is available
online at https://doi.org/10.6084/m9.figshare.c.
5136154.
Maths attitudes, school affect
and teacher characteristics
as predictors of maths
attainment trajectories
in primary and secondary
education
Danielle Evans and Andy P. Field
School of Psychology, University of Sussex, Brighton, UK
DE, 0000-0002-5330-3393; APF, 0000-0003-3306-4695
Maths attainment is essential for a wide range of outcomes
relating to further education, careers, health and the wider
economy. Research suggests a significant proportion of adults
and adolescents are underachieving in maths within the UK,
making this a key area for research. This study investigates the
role of childrens perceptions of the school climate (childrens
affect towards school and studentteacher relationships), their
attitudes towards maths and teacher characteristics as
predictors of maths attainment trajectories, taking the transition
from primary to secondary education into consideration. Two
growth models were fit using secondary data analysis of the
Avon Longitudinal Study of Parents and Children (ALSPAC).
The first model, which looked at predictors of maths
attainment in primary education, found significant associations
only between positive maths attitudes and increased maths
attainment. The second model, which looked at predictors of
maths attainment in secondary education, found significant
associations between increased maths attainment and positive
maths attitudes, decreased school belonging, positive student
teacher relationships and increased teacher fairness. The
findings suggest that the secondary education school
environment is particularly important for maths attainment.
1. Introduction
Aspects of numerical and mathematical skills are used by
adults every day. Whether this is as employees giving the
correct change or when using spreadsheets, as consumers when
© 2020 The Authors. Published by the Royal Society under the terms of the Creative
Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits
unrestricted use, provided the original author and source are credited.
calculating the savings associated with a 10% discount, when managing finances (i.e. understanding
interest rates and borrowing funds), or as parents when helping children with homework [1]. The
consequences of poor numeracy and low maths attainment are far-reaching and long-lasting. Low
maths attainment limits educational and career opportunities, and is linked to a higher rate of
unemployment and low socioeconomic status (SES), as well as increased health issues, and a higher
likelihood of homelessness and contact with the criminal justice system [26]. Poor numeracy is
reported to cost around 20.2 billion per year to the UK economy alone, not including the potential
costs associated with the health sector and criminal justice system [7].
When quantifying the extent of poor mathematical abilities in the UK, it is reported that 49% of
working-age adults have the equivalent maths skills of 6-year-old children, with only 22% having the
skills of the average16-year-old [8]. However, these statistics are somewhat dated (using data from
2011), meaning that the true extent of the maths crisis[9] currently is unknown. When comparing
the data from 2011 with the first wave in 2003, the percentage of numerateadults in the UK had
decreased [8], suggesting that it would not be entirely illogical to assume that the problem has
continued to worsen from 2011 until now. The poor maths performance seen in adults in the UK is
likely to be due to deficits in childhood learning but could also be due to poor retention or a lack of
practice of maths skills over time (see [10]). Investigating predictors of maths attainment in childhood
provides several benefits in helping to overcome the maths crisispresent in the UK. By uncovering
underlying factors that influence maths attainment, we can use this information to design evidence-
based strategies, which will hopefully increase the effectiveness of interventions aiming to improve
maths attainment and other positive outcomes associated with increased abilities.
Estimates of the heritability of maths suggest that attainment is moderately geneticaround two-thirds
of the variance in attainment can be explained by genetic factors, with the remaining variance explained by
aspects of the shared- and non-shared environment [11], and their interaction with genetic factors. Outside
of the home, a significant proportion of childrens time is spent in school. It is within this environment that
children acquire new knowledge and skills, and is also where significant social interactions with otherstake
place. Unsurprisingly, existing research suggests the school environment is influential in the development
of maths abilities and the performance of maths skills. However, the long-term effects are unknown.
Therefore, the present study aims to investigate which school-related factors are longitudinally
associated with maths attainment trajectories of school children in the UK, with a particular focus on
the school climate, studentteacher relationships and maths-related attitudes during the transitional
period from primary to secondary education.
1.1. The transition from primary to secondary education
Early adolescence is a period of substantial change and development. One key event associated with
considerable disruption during this time is the transition from primary to secondary education. In the
UK, this transition occurs when children are 11 years old when they transfer from their 6th year of
education in a primary school to their 7th year in a separate secondary school. The transition event
itself is negatively associated with academic, social and emotional wellbeing [12,13], with children
experiencing increased feelings of anxiety, loneliness and stress during the transitional period [1417].
Many changes occur within childrens environments stemming from the transition, particularly
relating to differences between primary and secondary education institutions. The differences present
between these environments could plausibly influence relationships between maths attainment and
the school climate, studentteacher relationships and attitudes towards maths around the transition to
secondary education, which will be discussed further in the following sections.
One clear environmental difference is that secondary schools are typically much larger than primary
schools, with several primary education institutions feedinginto one secondary school. Children
generally have several specialized subject teachers in secondary education compared with one
individual teacher for all subjects for the entire school year in primary education (though the presence
of specialist maths teachers is becoming increasingly common in English primary schools, helped by
government initiatives and training bursaries). Children report several concerns relating to this new
environment, such as becoming lost when navigating their new school buildings or being late for
class [18,19]. Prospective relationships in secondary education also cause some concern among
children during the transition process, especially regarding bullying and making new studentteacher
relationships [19]. The increased size of the physical and social environment, and the additional
interactions between children and their unfamiliar teachers and peers probably affect childrens
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perceptions of the school climate and studentteacher relationships, and how these factors are associated
with attainment.
This transitional period in adolescence is particularly interesting when investigating maths attainment
trajectories because of the impact of the education transition and the differences found in maths outcomes
between primary and secondary education students. For example, students in secondary education report
less involvement in maths class, less positive attitudes towards maths, decreased maths enjoyment,
decreased maths interest and increased maths anxiety compared with primary education students
[20,21]. These attitudestowards maths (i.e. interest, enjoyment, self-efficacy and anxiety) are linked to
maths attainment [2228], highlighting the importance of this period for intervention strategies aiming
to improve maths attainment. Further research also demonstrates poor maths performance across the
transition where declines in achievement and a lack of progress in maths has been found [2931], which
has been linked to increased maths anxiety at age 18 [32].
The changes found in attitudes towards maths (i.e. declining efficacy and interest) across the primary
secondary education transition appear to be related to aspects of the school environment, such as post-
transition teacher effectiveness [20]. Midgley et al. [33] found that maths attitudes (i.e. value, usefulness
and importance) significantly declined for students moving from teachers they perceived to be highly
supportive pre-transition to teachers they perceived to be less supportive post-transition, which was
particularly marked for low-achieving students. These findings together suggest that the wider school
environment is especially important for maths-related outcomes across the transition to secondary
education, and that the differing characteristics of primary and secondary education environments
should be investigated further when assessing maths attainment in adolescence.
1.2. School-related predictors of maths
1.2.1. The school climate and childrens affect towards school
The school climatehas been defined as the norms, goals, values, interpersonal relationships, teaching
and learning practices, and organizational structuresof a school, and relatedly, childrens affect towards
school encompassing their feelings of social, emotional and physical safety [34, p. 182]. A positive
school/classroom climate, favourable affect towards school and an academically focused environment
is positively associated with childrens general academic and maths attainment [3540]. Students
perceiving their classroom to be highly emotionally supportive are more likely to seek help from their
teachers and peers, which consequently is related to increased maths attainment [41]. The school
climate is also associated with adolescentswellbeing [38,42], with increased feelings of school
connectednessassociated with decreased emotional distress, suicidal involvement, violence and
substance use in US adolescents [43].
There are several changes within the school environment that occur with the transition to secondary
education which makes this transitional period particularly interesting in terms of the school climate.
Children transition from being the oldest in the school to the youngest in a larger, very unfamiliar
environment, probably affecting their sense of security. The total number of students also increases
significantly from primary to secondary education, with teachers typically interacting with multiple
classes of children in different years throughout the school day, meaning that children have a
decreased capacity to develop close relationships and attachments like they had with their teachers in
primary education [44]. These differences in the primary and secondary school environment, and
those highlighted previously, could affect adolescentsperceptions of the school climate and their
feelings towards school. It is likely that the change from a small classroom where children hold close
relationships with their teachers, to a larger departmentalised school with an increased focus on
discipline, affects their feelings of social, emotional and physical safety. Findings reported by Coelho
et al. [45] support this idea, highlighting the negative impact of the primarysecondary education
transition on school climate, with declines in ratings of peer relationships, fairness of rules, school
safety, school liking and studentteacher relationships post-transition. However, the transition for
Portuguese students in the study conducted by Coelho et al. is one of the earliest primarysecondary
education transitions to occur at age 9 compared with age 11 in the UK, meaning the effects could
potentially be different for older students. Although, in a study of US schools, Kim et al. [46] report
that K-8schools (i.e. schools that do not transition in grade 6 or 7) had a more positive social context
(characterized by school chaos, student conduct problems, staff professional climate, teacher agency
and teaching burden) compared with middle and junior high schools that do transition (usually into
grade 6 or 7), suggesting that the negative impacts associated with the transition to secondary
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education reported by Coelho et al. are also evident in older adolescents. Positive school affect also
appears to have a protective role; Vaz et al. [47] report an increased sense of school-belonging(an
aspect of school climate) in primary school is associated with decreased emotional symptoms
concurrently, and in the first year of secondary education.
1.2.2. Studentteacher relationships
Overall, the existing literature suggests that a positive school climate is important for childrensacademic
attainment and their socio-emotional functioning. The aforementioned studies have used a range of
definitions for school climate; however, one aspect that is commonly investigated within the school-
climate literature is the relationship students have with their teachers. Various aspects of studentteacher
relationships have been examined, though most studies focus on closeness, warmth, trust and fairness
perceived by students. Previous research has found that positive and warm studentteacher relationships
buffer the effects of childhood adversity on aspects of cognitive abilities [48], and protect against
depressive symptoms and misconduct in adolescents [49]. Positive studentteacher relationships are
associated with lower dropout rates for US high-school students [50] and influences student wellbeing
[51]. Others report associations between teacher mental health problems and studentsmental wellbeing [52].
As well as being important for general student wellbeing, positive studentteacher relationships also
play a pivotal role within maths attainment [53]. Increased studentteacher connectednessis associated
with increased maths attainment in Canadian adolescents, and also has a buffering effect between
bullying and maths attainment for boys [54]. Positive studentteacher relationships have been found to
mediate the effects of school-level poverty on maths achievement in Chinese students [55]. Teng [56]
supports this finding, highlighting the importance of studentteacher relationships for the maths
attainment of Chinese adolescents, with a marked effect for low-performing schools and underachievers.
Negative relationships also appear to have an effect on attainment. Bryce et al. [57] found student
teacher conflict negatively impacted academic achievement (maths and reading) through behavioural
engagement in US school children.
In addition to the effects associated with a positive studentteacher relationship, teachersown
attitudes, self-efficacy beliefs and abilities can influence the development of studentsattitudes
towards maths regarding gender stereotypes [58], and can affect studentsattainment [58,59].
Teachersenjoyment of maths also affects the instructional time given to maths in that teachers who
enjoy maths more spend more time engaging in maths tasks [60]. There is also some evidence to
suggest teachersgeneral mental wellbeing is linked to studentsmaths abilities through the quality of
the classroom learning environment [61], and in the feedback given to students [62], which is
particularly marked for low-achieving students. Research in this area is sparse, but generally suggests
that teachersmental health and their attitudes towards maths are linked to studentsmaths outcomes.
Similar to the school climate, changes in studentteacher relationships have been reported around the
transition to secondary education. In primary education, children are traditionally taught by a single
teacher per year for all subjects (though primary schools are increasingly using specialist teachers in
recent years) whereas, in secondary education, the majority of institutions are departmentalized in
that adolescents will be taught different subjects by different specialist teachers. This difference
between primary and secondary education is thought to alter the relationships students and teachers
have [63]. For example, Hughes & Cao [64] report a significant drop in teacher-rated warmtharound
the transition to secondary education for US adolescents, with larger decreases in warmth predictive
of lower maths attainment. Alternatively, Bru et al. [65] report no abrupt change in student-perceived
teacher support around the transition. These differences in findings could potentially lie within the
respondent (student or teacher), the sample used (US versus Norway) or the specific aspects of the
studentteacher relationship investigated, further highlighting the complexity of this association, and
the need for further research in this area.
1.3. Stageenvironment fit theory
One theoretical framework that may help to explain the negative effects and outcomes associated with the
transition into secondary education is the stageenvironment fit theory proposed by Eccles et al.[44].This
theory states that negative outcomes occur when there is a mismatch between adolescentsneeds and the
opportunities within their environments. Eccles et al. propose that there are developmentally
inappropriate changes within the school and classroom environment following the transition to
secondary education, which may result in a poor personenvironment fit. The changes discussed by
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Eccles et al. [44] include a greater emphasis on teacher control and discipline, decreased opportunities for
decision-making and responsibilities in class, fewer positive studentteacher relationships, whole-group
task instruction (i.e. all students completing the same tasks in class and for homework assignments
which increases social comparison, competitiveness and evaluation concerns), public forms of evaluation
and normative grading systems, and decreasing cognitive demands (i.e. through work involving copying
from the board or textbooks). These changes are proposed to be damaging to motivational constructs
post-transition, and can therefore potentially affect attainment and socio-emotional adaptation to
secondary education which could have long-lasting implications. Based on these changes, and the poor
fit between adolescentsneeds and those provided by the secondary education environment, it is
plausible that the relationships between school-related predictors and maths attainment will differ
between primary and secondary education.
1.4. The present study
To summarize, the transition to secondary education is regarded as a particularly stressful period for
young adolescents. The transition coincides with biological, psychological, environmental and social
changes and is associated with negative outcomes, especially where adolescents fail to adapt to their
new environment successfully. Various aspects of the school environment are associated with maths
attainment, including the school climate, studentteacher relationships and childrens attitudes
towards maths (often associated with teacher attitudes). These aspects are thought to differ
substantially between primary and secondary education, often reported as a consequence of the
transition event. However, there is an absence of research exploring the effects of the school climate
(childrens affect towards school and teacher characteristics), studentteacher relationships and
attitudes towards maths on maths attainment in primary and secondary education with little known
of the potential long-term effects. Given the alarming state of the maths abilities of children and
adults in the UK currently, identifying predictors of attainment early in development is important to
allow for effective interventions. Therefore, the present study aims to explore the aforementioned
factors as predictors of maths attainment trajectories in primary and secondary education.
This study presents two growth models examining variables in primary and secondary education. The
models use secondary data from the Avon Longitudinal Study of Parents and Children (ALSPAC) to
investigate predictors of the maths attainment trajectories (from age 7 to 16) of UK students. ALSPAC has
been used in previous studies investigating school-related factors including risk factors for school
exclusion [66], the effects of peer victimization [67] and examining school-related protective factors against
negative outcomes for children experiencing maltreatment in early childhood [68]. The current study is
the final part of a three-phase study looking at predictors of maths attainment using the ALSPAC sample.
The previous two phases [69,70], which focused on the home environment, parental, cognitive and
emotional factors, showed that working memory, internalizing symptoms, parentchild relationships,
parental education and school involvement significantly predict maths attainment. The current final phase
focuses on school-related predictors of maths attainment trajectories. The primary education model
investigates the effects of childrens affect towards school, relationships with teachers, attitudes towards
maths and primary education teacher characteristics (affect towards teaching, mental wellbeing and self-
esteem). The secondary education model investigates the effects of school belonging, negative emotion
towards school, relationships with teachers, attitudes towards maths and childrens feelings towards their
secondary education maths teacher. Primary education variables and secondary education variables are
analysed separately as they are not comparable across the transition. It is hypothesized that greater
positive affect towards the school environment, positive studentteacher relationships and favourable
attitudes towards maths and maths teachers will be associated with increased attainment in both primary
and secondary education. It is predicted that teachersself-rated characteristics (affect towards teaching,
mental wellbeing and self-esteem) will predict maths attainment where increased self-esteem and fewer
mental health symptoms will be associated with increased attainment.
2. Method
2.1. Sample
The Avon Longitudinal Study of Parents and Children (ALSPAC) recruited expectant mothers residing in
the South West of England, due to give birth between 1 April 1991 and 31 December 1992 [71,72]. The
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core ALSPAC sample consisted of 14 062 live births, of which 13 988 children were alive at 1 year.
ALSPAC also recruited additional participants post-birth which resulted in a total sample size of
15 589 fetuses, of which 14 901 children were alive at 1 year. The sample is generally representative;
however, there is a slight over-representation of white families with higher SES [71].
Data were collected from the child, the childs mother and her partner, and the childs school teachers,
as well as education-linked data from the National Pupil Database (NPD). The majority of the data were
collected through self-report postal questionnaires, with some of the data collected in Children in Focus
clinics, which a smaller subsample (10%) were invited to attend.
The study website contains details of all the data that are available through a fully searchable data
dictionary and variable search tool (see http://www.bristol.ac.uk/alspac/researchers/our-data/). All
participants provided written informed consent prior to the study. Ethical approval was obtained
from the ALSPAC Ethics and Law Committee and the Local Research Ethics Committees. Informed
consent for the use of data collected via questionnaires and clinics was obtained from participants
following the recommendations of the ALSPAC Ethics and Law Committee at the time.
2.1.1. Sample exclusions
The sample exclusions here are the same as those in the first two phases of the project, presented in Evans
et al. [70] and Evans & Field [69]. Only data for singletons and the first-born twin were retained for
analysis. Children identified as having special educational needs (SEN) at age 7 and/or age 11 were
also excluded from analysis, as were children with English as an additional language (combined
n= 2666). Attrition was particularly high due to the longitudinal design, so participants lacking
sufficient data (i.e. those with at least 50% missing data for the predictor variables) were excluded
from analysis, leading to a final sample size of 6490.
2.2. Outcome
2.2.1. Maths attainment
There are four key stages throughout childrens compulsory education in England, with key stage 1
(age 57) and key stage 2 (age 711) in primary education, and key stage 3 (age 1114) and key stage
4 (age 1416) in secondary education. The maths attainment of primary and secondary education
students is measured through examinations and assessments at the end of each key stage (i.e. at
age 67, 1011, 1314 and 1516).
In key stages 13, childrens progress is evaluated using national curriculum levels which are numerical
grades ranging from 1 to 8, with a higher score indicative of greater maths attainment. Governmental
guidelines suggest that it is expected that children achieve a level 2 at key stage 1, a level 4 at key stage
2 and between levels 5 and 6 at key stage 3. At key stage 4, adolescents can achieve an alphabetical
grade from the highest of A, through A,B,C,D,E,F,Gand the lowest grade of a U.Tobe
comparable with maths attainment at the other key stages, these alphabetical grades were coded into
numerical grades with the highest being grade 10 (i.e. A), down to the lowest grade of 2 (i.e. U).
National curriculum levels for maths were obtained by ALSPAC from local education authorities for
key stage 1 data, and the NPD for key stage 24 data (NPD variables: K2_LEVM, K3_LEVM and
KS4_APMAT), which consisted of a combination of teacher assessments and standardized tasks and
tests. It is important to highlight that this scoring differs from the current grading system in England
where key stage 3 tests are no longer administered, and where key stage 4 assessments are graded on a
19 scale.
In this study, the main outcomes were maths attainment in primary education just prior to the
transition to secondary education (age 11; key stage 2), maths attainment post-transition to secondary
education (age 14; key stage 3) and the growth in maths attainment over time.
2.3. Substantial predictors: primary education
Where measures were not pre-existing, validated questionnaires, measures were constructed from items
in the ALSPAC dataset relating to common constructs. In these cases, a polychor factor analysis and
parallel analyses were used to determine items that could be combined. The polychor [73] and nFactors
[74] packages in R were used for these analyses and the psych [75] package was used to determine
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internal consistency. A table of all the individual items for each of the measures where composites were
created is available in the electronic supplementary material.
2.3.1. Primary school affect
Childrens feelings towards primary school were assessed at age 11. Children were asked to report their
feelings towards school and teachers by stating their agreement with 11 statements on a 4-point scale
(disagree,somewhat disagree,somewhat agree and agree; scored as 03). Example statements included: my
school is a place where my teacher listens to what I say,my school is a place where other pupils are
very friendlyand my school is a place where I feel worried.
A polychoric factor analysis revealed two factors determined by parallel analysis, relating to affect
towards school, and relationships with teachers. Composites were created summing the scores for the
items making up each factor, with possible scores for affect towards school ranging from 0 to 24
(8 items; such as my school is a place where I get on well with the other pupils in my class), and
possible scores for relationships with teachers ranging from 0 to 9 (3 items; such as my school is a
place where my teacher treats me fairly in class). A higher score indicates more positive affect
towards school and teachers for both measures. Reliability was moderately high; Cronbachs
a
was
0.80 and 0.75 for affect towards school and relationships with teachers, respectively.
2.3.2. Attitudes to maths (age 10)
Childrens attitudes towards maths in primary education were measured at age 10. Children were asked
to rate their enjoyment, interest and abilities in maths by responding to 10 items on a 5-point scale (not
true,somewhat untrue,partly true,somewhat true and true; scored as 04). Example items include: I get
good marks in maths,I enjoy doing work in mathsand I am bad at maths. The responses were
coded in a way that a higher score indicated more positive attitudes towards maths. Polychoric factor
analysis and parallel analysis revealed a single factor; therefore, a composite was created summing the
responses to all 10 items with possible scores ranging from 0 to 40. Cronbachs
a
was high at 0.95.
2.3.3. Primary education teacher characteristics
Measures related to teacher characteristics were assessed in the final year of primary education (in year 6;
when children are age 1011). Three variables were included, consisting of the teachers feelings towards
teaching (teacher affect), their mental health and their self-esteem. The teachers affect towards teaching
was measured by asking teachers to state their agreement (on a 5-point scale from strongly disagree to
strongly agree; scored as 04) with six statements broadly covering their enjoyment of teaching, their
confidence in and enjoyment of teaching numeracy, and how much they find teaching worthwhile.
Polychoric factor analysis and parallel analysis revealed one factor for teacher affect, meaning a
composite could be made. The score for teachers affect was made from summing the scores for the
six items, with a higher score referring to more positive affect towards teaching (ranging from 0
to 24). Cronbachs
a
was adequate at 0.71.
Teacher mental health and self-esteem were measured using the Crown-Crisp Experiential Index
(CCEI) and the Bachman Self Esteem score. The CCEI [76] used by ALSPAC contains 23 items relating
to somatic, depressive and anxious symptoms. Possible scores range between 0 and 46, with a higher
score corresponding to more symptoms. The Bachman Self Esteem score [77] consists of 10 questions
with a possible score between 0 and 40. A higher score relates to higher self-esteem. Cronbachs
a
for
the aforementioned CCEI subscales ranges from 0.66 to 0.79 [78], and
a
for the Bachman Self Esteem
score is 0.75 [77].
2.4. Substantial predictors: secondary education
2.4.1. Secondary school affect
Feelings towards secondary school were measured at age 14. Adolescents were given the same 11
statements as the primary school affect measure above, and were asked to rate their agreement with
the statements on a 4-point scale (strongly disagree,disagree,agree and strongly agree; scored as 03).
Example statements included: my school is a place where I get on well with other pupils in my
classes,my school is a place where I feel proud to be a pupiland my school is a place where I feel
lonely. A polychoric factor analysis was conducted on the 11 items and parallel analysis revealed
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7
three factors relating to school belonging, negative emotion towards school and relationships with
teachers. Composites were created summing the scores for the items making up each of the three
factors. Possible scores for school belonging (6 items) ranged from 0 to 18, for negative emotion
(3 items) scores ranged between 0 and 9 and for relationships with teachers (2 items) scores ranged
from 0 to 6. A higher score indicates greater school belonging, less negative emotion towards school and
more positive relationships with teachers. School belonging had high reliability (Cronbachs
a
= 0.83),
relationships with teachers had moderately high reliability (Cronbachs
a
= 0.72), and negative emotion
towards school had adequate reliability (Cronbachs
a
=0.64).
2.4.2. Attitudes to maths (age 14)
Maths attitudes in secondary education were assessed at age 14. Adolescents were asked to indicate how
much they enjoyed doing maths, how much they find what they learn in maths useful and the level of
importance they place on being good at maths. Maths enjoyment and usefulness were measured on
5-point scales (i.e. doesnt like it at all to likes it very much and not very useful to very useful; scored as
04). The level of importance adolescents placed on being good at maths was measured on a 4-point
scale from not at all important to very important (scored as 03), which was recoded to be on a 5-point
scale without a neutral option. A polychoric factor analysis was conducted on the three items and
revealed one factor (using parallel analysis); therefore, a composite was made. The scores for each of
the items were summed together with possible scores ranging from 0 to 12, with a higher score
indicating positive attitudes towards maths. Reliability was moderately high; Cronbachs
a
= 0.68.
2.4.3. Feelings towards maths teacher
At age 14, adolescents were given 18 statements regarding their feelings and perceptions of their maths
teacher, and were asked to rate their feelings on a 5-point scale (from strongly disagree to strongly agree;
scored as 04). Using polychoric factor analysis and parallel analysis, two factors were found from the
18 items relating to positive teaching (12 items), and teacher fairness towards pupils (5 items). The
scores for the individual items were summed to create two factors, for positive teaching scores could
range from 0 to 48 and for teacher fairness possible scores could range from 0 to 20. Positive teaching
included statements of teacher competence and measures of positive teaching practices such as my
maths teacher understands maths really well,everyone is encouraged to do their very bestand my
maths teacher gives us time to really explore and understand new things. For teacher fairness,
example items included: my maths teacher only cares about the clever students,my maths teacher
treats boys and girls differentlyand my maths teacher treats some students better than other
students. A higher score on both measures indicates more positive teaching practices and greater
perceived teacher fairness towards pupils. High reliability was found for both measures, Cronbachs
a
= 0.90 and 0.85 for positive teaching practices and teacher fairness, respectively.
2.5. Contextual predictors
2.5.1. Biological sex
Biological sex was recorded at birth, and included as a predictor due to potential differences in maths
attainment between males and females. Females accounted for 55.3% of the sample. In both models,
females were used as the reference group.
2.5.2. Socioeconomic status
During the mothers pregnancy (at 32 weeks gestation), SES of both parents (where available) was
assessed using the Cambridge Social Interaction and Stratification Scale (CAMSIS). The CAMSIS
measures occupational structure based upon social interactions [79]. Scores can range between 1 (least
advantaged) and 99 (most advantaged) with a mean of 50 and a standard deviation of 15 in the
population [80]. The highest score of either parent (where both were available) was used in analysis.
2.5.3. Parental education
Parental education qualifications have been shown to predict maths attainment trajectories in previous
studies [69]. The childs parents were asked about their highest educational qualifications during
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8
pregnancy (at 32 weeks gestation), which were coded into the following five categories: no
qualifications/no higher than CSE or GCSE, vocational qualifications (i.e. teaching or nursing
qualifications), O level or equivalent, A level or equivalent, and university degree. The highest
qualification held by either parent (if both were available) was used in analysis; 7.3% had a CSE or
below, 4.9% had a vocational qualification, 25.1% had an O level, 35.1% had an A level and 27.5%
had a degree. Having a CSE or below was used as the reference group in both models.
2.5.4. Parentchild relationships
Parentchild relationships were included based on previous findings [69] and were evaluated using
the Assessment of MotherChild-Interaction with the Etch-a-Sketch (AMCIES) [81] (Wolke, Rios &
Unzer, 1995, unpublished manuscript) task during the clinic in focussessions at age 12.5.
The AMCIES involves observing parent and child dyads while they play with an Etch-a-Sketch toy.
Specifically, the dyads were asked to draw a house using the Etch-a-Sketch, with either the parent or
child responsible for drawing horizontal lines, and the other responsible for drawing vertical lines.
To complete the task successfully, parents and their children are required to work very closely
together and assist one another. Following the task, the dyads were rated by the ALSPAC team on
their harmony, i.e. whether the relationship between them and the observed interactions were
particularly negative or positive. The following 5-point scale was used to code the interactions: many
conflicts (scored as 0), some conflicts (generally negative with some conflict),neutral (atmosphere is
neither positive or negative),quite agreeable (generally positive) and very agreeable (very positive and
harmonious) (scored as 4). A higher score refers to greater harmony (and a more positive relationship)
between the parent and child. The AMCIES has shown good reliability in other samples (Cronbachs
a
= 0.760.80; [82]).
2.5.5. Parental school involvement
Parental involvement in school activities was rated by the childs teacher at age 11. The activities
included: helping in class,helping with out of class activities,attending parent-teacher sessions
and being involved in another school activity. The childs teacher was asked to indicate whether the
childs parents had been involved in any of these four activities by responding with yes or no to each
activity, which were coded as 1 and 0, respectively. The responses for the four items were summed to
create a score between 0 and 4, with a higher score indicating more parental involvement in school
activities. Parental involvement in school has been found to predict maths attainment trajectories
previously [69].
2.5.6. Working memory and IQ
Working memory (at age 10) and IQ (at age 8) were assessed during Clinic in Focussessions. Childrens
total IQ score was measured using the performance (short-form tests: picture completion, picture
arrangement, block design and object assembly, full-form test: coding) and verbal (short-form tests:
information, similarities, arithmetic, vocabulary and comprehension) subscales of the Wechsler
Intelligence Scale for Children (WISC-III; [83]). The scores for each of the short-form tests were
transformed to be on the same scale as though the entire test had been administered to reduce
fatigue. The WISC-III holds good testretest reliability (0.800.89; [84]).
Childrens working memory capacity was measured using the Counting Span Task [85] administered
on a computer. In this task, children are presented with screens of red and blue dots and are asked to
count them out loud. After counting them correctly, children are asked to recall the number of red
dots on the screens, in the same order they are presented. All screens are displayed, regardless of the
childs performance. Children were shown two practice screens followed by three sets of two screens,
three sets of three screens, three sets of four screens and three sets of five screens, totalling to 42 trials.
The global score was used representing the number of trials children answered correctly (i.e. 042).
Both working memory and IQ are known predictors of maths attainment [70].
2.5.7. Internalizing symptoms
Childrens internalizing symptoms at age 11 were measured using the Strengths and Difficulties
Questionnaire (SDQ; [86]), and were included in this study based on previous findings [70]. The SDQ
contains 25 items assessing emotional symptoms, peer problems, conduct problems, prosocial
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9
behaviour and hyperactivity. Parents rated their childs behaviour on each of the five subscales, with
possible responses of not true,somewhat true and certainly true, which were coded as 0, 1 and 2,
respectively, meaning that scores could range between 0 and 10 for each subscale. An internalizing
symptomsscore was created by summing the childs scores for the emotional symptoms and peer
problems subscales, with possible scores ranging from 0 to 20. A higher score is indicative of greater
internalizing symptoms and problems. Example items of the internalizing symptoms scale include
child often seems worriedand child is rather solitary, tends to play alone. The SDQ overall has
good concurrent and predictive validity [86], and satisfactory internal consistency (Cronbachs
a
for
emotional difficulties = 0.66, and for peer problems
a
= 0.53; [87].
2.6. Data analysis
2.6.1. Exclusions and missing data
This study follows the same exclusion criteria as in Evans et al. [70] and Evans & Field [69]. The
initial cohort was formed of 13 988 children alive at 1 year. Additional recruitment resulted in 14 901
children alive at 1 year (including singletons and twins; triplets and quadruplets were excluded due
to rarity). Withdrawal from the study led to a sample size of 14 684. Data from singletons and
the first-born twin were retained for analysis (N= 14 498). Fourteen children were excluded as
their first, or second main language was not English (N= 14 484). Two thousand six hundred and
fifty-two children reported to have SEN (identified by teachers at ages 78 and 1011) were excluded
(N= 11 832). Where 50% or more of the data for the predictor variables were missing, 5342
participants were excluded, leaving a final sample size of 6490 (none of which were complete cases).
To address the issue of high attrition rates and missing data in the ALSPAC dataset (for missing data
per variable, see table 1), multiple imputation was performed in R [88] using the semTools [89] and Amelia
packages [90]. Eighty imputations were performed and the results were pooled [91]. The outcome
variables (maths attainment KS1KS4) were included in the imputation model but were not imputed.
Instead, to address the missing outcome data, full information maximum likelihood (FIML) estimation
was used [92].
2.6.2. Statistical analysis strategy
All analyses were conducted in R v. 3.4.3 [88]. Two latent growth models predicting maths attainment
trajectories in primary and secondary education were fit using the lavaan package [93], which are
described in more detail below.
2.6.3. Primary education model
The primary education model evaluates the possible effects of variables measured in primary education,
and whether these predict maths attainment trajectories across the transition from primary to secondary
education. The variables entered into the primary education model were as follows: school affect,
studentteacher relationships, maths attitudes (age 10), teacher affect, teacher CCEI, teacher self-esteem,
parental school support, childs sex, internalizing symptoms, IQ, working memory, SES, parental
education and parentchild relationships. These predictors were included as exogenous observed
variables that predict the intercept and slope of growth in maths attainment.
Maths attainment at 7, 11, 14 and 16 years were endogenous observed variables predicted from
latent variables representing the intercept and slope for growth in maths attainment over time.
The loadings for the paths from the slope latent variable to the four maths attainment outcomes
were constrained to be 4 (maths at age 7), 0 (maths at age 11), 3 (maths at age 14) and 5 (maths at
age 16) so that the intercept represented maths attainment just prior to the school transition at age 11
(figure 1).
2.6.4. Secondary education model
The secondary education model focuses on the variables measured in secondary education, and whether
these predict maths attainment trajectories following the transition from primary to secondary education.
The variables entered into the secondary education model were as follows: school belonging, student
teacher relationships, negative emotions towards school, maths attitudes (age 14), positive maths
teaching practices, maths teacher fairness, childs sex, internalizing symptoms, IQ, working memory,
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10
SES, parental education and parentchild relationships. As with the primary education model, these
predictors were included as exogenous observed variables that predict the intercept and slope of
growth in maths attainment.
The same measures of maths attainment at 7, 11, 14 and 16 years were used as endogenous observed
variables predicted from latent variables representing the intercept and slope for growth in maths
attainment. The loadings for the paths from the slope latent variable to the four maths attainment
outcomes were constrained to be 7 (maths at age 7), 3 (maths at age 11), 0 (maths at age 14) and 2
(maths at age 16) so that the intercept represented maths attainment following the transition to
secondary education at age 14 (figure 2).
For both models, all predictors were entered simultaneously. Correlation coefficients for the variables
are displayed in table 2 (primary education variables) and table 3 (secondary education variables). SES,
IQ and working memory were all centred prior to analysis as there was no meaningful zero in these
measures. For the primary education model, scores for school affect, teacher affect, studentteacher
relationships and teacher self-esteem were centred. For the secondary education model, scores for
school belonging, studentteacher relationships, negative emotions towards school, positive maths
teaching practices and maths teacher fairness were centred.
Two previous studies [69,70] found working memory, internalizing symptoms, parental school
support, parental education and a positive parentchild relationship significantly predicted maths
attainment trajectories in this sample. Due to these findings, these predictors were also included in the
present analysis to adjust for their effects.
Table 1. Summary statistics for the key study measures. P, measured in primary education; S, measured in secondary education;
WM, working memory; SDQ, internalizing symptoms; ST, studentteacher; KS, key stage; MD, missing data.
measure nmin max mdn M95% CI s%MD
school affect (P) 5412 0.00 24.00 21.00 20.18 ½20:09, 20:2711.38 17%
ST relationships (P) 5716 0.00 9.00 8.00 7.52 ½7:48, 7:562.82 12%
maths attitudes (P) 5390 0.00 40.00 32.00 29.35 ½29:08, 29:63105.76 17%
teacher affect (P) 3631 5.00 24.00 20.00 19.43 ½19:32, 19:5512.91 44%
teacher CCEI (P) 3698 0.00 38.00 11.00 12.97 ½12:72, 13:2260.54 43%
teacher
self-esteem (P)
3679 17.00 40.00 33.00 32.27 ½32:10, 32:4528.82 43%
school belonging (S) 3069 0.00 18.00 12.00 12.45 ½12:35, 12:557.90 53%
ST relationships (S) 4816 0.00 6.00 4.00 4.07 ½4:04, 4:101.29 26%
negative emotion (S) 3970 0.00 9.00 7.00 6.81 ½6:76, 6:862.36 39%
maths attitudes (S) 5404 0.00 12.00 8.00 8.25 ½8:19, 8:314.97 17%
positive teaching (S) 5317 0.00 48.00 34.00 32.76 ½32:55, 32:9863.72 18%
teacher fairness (S) 5218 0.00 20.00 13.00 12.96 ½12:84, 13:0819.52 20%
SES 5135 26.31 95.70 58.40 59.65 ½59:33, 59:97137.24 21%
IQ 5185 49.00 151.00 107.00 107.19 ½106:77, 107:60237.15 20%
WM 5115 0.00 42.00 19.00 19.32 ½19:11, 19:5357.39 21%
SDQ 5489 0.00 20.00 2.00 2.37 ½2:30, 2:446.46 15%
parentchild
harmony
5091 0.00 4.00 3.00 3.24 ½3:22, 3:260.63 22%
school support 3770 0.00 4.00 1.00 1.78 ½1:74, 1:811.15 42%
KS1 maths 4961 0.00 3.00 2.00 2.32 ½2:31, 2:340.28 24%
KS2 maths 5476 1.00 6.00 4.00 4.37 ½4:35, 4:390.44 16%
KS3 maths 4713 1.00 8.00 6.00 6.35 ½6:31, 6:381.24 27%
KS4 maths 5137 2.00 10.00 8.00 7.50 ½7:45, 7:542.29 21%
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3. Results
3.1. Descriptive statistics
Summary statistics for the variables in the primary and secondary education models are in table 1. Maths
grades were generally in line with national guidelines and expectations for all key stages. Children are
expected to progress by half a grade each year in schools following the national curriculum in the
UK. For both the primary education model (0.49 grades per year on average) and the secondary
education model (0.46 grades per year on average), childrens average growth in attainment per year
was consistent with the wider population.
Both models provided satisfactory fit indices (primary education model: CFI = 0.936, TLI = 0.876,
RMSEA = 0.104 [90% CI = 0.100, 0.107], SRMR = 0.05; secondary education model: CFI = 0.936, TLI =
0.876, RMSEA = 0.104 [90% CI = 0.101, 0.107], SRMR = 0.05).
1
school
affect
S–T
relation-
ships
maths
attitudes
teacher
affect
teacher
CCEI
teacher
self-
esteem
sex parental
ed SES
IQ
WM
SDQ
P–C
harmony
school
support
slope
intercept
1111
–4
maths KS1
(6–7 years)
maths KS2
(10–11 years)
maths KS3
(13–14 years)
maths KS4
(15–16 years)
035
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
11
1
Figure 1. Latent growth model for maths attainment trajectories in primary education. The intercept represents maths attainment at
age 11, and the slope represents maths attainment from age 7 to 16. Paths between predictor variables are implied but not
illustrated. WM, working memory; SDQ, internalizing symptoms; ST, studentteacher; ed, education; PC, parentchild.
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3.2. Primary education model
3.2.1. Predictors of maths attainment at age 11 (intercept)
Table 4 shows the model parameters for the intercept of the primary education model. Of the substantive
predictors, the only variable that significantly predicted maths attainment at the intercept was attitudes
towards maths at age 10 ( p< 0.001). School affect, studentteacher relationships, teacher-rated affect,
teacher CCEI and teacher self-esteem did not significantly predict maths attainment (table 4). Of the
contextual predictors, as expected, sex, parental education, SES, IQ, WM, internalizing symptoms
(SDQ) and parental school support all significantly predicted maths attainment at age 11.
Maths attitudes in primary education could range between 0 and 40 with a higher score indicating more
positive attitudes towards maths. The effect size of maths attitudes on maths attainment in primary education
was 0.012, meaning that an increase on the maths attitudes scale by 1 point equates to an increase in maths
1
school
belong-
ing
S–T
relation-
ships
negative
school
emotion
maths
attitudes
positive
teaching
teacher
fairness
sex parental
ed SES
IQ
WM
SDQ
P–C
harmony
school
support
slope
intercept
1111
–3
maths KS1
(6–7 years)
maths KS2
(10–11 years)
maths KS3
(13–14 years)
maths KS4
(15–16 years)
02
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
11
1
–7
Figure 2. Latent growth model for maths attainment trajectories in secondary education. The intercept represents maths attainment
at age 14, and the slope represents maths attainment from age 7 to 16. Paths between predictor variables are implied but not
illustrated. WM, working memory; SDQ, internalizing symptoms; ST, studentteacher; ed, education; PC, parentchild.
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Table 2. Correlation matrix of the primary education measures and the contextual variables. The upper triangle displays the correlation coefcients and the lower triangle displays the p-values. ST, studentteacher;
SES, socioeconomic status; WM, working memory; SDQ, internalizing symptoms; PC, parentchild; KS, key stage.
variable Ms.d. 12345 678910111213141516
1. school affect 20.18 3.37 0.48 0.16 0.04 0.00 0.00 0.01 0.02 0.04 0.28 0.02 0.05 0.05 0.07 0.04 0.05
2. ST relationships 7.52 1.68 0.00 0.11 0.02 0.01 0.02 0.01 0.02 0.02 0.12 0.03 0.06 0.00 0.01 0.01 0.02
3. maths attitudes 29.35 10.28 0.00 0.00 0.03 0.03 0.02 0.01 0.14 0.15 0.10 0.01 0.05 0.22 0.29 0.27 0.22
4. teacher affect 19.43 3.59 0.05 0.39 0.14 0.43 0.34 0.03 0.02 0.03 0.01 0.01 0.07 0.01 0.02 0.01 0.00
5. teacher CCEI 12.97 7.78 0.90 0.55 0.10 0.00 0.49 0.06 0.03 0.04 0.01 0.01 0.02 0.03 0.05 0.02 0.02
6. teacher self-esteem 32.27 5.37 0.83 0.22 0.36 0.00 0.00 0.04 0.00 0.02 0.00 0.01 0.04 0.01 0.01 0.00 0.00
7. SES 59.65 11.72 0.37 0.36 0.37 0.12 0.00 0.04 0.28 0.16 0.05 0.02 0.15 0.17 0.25 0.30 0.32
8. IQ 107.19 15.40 0.19 0.32 0.00 0.39 0.10 0.95 0.00 0.34 0.09 0.07 0.14 0.47 0.57 0.64 0.58
9. WM 19.32 7.58 0.01 0.20 0.00 0.16 0.05 0.35 0.00 0.00 0.06 0.02 0.08 0.26 0.34 0.36 0.32
10. SDQ 2.37 2.54 0.00 0.00 0.00 0.45 0.46 0.83 0.00 0.00 0.00 0.01 0.04 0.09 0.13 0.12 0.11
11. PC harmony 3.24 0.79 0.30 0.02 0.49 0.72 0.50 0.48 0.11 0.00 0.13 0.66 0.01 0.09 0.05 0.11 0.09
12. school support 1.78 1.07 0.00 0.00 0.01 0.00 0.29 0.02 0.00 0.00 0.00 0.01 0.58 0.11 0.14 0.18 0.20
13. KS1 maths 2.32 0.53 0.00 0.78 0.00 0.59 0.06 0.76 0.00 0.00 0.00 0.00 0.00 0.00 0.54 0.56 0.50
14. KS2 maths 4.37 0.67 0.00 0.44 0.00 0.24 0.00 0.67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.76 0.69
15. KS3 maths 6.35 1.11 0.01 0.68 0.00 0.76 0.31 0.79 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.85
16. KS4 maths 7.50 1.51 0.00 0.28 0.00 0.86 0.24 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
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Table 3. Correlation matrix of the secondary education measures and the contextual variables. The upper triangle displays the correlation coefcients and the lower triangle displays the p-values. ST, studentteacher;
SES, socioeconomic status; WM, working memory; SDQ, internalizing symptoms; PC, parentchild; KS, key stage.
variable Ms.d. 1234567 8 910 11 12 13 14 15 16
1. school belonging 12.45 2.81 0.39 0.52 0.18 0.22 0.18 0.02 0.04 0.04 0.17 0.00 0.00 0.00 0.00 0.06 0.03
2. ST relationships 4.07 1.14 0.00 0.34 0.19 0.26 0.31 0.07 0.10 0.07 0.06 0.04 0.08 0.09 0.11 0.17 0.21
3. school emotion 6.81 1.53 0.00 0.00 0.10 0.13 0.16 0.07 0.10 0.00 0.21 0.00 0.01 0.01 0.00 0.01 0.01
4. maths attitudes 8.25 2.23 0.00 0.00 0.00 0.45 0.30 0.00 0.06 0.06 0.04 0.02 0.02 0.11 0.15 0.21 0.20
5. positive teaching 32.76 7.98 0.00 0.00 0.00 0.00 0.62 0.00 0.04 0.01 0.04 0.02 0.00 0.06 0.07 0.12 0.11
6. teacher fairness 12.96 4.42 0.00 0.00 0.00 0.00 0.00 0.06 0.09 0.02 0.05 0.03 0.02 0.07 0.09 0.15 0.17
7. SES 59.65 11.72 0.34 0.00 0.00 0.75 0.73 0.00 0.28 0.16 0.05 0.02 0.15 0.17 0.25 0.30 0.32
8. IQ 107.19 15.40 0.08 0.00 0.00 0.00 0.02 0.00 0.00 0.34 0.09 0.07 0.14 0.47 0.57 0.64 0.58
9. WM 19.32 7.58 0.07 0.00 0.82 0.00 0.43 0.24 0.00 0.00 0.06 0.02 0.08 0.26 0.34 0.36 0.32
10. SDQ 2.37 2.54 0.00 0.00 0.00 0.01 0.01 0.00 0.00 0.00 0.00 0.01 0.04 0.09 0.13 0.12 0.11
11. PC harmony 3.24 0.79 1.00 0.01 0.77 0.32 0.30 0.05 0.11 0.00 0.13 0.66 0.01 0.09 0.05 0.11 0.09
12. school support 1.78 1.07 0.84 0.00 0.53 0.23 0.89 0.23 0.00 0.00 0.00 0.01 0.58 0.11 0.14 0.18 0.20
13. KS1 maths 2.32 0.53 0.88 0.00 0.63 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.54 0.56 0.50
14. KS2 maths 4.37 0.67 0.88 0.00 0.84 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.76 0.69
15. KS3 maths 6.35 1.11 0.01 0.00 0.76 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.85
16. KS4 maths 7.50 1.51 0.16 0.00 0.48 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
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attainment at age 11 by 0.012 levels. When looking at this effect in context, this means that the difference
between children with the most positive attitudes to maths (i.e. those scoring 40), compared with those
with the lowest score (i.e. those scoring 0), the difference in attainment in primary education would be
the equivalent to almost a yearsprogressinmaths(400.012 = 0.48).
When looking at the contextual predictors, the results generally replicated previous findings; males
were found to have slightly higher maths attainment, children to parents with a degree or A level had
higher maths attainment compared with children to parents with a CSE or below, parents to children
with vocational qualifications had lower attainment. Increased internalizing symptoms predicted
lower attainment, and higher SES, IQ, working memory, parental school involvement and increased
parentchild harmony all predicted higher maths attainment at age 11 (table 4). For a detailed
discussion of these findings, see Evans et al. [70] and Evans & Field [69].
3.2.2. Primary education predictors of the rate of change
Table 5 shows the model parameters for the slope of the primary education model (i.e. the rate of change
(ROC) over time). Of the substantive predictors, school affect, studentteacher relationships, teacher-
rated affect, teacher CCEI and teacher self-esteem did not significantly predict maths attainment
growth. Maths attitudes significantly predicted the slope of maths attainment, with more positive
attitudes linked to an increased ROC over time (b= 0.001, p< 0.001). However, this effect is extremely
smallwhen comparing children with the most positive attitudes with children with the most
negative, the associated difference in attainment per year is around 0.04 for the maths-positive students.
Of the contextual predictors, the significant predictors of an increased slope for maths attainment
were parental education (for those with a degree or A level), and higher SES, IQ, working memory,
parental school involvement and increased parentchild harmony. Increased internalising symptoms
were associated with a decreased ROC (see [70]).
Overall, the results for the primary education model suggest that the most important substantive
predictor of maths attainment at age 11, and of the ROC over time is attitudes towards maths, with
general school affect and teacher characteristics lacking a substantial effect on maths attainment in
primary education.
Table 4. Model parameters for predictors of the intercept of maths attainment in primary education (age 11).
b
is the
standardized parameter estimate.
predictor b95% CI
b
p-value
school affect 0.001 ½0:004, 0:0070.007 0.643
ST relationships 0.001 ½0:012, 0:0100.003 0.810
maths attitudes 0.012 ½0:010, 0:0130.173 0.000
teacher affect 0.003 ½0:008, 0:0020.017 0.223
teacher CCEI 0.002 ½0:004, 0:0010.018 0.230
teacher self-esteem 0.001 ½0:005, 0:0020.009 0.535
sex 0.049 ½0:015, 0:0820.036 0.004
Edu: CSE versus vocational 0.092 ½0:174, 0:0100.030 0.028
Edu: CSE versus O level 0.052 ½0:006, 0:1100.033 0.078
Edu: CSE versus A level 0.132 ½0:075, 0:1890.092 0.000
Edu: CSE versus degree 0.271 ½0:206, 0:3360.178 0.000
SES 0.004 ½0:003, 0:0060.076 0.000
IQ 0.020 ½0:019, 0:0210.450 0.000
WM 0.012 ½0:010, 0:0140.133 0.000
SDQ 0.013 ½0:020, 0:0060.049 0.000
parentchild harmony 0.038 ½0:017, 0:0590.044 0.000
school support 0.025 ½0:009, 0:0410.039 0.002
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3.3. Secondary education model
3.3.1. Predictors of maths attainment at age 14 (intercept)
The parameters for the secondary education model are reported in table 6. The statistically significant
substantive predictors of maths attainment at age 14 were school belonging (p= 0.001), student
teacher relationships ( p< 0.001), attitudes towards maths at age 14 ( p< 0.001) and maths teacher
fairness ( p= 0.002). Negative emotion towards school, and positive teaching in maths did not
significantly predict maths attainment in secondary education ( ps = 0.404 and 0.118, respectively).
Unexpectedly, school belonging was negatively associated with attainment, meaning that students
reporting greater school belonging in secondary education had lower maths attainment at age 14
(b=0.018); however, this effect was relatively small. Studentteacher relationships had a stronger
effect on maths attainment (b= 0.059), whereby students rating their relationship with their teachers as
more positive had higher maths attainment. When comparing the lowest scores with the highest, this
difference would equate to approximately one-third of a grade increase for the students rating their
studentteacher relationships as highly as possible on the scale, which is generally a small effect.
Attitudes towards maths were associated with maths attainment in secondary education, where more
positive attitudes equated to increased maths attainment. Maths attitudes could range from 0 to 12,
meaning that a 1-unit increase for maths attitudes on this scale equated to an increase in attainment
by 0.064 national curriculum levels. When comparing the lowest-rated maths attitudes (i.e. the most
negative) with the highest-rated maths attitudes (i.e. the most positive), the difference in attainment
would be around 0.77 levels. Maths teacher fairness also significantly predicted maths attainment,
with greater perceived fairness and equality equating to a 0.011 unit increase in attainment. However,
this effect was extremely small.
When looking at the contextual predictors, all variables predicted maths attainment in regard to
statistical significance (all ps < 0.05), with the only exception of parental education when looking at
differences between children to parents with an O level compared with those with a CSE and below
(p= 0.101). Being male, having higher SES, IQ and working memory were linked to higher
attainment, greater internalizing symptoms predicted decreased attainment, and both increased
parentchild harmony, and parental school support equated to increased attainment (see [69] for
further discussion).
Table 5. Model parameters for predictors of the slope of maths attainment in primary education.
b
is the standardized
parameter estimate.
predictor b95% CI
b
p-value
school affect 0.000 ½0:001, 0:0010.005 0.783
ST relationships 0.001 ½0:002, 0:0030.012 0.509
maths attitudes 0.001 ½0:001, 0:0020.118 0.000
teacher affect 0.001 ½0:002, 0:0000.025 0.151
teacher CCEI 0.000 ½0:001, 0:0000.012 0.514
teacher self-esteem 0.000 ½0:001, 0:0010.005 0.765
sex 0.005 ½0:002, 0:0120.021 0.197
Edu: CSE versus vocational 0.014 ½0:032, 0:0030.029 0.098
Edu: CSE versus O level 0.008 ½0:005, 0:0200.029 0.221
Edu: CSE versus A level 0.033 ½0:021, 0:0450.140 0.000
Edu: CSE versus degree 0.069 ½0:055, 0:0830.273 0.000
SES 0.001 ½0:001, 0:0010.096 0.000
IQ 0.003 ½0:002, 0:0030.364 0.000
WM 0.002 ½0:001, 0:0020.109 0.000
SDQ 0.002 ½0:003, 0:0000.041 0.012
parentchild harmony 0.006 ½0:001, 0:0100.039 0.014
school support 0.005 ½0:002, 0:0090.051 0.002
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17
3.3.2. Secondary education predictors of the rate of change
Table 7 shows the model parameters for the secondary education ROC in maths attainment. Of the
substantive predictors, school belonging, studentteacher relationships, maths attitudes and maths
teacher fairness, all significantly predicted the slope of maths attainment (all ps < 0.001). Negative
emotion towards school, and positive teaching in maths did not significantly predict growth in maths
attainment (table 7).
Consistent with the intercept, greater school belonging predicted a slower ROC in maths attainment,
whereby a 1 unit increase in school belonging equated to a decrease in the ROC by 0.003. However, this
effect is extremely small, given that the average change in attainment was 0.46 grade levels per year.
Similarly, the effects of studentteacher relationships and maths teacher fairness were also particularly
small, with more positive studentteacher relationships and increased teacher fairness associated with
an increased ROC by 0.009 and 0.002, respectively. More positive maths attitudes were linked to an
increased ROC (b= 0.008), suggesting that adolescents with a more positive attitude towards maths at
age 14 progressed at a quicker rate, though ultimately, this is a small effect.
Of the contextual predictors, there were no significant differences in the ROC between male and
female students. Children to parents with a degree or A level had an increased ROC. Higher SES, IQ
and working memory equated to an increased ROC. Increased internalizing symptoms equated to a
slower ROC, and greater parentchild harmony and parental school involvement predicted a faster
ROC (see [69]).
Generally, the results for the secondary education model suggest that there are aspects of
the secondary school environment that are important for maths attainment trajectories within
secondary education, and that there are also child-specific factors, specifically their attitudes towards
maths, that have strong associations with maths attainment; however, broadly the effects on
attainment were quite small.
4. Discussion
The aim of this study was to explore predictors of maths attainment trajectories in primary and
secondary education by focusing specifically on the school climate and childrens affect towards
Table 6. Model parameters for predictors of the intercept of maths attainment in secondary education (age 14).
b
is the
standardized parameter estimate.
predictor b95% CI
b
p-value
school belonging 0.018 ½0:028, 0:0070.047 0.001
ST relationships 0.059 ½0:034, 0:0840.066 0.000
negative school emotion 0.008 ½0:011, 0:0270.012 0.404
maths attitudes 0.064 ½0:052, 0:0760.139 0.000
positive teaching 0.003 ½0:007, 0:0010.026 0.118
teacher fairness 0.011 ½0:004, 0:0180.048 0.002
sex 0.078 ½0:029, 0:1280.038 0.002
Edu: CSE versus vocational 0.122 ½0:242, 0:0020.027 0.047
Edu: CSE versus O level 0.071 ½0:014, 0:1560.030 0.101
Edu: CSE versus A level 0.224 ½0:140, 0:3080.105 0.000
Edu: CSE versus degree 0.458 ½0:362, 0:5540.201 0.000
SES 0.007 ½0:004, 0:0090.076 0.000
IQ 0.028 ½0:026, 0:0300.422 0.000
WM 0.019 ½0:015, 0:0220.138 0.000
SDQ 0.022 ½0:032, 0:0120.055 0.000
parentchild harmony 0.049 ½0:019, 0:0800.038 0.002
school support 0.040 ½0:017, 0:0630.042 0.001
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18
school, studentteacher relationships, teacher characteristics, attitudes towards maths and perceptions of
the maths teacher.
4.1. Summary of main results
The primary education model investigated the associations between maths attainment trajectories of
adolescents and their affect towards school, perceived studentteacher relationships, attitudes towards
maths and characteristics of their teacher (affect towards teaching, mental wellbeing and self-esteem)
in primary education, while adjusting for known predictors and demographic variables. The only
statistically significant predictor of maths attainment was childrens attitudes towards maths, where
more positive attitudes towards maths predicted increased attainment at age 11, and an increased
ROC over time. The magnitude of the effect of maths attitudes for attainment at age 11 was moderate;
a 10 unit increase on the maths attitudes scale equated to an increase in attainment by 0.12 national
curriculum levels. When comparing children with the lowest score for maths attitudes (0), with the
highest (40), this difference would be close to a years worth of progress (i.e. almost half a grade
level). The size of the effect on yearly progress was small; a 10 unit increase on the maths attitude
scale equates to an increased ROC of 0.01 grade levels per year. Affect towards school, student
teacher relationships and teacher characteristics were not found to significantly predict maths
attainment at age 11, nor the ROC.
The secondary education model examined school belonging, negative emotion towards school,
relationships with teachers, attitudes towards maths and perceptions of the maths teacher (positive
teaching practices and fairness) in secondary education as predictors of maths attainment after
adjusting for known predictors and demographic variables. School belonging, studentteacher
relationships, maths attitudes and maths teacher fairness were significantly associated with maths
attainment at age 14, and the ROC. Unsurprisingly, studentteacher relationships rated as more
positive and greater maths teacher fairness were associated with increased attainment trajectories,
though the effects were relatively small. Maths attitudes were positively associated with maths
attainment at age 14 and an increased ROC over time with a considerable effect size. School belonging
was negatively associated with maths attainment, meaning that increased school belonging was linked
Table 7. Model parameters for predictors of the slope of maths attainment in secondary education.
b
is the standardized
parameter estimate.
predictor b95% CI
b
p-value
school belonging 0.003 ½0:004, 0:0010.061 0.001
ST relationships 0.009 ½0:006, 0:0130.093 0.000
negative school emotion 0.001 ½0:002, 0:0030.010 0.600
maths attitudes 0.008 ½0:006, 0:0090.148 0.000
positive teaching 0.000 ½0:001, 0:0000.030 0.150
teacher fairness 0.002 ½0:001, 0:0030.068 0.001
sex 0.005 ½0:002, 0:0120.022 0.162
Edu: CSE versus vocational 0.013 ½0:030, 0:0030.027 0.116
Edu: CSE versus O level 0.007 ½0:004, 0:0190.029 0.220
Edu: CSE versus A level 0.033 ½0:021, 0:0440.138 0.000
Edu: CSE versus degree 0.067 ½0:053, 0:0800.264 0.000
SES 0.001 ½0:001, 0:0010.090 0.000
IQ 0.003 ½0:002, 0:0030.357 0.000
WM 0.002 ½0:001, 0:0020.118 0.000
SDQ 0.002 ½0:003, 0:0010.046 0.003
parentchild harmony 0.005 ½0:001, 0:0090.035 0.023
school support 0.005 ½0:002, 0:0080.047 0.003
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19
to decreased maths attainment at age 14, and a slower ROC over time. Positive teaching practices in
maths and negative emotion towards school were not significantly associated with maths attainment.
Based on the wider literature, it was expected that positive attitudes towards maths would be
associated with increased attainment in both school environments, which was supported by the
results with moderately large effect sizes present in both models. The findings suggest that children
who enjoy maths and perceive it to be useful, interesting and important achieve higher grades than
their peers who feel more negatively about maths. However, it is important to note that this result
does not imply causality. It could be that enjoying maths increases grades through greater motivation,
practice and effort, but also, that feeling competent in maths and achieving good grades increases
enjoyment. It is highly likely that there is a reciprocal relationship where attitudes affect achievement,
and achievement affects attitudes, which has been found in existing research [94]; however, this idea
could not be examined in this study.
When looking at the findings for the secondary education model, it appears that school-related factors
in secondary education have a greater effect on maths attainment trajectories, where more positive
studentteacher relationships, greater perceived maths teacher fairness and lower school-belonging
were significantly associated with increased attainment. It was expected that positive studentteacher
relationships and teacher fairness would be positively associated with attainment. However, it is
somewhat surprising that student-reported school-belonging was negatively associated with
attainment. It appears that the school-climate declines around the transition [45]; however, this still
does not explain the negative association with maths as found here. One possible explanation is that
the measure used for school belonging in this study contained items relating to the childs peer
relationships, and as such, could reflect their perceived popularity. For example, items for the school
belonging composite included my school is a place where I know people who think a lot of me,my
school is a place where I get on well with other pupils in my classesand my school is a place where
other pupils are very friendly. Therefore, it could be that adolescents who perceive their peers as
more accepting and friendly, are those with a greater number of friendships and are considered
popular, which has been associated with decreased attainment [95]. Another potential explanation
could be that students who are especially giftedin maths may not feel comfortable socially within
their school or may not find it sufficiently challenging intellectually. Peer victimization is high for
gifted students [96], and so it could be that high-achieving maths students do not view their school as
a place they get on well with other pupils. In addition, stronger mathematicians may feel less
engaged by classwork they do not find particularly challenging, and so may not identify strongly
with their school and their educational environment. However, additional research is needed to
investigate these possibilities further.
The findings here support the idea that positive studentteacher relationships are an important part
of the school climate associated with long-term positive outcomes. This measure generally focused on all
teachers students interacted with. However, when focused on the adolescents maths teacher specifically,
this study found support for teacher fairness as a predictor of maths attainment trajectories, but not for
positive teaching practices (relating to the perceived efficacy of the teacher, their encouragement and their
emphasis on the importance of effort). The significant finding of teacher fairness suggests that students
who perceive their maths teacher as treating all students equally (regardless of gender or ability) had
increased maths attainment trajectories. This is supported by existing research particularly on the
damaging effects of gender stereotypes in maths (e.g. [58]), and further demonstrates the importance
of treating students equally, regardless of their characteristics and abilities.
Positive teaching practices (i.e. the teacher tries to make maths interesting, tells the class why maths is
important and understands maths really well) were not found to predict maths attainment significantly.
This finding implies that the perceived competence of the maths teacher is not associated with students
maths attainment, and other teacher-related factors (such as teacher fairness) are more important in
secondary education. This finding is unexpected; however, one possible explanation for the absence of
a significant finding could be that at average levels of teacher fairness (in the model, this variable was
centred), the instructional quality of teachers is less important. It could be that when students perceive
themselves to be viewed equally, they are less likely to become disengaged with difficult work,
regardless of their abilities and the competency of their teacher, provided that they are treated
similarly to their peers. However, further analyses and research would be needed to explore this idea.
Negative emotion towards school, including feelings of loneliness, worry and restlessness, was not
found to significantly predict maths attainment. One possible explanation for the absence of a
significant association could be that negative emotion towards school was measured at only one
specific timepoint, meaning that any changes in affect towards school would not be accounted for. To
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20
illustrate, adolescents could be experiencing short-term but heightened stress and emotion towards
school relating to exams or assessments, the breakdown of friendship groups, or issues with bullying
and victimization. Their feelings towards any school-related short-term stressors may have been
reflected in their responses to the questionnaire, but may not have been long-lasting enough to affect
their overall attainment. However, this idea can only be speculated as multiple measures of emotion
towards school over time were not available.
When looking at the results of the models together, there are several interesting findings. Firstly, the
absence of a significant association between school- and teacher-related variables in primary education
and maths attainment is surprising. Based on the existing literature, it was predicted that a positive
school climate, a warm studentteacher relationship and positive teacher characteristics (i.e. positive
affect towards teaching, high self-esteem and fewer mental health symptoms) in primary education
would be associated with increased maths attainment. These findings suggest that the effects
associated with poor secondary education experiences could be more substantial than positive
primary education experiences. It could be that the significant associations found in the secondary
education model reflect the greater importance of the secondary education environment for
attainment, or the lack of fit between adolescentschanging needs and their educational environment
as proposed by the stageenvironment fit theory [44]. Eccles et al. [44] suggest that there are fewer
opportunities for positive studentteacher relationships in secondary education, especially where
children transition from having one teacher per year in primary education to interacting with multiple
teachers throughout the day in secondary education, which may help explain why studentteacher
relationships were associated with maths attainment in secondary education but not in primary
education. The school climate is also thought to differ substantially between primary and secondary
education (such as a greater emphasis on discipline, social comparison and public evaluation in
secondary education) which could explain why childrens affect towards school was associated with
maths attainment in secondary education, but not in primary education. It appears that children
experiencing maladaptive transitions to secondary education, where their needs are vastly different to
their environment, are potentially the most at-risk of poor attainment, which is supported by previous
research [12]. Other possible explanations could be that the effects are due to the differences in
measures used in both models; however, further analyses would be needed to assess this further.
4.2. Contextual predictors
These variables were included to adjust for known effects from previous studies. They are discussed in
detail in Evans et al. [70] and Evans & Field [69], and so here we will briefly summarize the key points.
The results suggest that males have significantly greater maths attainment at ages 11 and 14, but their rate
of growth per year is not significantly different from females, implying that by early adolescence males
have a slight grade-advantage. It is apparent that even when school-related factors and attitudes towards
maths are adjusted for, there are still differences in maths attainment between adolescent males and
females.
Unsurprisingly, greater IQ, SES and working memory predicted greater attainment at age 11 and 14,
and an increased ROC over time in both models. Fewer internalizing symptoms, greater parental school
support and a more positive parentchild relationship were also associated with increased maths
attainment trajectories in both models. Parental education qualifications were also found to
significantly predict maths attainment trajectories. In both models, when compared with children of
parents with a CSE qualification or below, having a vocational qualification was associated with
decreased attainment (not significant for the ROC), and having an A level or degree was associated
with increased attainment. There were no significant differences between children to parents with an
O level and a CSE or below for attainment at age 11 and 14 or the ROC. Overall, the findings indicate
that higher levels of parental education qualifications are generally linked to increased maths
attainment trajectories.
4.3. Implications, limitations and future research directions
Together, the findings suggest that the secondary education school environment and childrens attitudes
towards maths have important implications for childrens maths attainment throughout school. Based on
these findings, there are several recommendations for educational strategies to help improve maths
attainment. We could not assess causal links in this study, but it appears that improving childrens
attitudes towards maths might help improve their attainment. This has been achieved by the Maths
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21
Counts programme [97]; however, it is likely that the associated increase in maths abilities prompted by
this programme also increases childrens attitudes towards maths.
Focusing predominantly on the secondary education environment could also be useful when
targeting childrens attainment. In this study, we found that studentteacher interactions (specifically
studentsrelationships with teachers and their maths teachers fairness) in secondary education had a
significant association with attainment. These findings imply that one potential focal area for maths
interventions could involve improving these relationships and interactions. However, it is important to
note that it is also possible that children underachieving in maths have worse relationships with their
teachers as a result of their poor performance, i.e. where children have received harsh feedback, or
have experienced unpleasant public evaluation of their low abilities, and consequently dislike their
teachers.
Another key finding of this study was the negative association between school belonging in
secondary education and maths attainment, which implies that high-achieving maths students may
not feel particularly happy in their secondary school. Based on this idea, secondary schools could
potentially help students feel more comfortable in their surroundings by providing a warmer school
climate and by making adolescentseducational environment a more positive place to be.
Overall, these findings provide insight into what aspects educational interventions could potentially
focus on when aiming to improve maths attainment. Future research should focus on determining the
causality of these associations to better understand how these factors affect attainment, and to identify
the most effective methods to improve maths outcomes.
The application and interpretation of these findings are affected by methodological limitations that
warrant further discussion. Firstly, this study aimed to focus on the effects of the transition to
secondary education, comparing school-related factors across the transition to secondary education
and how they may affect maths attainment trajectories. However, the timings of the measures used
are not directly before and following the transition, meaning that we cannot say with any certainty
that the transition event itself had a direct impact on the outcomes. Additionally, the measures are not
directly comparable pre- and post-transition meaning that we were unable to look at any changes
over time in school-related affect, studentteacher relationships and maths attitudes. Another
weakness of the study was due to the availability of measures within the ALSPAC dataset. It was not
possible to include several measures that have been linked to maths outcomes in previous studies
(such as teachersattitudes towards maths and their maths anxiety for example), or to include
variables that were measured in both primary and secondary education (i.e. attitudes towards maths
teacher). Including these predictors would have been useful in obtaining a more comprehensive
model of maths attainment trajectories, and by assessing the relative importance of different factors
for attainment in primary and secondary education.
Despite the clear advantages of using a large birth cohort such as ALSPAC, including the large
sample size and breadth of measures available, there are limitations to be considered relating to the
generalizability of the findings. For example, adolescents within the ALSPAC sample have slightly
higher grades than the population [71]. There was also very little bullying reported by parents of
children in ALSPAC, which when compared with current figures for the rest of the UK [98] suggests
that the ALSPAC sample had relatively positive school experiences and peer relationships. Future
research would benefit from a more diverse sample as it could be that victimized children view their
school-climate and studentteacher relationships differently compared with non-victimized children,
thus experiencing different school affect than those in this study.
5. Conclusion
Overall, of all the variables analysed here, this study found that the most important school-related
predictor of maths attainment trajectories in primary and secondary education was childrensmaths
attitudes. This effect was unsurprisingly strong with gains in attainment up to half a grade level at age
11, and around three-quarters of a grade level at age 14 when comparing children with the worst-rated
maths attitudes with children with the best-rated maths attitudes. There were differences between
primary and secondary variables where aspects of the school climate (studentteacher relationships and
school belonging) had a significant association with attainment in secondary education, but not in
primary education. However, it cannot be determined from this study alone whether the differences in
the predictive power of variables in primary and secondary education were due to the transition event,
structural differences between primary and secondary education, other age-related changes in
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22
development or differences between measures used in the models. Due to methodological limitations and
inconsistencies within the literature, the practical applications of the findings are reduced. However, it is
apparent that schools should aim to emphasize and encourage positive studentteacher relationships
(particularly in secondary education where opportunities for this is reduced), develop childrens
positive attitudes towards maths and ensure teachers treat all students equally.
Ethics. Ethical approval for this research was granted by the University of Sussex Cross-Schools Research Ethics
Committee under submission code ER/DE84/1. Ethical approval was obtained from the ALSPAC Ethics and Law
Committee and the Local Research Ethics Committees. Informed consent for the use of data collected via
questionnaires and clinics was obtained from participants following the recommendations of the ALSPAC Ethics
and Law Committee at the time.
Data accessibility. Data used for this submission will be made available on request to the Executive
(alspacexec@bristol.ac.uk). The ALSPAC data management plan (http://www.bristol.ac.uk/alspac/researchers/
data-access/documents/alspac-datamanagementplan.pdf) describes in detail the policy regarding data sharing,
which is through a system of managed open access. Code for analysis is available at https://osf.io/vjzad/?view_
only=26b61405b5784ed4a9cd061d7518640a.
Authorscontributions. D.E. and A.P.F. conceived the study. D.E. conducted initial data processing and ran all statistical
analyses. D.E. wrote the manuscript and A.P.F. reviewed and revised the manuscript and data analysis process at
all stages. All authors gave final approval for publication.
Competing interests. We declare we have no competing interests.
Funding. The UK Medical Research Council and the Wellcome Trust (grant no. 102215/2/13/2) and the University of
Bristol provide core support for ALSPAC. A comprehensive list of grants funding is available on the ALSPAC website
(http://www.bristol.ac.uk/alspac/external/documents/grant-acknowledgements.pdf). This research was specifically
funded by Department for Education and Skills (grant no. EOR/SBU/2002/121) and the Wellcome Trust and MRC
(grant no. 092731). This publication is the work of the authors and they will serve as guarantors for the contents of
this paper. This specific research project did not receive any funding.
Acknowledgements. The authors are extremely grateful to all the families who took part in this study, the midwives for
their help in recruiting them and the whole ALSPAC team, which includes interviewers, computer and laboratory
technicians, clerical workers, research scientists, volunteers, managers, receptionists and nurses.
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... Studies examining school related factors mainly focussed on the influence of the learning environment and its implications on students' mathematics learning. Findings from these studies suggest that the aspects such as perceived teacher support, teacher enthusiasm, student perceived autonomy and perceived performance are significantly related with postprimary students' mathematics learning (Deieso & Fraser, 2019;Evans & Field, 2020a;Fryer & Oga-Baldwin, 2019;Lazarides et al., 2018). These studies highlighted that declined levels of interest in mathematics and perceived support from teachers negatively impacted on students' enjoyment and involvement in mathematics learning in post-primary school. ...
... They reported that student-perceived instructional quality was more strongly (positively) associated with mathematics achievement as compared to the perceptions of student-teacher relationships. Evans & Field (2020a) found a negative association between student-reported school belonging and their mathematical attainment suggesting high-achieving students' dissatisfaction with the school climate. ...
... The quality of these relationships have been found to have a direct influence on students' mathematics achievement and levels of mathematics anxiety (Semeraro et al., 2020). Positive relationships with teachers are also important in the development of students' socio-emotional skills and can lead to increased mathematics attainment and positive attitudes for mathematics learning (Evans & Field, 2020a;Semeraro et al., 2020). Students' relationship with peers can also influence their experiences. ...
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This study presents the findings from a scoping review of literature (2016-2020) to explore factors that influence students' experiences of the mathematics transition from primary to post-primary education. Synthesis of findings identified three factors, namely student self-regulation, school and academic-related, and social factors that contribute to shape students' experiences. Findings suggest that no single factor can be attributed to influence students' experiences of mathematics transition and an interplay between various factors contributes to these experiences. The review also highlights a gap in research on the social factors influencing students' experiences of mathematics transitions.
... Higher self-efficacy and valuing of mathematics School context/climate Carmichael, 2015;Carolan, 2013;Jansen et al., 2012;Jordan et al., 2010;Kieffer, 2013;Madjar et al., 2018;Martin et al., 2015;Mudaly & Sukhdeo, 2015;Rice, 2001;Wigfield et al., 1991 III. Social Home and family environment Carmichael, 2015;Evans & Field, 2020b;Evans et al., 2020;Friedel et al., 2010;Gniewosz et al., 2012;Martin et al., 2015;Pesu et al., 2018;Rice, 2001 Relationships Arens & Moller, 2016;Attard, 2010Attard, , 2011Attard, , 2012Attard, , 2013Bicknell & Hunter, 2012;Evans & Field, 2020a;Friedel et al., 2010;Gniewosz et al., 2012;Lazarides et al., 2019;Mackay, 2006;Mudaly & Sukhdeo, 2015;Semeraro et al., 2020;Stroet et al., 2015;Tytler et al., 2008;Yao et al., 2018 Page 10 of 23 Kaur et al. International Journal of STEM Education (2022) 9:13 are positively associated not only with engagement in secondary school mathematics (Martin et al., 2015), but also contributes to students' academic well-being and educational aspirations (Widlund et al., 2018). ...
... The reviewed studies also suggest that parental factors and home environment are strong predictors of mathematics engagement and achievement across transition. Using a secondary analysis of data from a national longitudinal study in the UK, Evans and Field (2020b) found that positive relationship with parents, level of parents' education and their school involvement play an influential role in mathematics attainment at the transition (at age 11). Additionally, parental emotional support, e.g. ...
... Impact on mathematics achievement Anderman & Midgley, 1997;Carmichael, 2015;Carolan, 2013;Evans & Field, 2020b;Lazarides et al., 2020;Lee, 2010;Mackay, 2006;Mudaly & Sukhdeo, 2015;Pajares & Graham, 1999;Paul, 2014;Rice, 1997;Semeraro et al., 2020;Smyth et al., 2004;Whitley et al., 2007;Widlund et al., 2018;Yao et al., 2018 Shifts in attitudes and motivation Anderman & Midgley, 1997Athanasiou & Philippou, 2006Attard, 2010Attard, , 2012Attard, , 2013Darragh, 2013;Eccles et al., 1993;Friedel et al., 2010;Galton et al., 2003;Jansen et al., 2012;Lazarides, et al., 2019;Martin et al., 2015;Mudaly & Sukhdeo, 2015;Pajares & Graham, 1999;Paul, 2014;Widlund et al., 2018 Identity development Arens et al., 2013;Athanasiou & Philippou, 2010;Becker & Neumann, 2018;Darragh, 2013;Entwisle et al., 1994;Field et al., 2019;Friedel et al., 2010;Gniewosz et al., 2012;Ma & Xu, 2004;Madjar et al., 2018;Muzzatti & Agnoli, 2007;Pajares & Graham, 1999;Pesu et al., 2018;Suren & Kandemir, 2020;Widlund et al., 2018;Wigfield et al., 1991;Yao et al., 2018 Page 14 of 23 Kaur et al. International Journal of STEM Education (2022) 9:13 Studies also provide evidence of the impact of transition on aspects related to the development of mathematical identities of students. ...
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A systematic literature review of international empirical research was conducted to understand the impact of primary‒secondary transition on children’s experiences, outcomes and protective/risk factors. The review covered the period 2008‒2018 and met the gap in previous literature reviews. Using the EPPI‐Centre approach, authors included 96 studies in the review. Synthesis of the findings suggested that, in the main, perceived and real relationships with teachers and peers led to positive or negative experiences. Pupils and parents were primarily concerned with changes in relationships during the transition from primary to secondary school. Some studies reported that transition can also have a positive effect on opportunities for establishing new friendships. There was a decline in educational and wellbeing outcomes, and there was a link between the two. However, we cannot say with any confidence whether this impact on outcomes was as a result of the transition to secondary school, and whether it was sustained over time. Protective and risk factors were related to the child and significant others in their ecosystem. There were contradictory findings about the impact of organisational and educational systems. A limited number of studies examined the differential impact of transitions on children with additional support needs. This review is the first to bring together various aspects of transitions and as a result provides some unique insights and makes an original contribution. It became clear that it is difficult to predict the impact of interactions between experiences, outcomes and factors, given the gaps in existing literature. The paper concludes with recommendations for policy, practice and future research.
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The current mixed-methods study investigated the development of mathematics efficacy trajectories for novice teachers over the course of their teacher preparation and into their first two years of teaching. Participants (N = 245) were graduates of an elementary STEM-focused program from a major university in the United States. Overall, quantitative results showed that participants’ efficacy trajectory increased during their teacher preparation program and decreased during their first years of teaching. Additionally, efficacy trajectories were identified for particular groups that displayed patterns of either increased or decreased efficacy over time. Qualitative data helped explain when and why changes in teaching efficacy take place.
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We tested the role of teacher-child closeness in moderating the associations between early childhood adversity, measured as a cumulative risk index, and child outcomes during the kindergarten year. Using the ECLSK:11, a national dataset of kindergarteners in the 2010-11 academic year, we examined three dimensions of executive function (cognitive flexibility, inhibitory control, working memory), as well as early reading and math scores, as key skills that facilitate the transition to school. Cumulative risk was negatively associated with all outcomes, and teacher child closeness was positively associated with all outcomes. Teacher-child closeness moderated the relation between cumulative risk and working memory and cumulative risk and reading scores in a protective manner, but not cognitive flexibility, inhibitory control, or math scores. Implications for research in early childhood adversity and education are discussed.