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Extracts from: "What Works For Children with Mathematical Difficulties?" Research Papers

Best learning strategiesCommon types of mathematical difficulty: what aspects of arithmetical thinking tend to cause most trouble?

Despite such variable patterns of strengths and weaknesses, some areas of arithmetic do appear to create more problems than others for children.

One of the areas most commonly found to create difficulties is memory for arithmetical facts.

For some children, this is a specific, localized problem; for children with more severe mathematical difficulties it may be associated with exclusive reliance on cumbersome counting strategies.

Other common areas of difficulty include word problem solving, representation of place value and the ability to solve multi-step arithmetic problems.

Paper: What Works for Children with Mathematical Difficulties?, 2004

4.2.1 The incidence and characteristics of arithmetical difficulties

There have been several studies of arithmetical difficulties and their characteristics.

As will be seen in the section on the history of individualized interventions, research has been carried out on arithmetical errors and faulty procedures since at least the 1920s.

Many people experience difficulties with mathematics.

For example, Bynner and Parsons (1997) gave some Basic Skills Agency literacy and numeracy tests to a sample of 7-year-olds from the National Child Development Study cohort (which had included all individuals born in Britain in a single week in 1958).

The numeracy tests included such tasks as working out change, calculating area, using charts and bus and train timetables, and working out percentages in practical contexts.

According to the standards laid down by the Basic Skills Agency, nearly one-quarter of the cohort had 'very low' numeracy skills that would make everyday tasks difficult to complete successfully.

This proportion was about four times as great as that classed as having very low literacy skills.

Most of the adults with numeracy difficulties had already been experiencing difficulties with school mathematics at the age of 7.

The reasons for these people's mathematical difficulties are undoubtedly various.

Paper: What Works for Children with Mathematical Difficulties?, 2004


Children's arithmetical difficulties are highly susceptible to intervention. Individualized work with children who are falling behind in arithmetic has a significant impact on their performance. The amount of time given to such individualized work does not, in many cases, need to be very large to be effective.

Paper: What Works for Children with Mathematical Difficulties?, 2004

1.3 Children’s difficulties with arithmetic

Many children have difficulties with some or most aspects of arithmetic.

It is hard to estimate the proportion who have difficulties, since this depends on the criteria that are used (Mazzocco and Myers, 2003; Desoete et al, 2004). 

Moreover, as arithmetical thinking involves a wide variety of components, there are many forms and causes of arithmetical difficulty, which may assume different degrees of importance in different tasks and situations.

It is likely that at least 15% to 20% of the population have difficulties with certain aspects of arithmetic .....

..... which are sufficient to cause significant practical and educational problems for the individual (Bynner and Parsons, 1997 and 2005; Every Child a Chance Trust, 2008).

The proportion with severe specific difficulties, which are sometimes describable as dyscalculia, is much lower, though still significant: often estimated at around 6%.

Paper: What Works for Children with Mathematical Difficulties?, 2010

1.7 Some aspects that present difficulty for children

Although children may be identified as having very specific barriers to learning overall, there are aspects of arithmetic that create particular problems for many children.

The most consistent finding about children with mathematical difficulties is that many have particular difficulty in retrieving arithmetic facts resulting in an excessive reliance on counting strategies, at an age when other children of the same age are relying much more on fact retrieval (Russell and Ginsburg, 1984; Ostad, 1997, 1998; Cumming and Elkins, 1999; Gifford, 2005).

Word problem solving is also often difficult (Russell and Ginsburg, 1984); and so is multi-step arithmetic (Bryant, Bryant and Hammill, 2000).

Paper: What Works for Children with Mathematical Difficulties?, 2010

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