The Nuffield Foundation has published a systematic review by researchers at Ulster University that analyses the outcomes of classroom-based mathematical interventions.
The systematic review included studies that assessed the
outcomes of interventions aimed at improving maths achievement in primary
school children. Forty-five randomised controlled trials were included along
with thirty-five quasi-experimental studies. The studies were published between
2000 and 2017, and were mostly conducted in the US and Europe.
The results of the review suggest that there are effective
strategies teachers can use to help with learning maths and being fluent with
mathematical facts. It also found there are many different ways teachers can
support children to have a wide bank of strategies to complete mathematical
problems, and for children to know when is best to apply them. Technology in
the classroom can also be helpful as long as these tools have been developed
with a clear understanding of how children learn.
The report concludes that the evidence base on mathematical
interventions is weak, and recommends that researchers should test how
effective mathematical interventions are in order to help teachers support
to improve mathematical achievement in primary school-aged children. A systematic
review (June 2019), Nuffield Foundation
QuickSmart Numeracy is a 30-week maths tutoring programme from Australia that uses teaching assistants as tutors. Its goal is to increase basic maths fact automaticity/fluency in pupils in Year 4 and Year 8 who perform in the bottom third of their national cohort as measured on standardised testing, the premise being that increased maths fluency allows pupils to devote their concentration to maths concepts instead of fact recall. Researchers from the Teachers and Teaching Research Centre in the School of Education at the University of Newcastle, Australia, recently examined the effects of the programme on pupil achievement in a randomised controlled trial.
Subjects were 288 Year 4 and Year 8 pupils from 70 classrooms in 23 Sydney Catholic Schools in New South Wales who scored below the 30th percentile on national standardised testing. Baseline testing was done in March 2017 using the Australian Council for Educational Research (ACER) Progressive Achievement Test – Mathematics (PAT-M), with post-testing in May 2018, six months after the intervention ended in December 2017. There were no significant differences between the experimental and control groups at pre-test. Randomisation among pupils who qualified for tutoring was done in each class, with all pupils attending regular maths classes and pairs of experimental pupils being pulled from other classes to also receive half-an-hour of QuickSmart tutoring three times a week for 30 weeks.
Results showed a non-significant difference (+0.08) favouring
the experimental group in Year 4, and an effect size of +0.01 (n.s.) for Year
8. Authors noted that not all of the pupils received the targeted hours of
tutoring due to recruitment and testing processes.
The Institute for Effective Education (IEE) has published a new
report from a project funded by their Innovation Evaluation Grants. The IEE
Innovation evaluations are small-scale and test the kinds of innovations that
schools are interested in.
Thirty-four Year 4 classes took part in the evaluation of Improving times table fluency, which was conducted by Underwood West Academy. A total of 876 children were included in the study.
Five groups of four or five classes were created by matching the pre-test scores on a 25-item tables test and the percentage of children in receipt of pupil premium. All groups had similar pre-test scores and similar percentages of children in receipt of pupil premium. Each class used a different balance of conceptual and procedural activities during times tables lessons. Conceptual activities were games that focused on the connections and patterns in tables facts, while procedural activities were games in which pupils practised multiplication facts.
Pupils had four 15-minute times tables lessons each week, and the
intervention lasted for 12 weeks. Before the intervention started, all
participating pupils carried out a simple times tables test comprising 25
spoken multiplication questions. The same test was repeated as a post-test.
The results of the trial showed that no one balance of practice
activities was more effective than another. The report concludes that times
tables may be best taught by using a balanced approach – teaching both the
concepts behind them and practising them in a range of ways with low-stakes
Increasing times table fluency (May 2019), Institute
for Effective Education
The results of a randomised controlled trial, published in Journal of Educational Psychology, suggest that a greater emphasis on interleaved practice may dramatically improve maths test scores for grade 7 (Year 8) pupils. Whereas most mathematics worksheets consist of a block of problems devoted to the same skill or concept, an interleaved worksheet is arranged so that no two consecutive problems require the same strategy.
and colleagues conducted the study with 54 classes in a large school district
in Florida during the 2017–2018 school year. Over a period of four months, the
classes periodically completed either interleaved or blocked worksheets, and
then both groups completed an interleaved review worksheet. All pupils
completed the same problems. One month later, pupils took an unannounced test
which was set by the researchers. Pupils who had completed the interleaved
assignments performed much better on the unannounced test than those in the
blocked assignment group (effect size = +0.83).
researchers suggest that the large effect sizes observed in the study for
interleaved maths practice may be due to the learning strategies it involves,
which force the pupil to choose an appropriate strategy for each problem on the
basis of the problem itself. They also identified some limitations of the study
– particularly that the interleaving pupils took longer to complete their
worksheets so effectively spent more time on each topic.
Source: A randomized controlled trial of interleaved
mathematics practice (May 2019). Journal of
While mathematics is often considered a hard subject, not all difficulties with the subject result from cognitive difficulties. Many children and adults experience feelings of anxiety, apprehension, tension or discomfort when confronted by a maths problem. Research conducted by the Centre for Neuroscience in Education at the University of Cambridge examined the maths performance of more than 2,700 primary and secondary pupils in the UK and Italy who were screened for maths anxiety and general anxiety. Researchers then worked one-to-one with the children in order to gain deeper understanding of their cognitive abilities and feelings towards maths using a series of cognitive tasks, questionnaires, and interviews.
Emma Carey and colleagues found that a general feeling that
maths was more difficult than other subjects often contributed to feelings of
anxiety about the subject, and that teachers and parents may inadvertently play
a role. Girls in both primary and secondary school were found to have higher
levels of both maths anxiety and general anxiety.
Pupils indicated poor test results, or negative comparisons
to peers or siblings, as reasons for feeling anxious. Secondary school pupils
also indicated that the transition from primary to secondary school was a cause
of maths anxiety, as the work seemed harder and there was greater pressure on
tests and increased homework.
The report sets out a series of recommendations, including:
Teachers should be aware that maths anxiety can
affect pupils’ maths performance.
Teachers and parents need to be aware that their
own maths anxiety might influence pupils’ math anxiety.
Teachers and parents also need to be aware that gendered
stereotypes about maths ability might contribute to the gender gap in maths
Reducing classroom pressure and using methods
like free writing about emotions before a test could help to alleviate maths
Source: Understanding mathematics
anxiety: Investigating the experiences of UK primary and secondary school
students (March 2019), Centre for
Neuroscience in Education, University of Cambridge
A new resource from Deans for Impact summarises current cognitive-science research related to how young children – from birth to age eight – develop skills across three domains: agency, literacy and numeracy.
It aims to
give guidance to anyone working in education who is interested in understanding
the science of how young children develop control of their own behaviour and
intentions, how they learn to read and write, and how they develop the ability
to think mathematically.
domain, the report identifies key questions about learning and provides a short
list of the principles from learning science that inform the answers to these
questions. The resource then connects these principles to a set of practical
implications for specific teaching strategies. The original research is clearly
referenced for anyone wishing to find out more.
Source: The science of early learning: How do young
children develop agency, literacy, and numeracy? (2019), Deans for Impact.