Interleaved practice improves maths test scores

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.

Doug Rohrer 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).                

The 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 Educational Psychology

Understanding maths anxiety

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 performance.
  • Reducing classroom pressure and using methods like free writing about emotions before a test could help to alleviate maths anxiety.

Source: Understanding mathematics anxiety: Investigating the experiences of UK primary and secondary school students (March 2019), Centre for Neuroscience in Education, University of Cambridge

How do young children develop agency, literacy, and numeracy

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.

For each 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.

Positive results for early years maths apps

A randomised controlled trial of two new maths apps to support young children’s early maths development has shown positive results. The apps, “Maths 3–5” and “Maths 4–6”, are based on core mathematical concepts in number and shape, and space and measure, which are covered in the Early Years Foundation Stage, and also start to introduce children to topics covered in Key Stage 1.

Laura Outhwaite and colleagues conducted the randomised controlled trial of the apps with 389 children aged 4–5 years from 12 schools in the UK. The trial took place over 12 weeks in the last weeks of their Reception school year before pupils moved to Key Stage 1. Pupils were randomised to either use the apps in addition to standard maths teaching activities (treatment); use the apps instead of a regular small group-based maths activity (time-equivalent treatment), or continue with usual maths teaching activities (control).

The results showed that pupils in the treatment group made more progress on standardised assessments of maths performance over 12 weeks than pupils in the control group (effect size = +0.31). Similarly, pupils in the time-equivalent treatment made more progress in maths performance than pupils in the control group (effect size = +0.21). There was no significant difference in maths performance between pupils in the two treatment groups (effect size = +0.08).

A randomised controlled trial of apps developed for primary children in Malawi, which we covered in a previous issue of Best Evidence in Brief, also showed positive results for maths achievement.

Source: Raising early achievement in math with interactive apps: A randomized control trial (February 2019), Journal of Educational Psychology, 111(2)

Effects of initial skill and group size in the ROOTS Tier-2 maths intervention

Many factors influence a child’s responsiveness to an academic programme. The University of Oregon’s Ben Clark and colleagues recently evaluated the effects of baseline maths skills and their interaction with group size on the maths achievement of at-risk kindergartners (Year 1) in the ROOTs programme.

The ROOTS programme is a 50-lesson Tier-2 maths programme that addresses whole-number concepts and skills as a supplement to maths teaching. In this study, the researchers examined data from a randomised evaluation (Clark et al., 2017) studying kindergartners from 69 classrooms during two separate school years. Subjects were tested using five measures of whole-number sense each autumn, and those whose scores fell below a determined threshold were assigned to either a 2:1 ROOTS group (n=120), a 5:1 ROOTS group (n=295), or to the no-intervention control group (n=177). ROOTS pupils received 20-minute small-group sessions five times a week during ten weeks spanning late fall to early spring. Post-tests in the spring of kindergarten (Year 1) and then six months into first grade (Year 2) found that the pupils with lower initial maths skills demonstrated greater gains than others on two of the six outcome measures of the TEMA-3, although there was no correlation with intervention group size.

Source: Exploring the relationship between initial mathematics skill and a kindergarten mathematics intervention (January 2019) Exceptional Children, 85(2)

Does a parent’s anxiety about maths negatively affect their child’s maths achievement?

A maths app may help eliminate the negative association between parents’ maths anxiety and children’s maths achievement in early elementary (primary) school, according to a study published in the Journal of Experimental Psychology.

The researchers tracked the maths achievement of 587 pupils from 40 classrooms in the Chicago area from first to third grade (Year 2 to 4). In the first grade, pupils and their families were randomly assigned tablets loaded with either a maths app or a similar reading app.

Parents were also given a questionnaire to complete in order to assess a variety of attitudes and behaviours related to maths and reading. Maths anxiety was measured using the Mathematical Anxiety Rating Scale. At the end of the first grade, parents were given a second survey to complete. Children’s maths achievement was measured using the applied problems subset of a nationally-standardised test.

By the end of third grade (Year 4), children of maths-anxious parents who were in the reading app control group had learned less maths than children of parents with no maths anxiety; learning the equivalent of approximately five fewer months of maths. However, this was not the case for children in the maths app intervention group, and children with maths-anxious parents showed the same maths progress as pupils with parents who had no maths anxiety.

These results suggest that parents’ maths anxiety is negatively associated with children’s maths achievement in early elementary school, and that the decreased negative association observed in the intervention group is due in part to a change in parents’ attitudes. The researchers conclude that when families used the app together, parents’ attitudes toward maths changed and they were able to disassociate their own maths anxiety from their children’s ability in maths.

Source: Disassociating the relation between parents’ math anxiety and children’s math achievement: Long-term effects of a math app intervention (December 2018), Journal of Experimental Psychology: General, Vol 147(12)