Dynamo Maths – what works! evidence, has been carried out in two stages:

– Firstly it is the validation of the NumberSenseMMR™ framework used in Dynamo Maths to confirm correlation of developmental stages and alignment to Dyscalculia definition.

– Secondly, the standardisation of Dynamo Assessment using a large sample data of 3465 students across 368 schools. This study has now been extended to USA, South Africa and Europe.

### 1. Validation of the NumberSenseMMR™ Framework

The consistency of the Dynamo Maths framework was conducted independently by the University of Oxford and led by Dr. Ann Dowker (2016).

The study used the assessment data collected from 3465 students in 368 schools across England, Wales, Scotland and Europe (English-speaking schools using the UK curriculum).

The correlation analysis was carried out on the assessment data that was grouped into Number Meaning, Number Magnitude and Number Relationship components (Visual Numbers, counting through to Multiplication) by adding scores.

The data was analysed from ages 7 through to 11, to avoid the influence of too many small and diverse age groups.

The analysis showed all the components in the NumberSenseMMR™ framework correlated significantly at (p < 001) with one another.

The analysis shown in the table below showed Number Magnitude was a highly significant independent predictor (beta = 0.313; t = 12.92; p < 0.001).

Similarly, Number Meaning (beta = 0.091; t = 3.784; p < 0.001) was also a significant independent predictor and Age was also significant (beta = 0.48; t = 2.46; p < 0.014).

Arguably, Age could be excluded from the multiple regression analysis as the data did not contain a truly continuous age variable

The ANOVA analysis in Table 2 shows participant variance analysis with Age as the factor and the Number Meaning, Number Magnitude and Number Relationship components as the dependent variables.

The analysis showed that there was high significant effect of Age on Number Meaning score (F(4,2381) = 13.26; p = 0.001). The mean scores were 18.65 (s.d 2.113) for 7-year-olds; 18.99 (s.d 1.76) for 8-year-olds; 19.3 (s.d 1.39) for 9-year-olds; 14.038 (s.d 5.198) for 10-year-olds; and 14.54 (s.d 1.66) for 11-year-olds.

The Tamhane2 post hoc tests showed that there were no significant differences between 7- and 8-year-olds, 8- and 9-year-olds, 9- and 10-year-olds or 9- and 11-year-olds or 10-and 11-year-olds; but there were highly significant differences between 7- and 9-year-olds, 7- and 10-year-olds, 7- and 11-year-olds, 8- and 10-year-olds, 9- and 10-year-olds and 9- and 11-year-olds. All significant differences were in the direction of older pupils scoring higher.

The analysis showed that there was high significant effect of Age on Number Magnitude score (F(4,2381) = 24.467; p = 0.001). The mean scores were 12.18 (s.d 4.74) for 7-year-olds; 11.78 (s.d 4.75) for 8-year-olds; 12.87 (s.d 5.177) for 9-year-olds; 14.038 (s.d 6.63) for 10-year-olds; and 14.54 (s.d 5.48) for 11-year-olds.

The Tamhane2 post hoc tests showed that there were no significant differences between 7- and 8-year-olds, 7- and 9-year-olds, 8- and 9-year-olds or 10- and 11-year-olds; but there were highly significant differences between 7- and 10-year-olds, 7- and 11-year-olds, 8- and 9-year-olds, 8- and 10-year-olds, 8- and 11-year-olds, 9- and 10-year-olds and 9- and 11-year-olds. All significant differences were in the direction of older pupils scoring higher.

The analysis showed there was high significant effect of Age on Number Relationship score (F(4,2381) = 12.86; p = 0.001). The mean scores were 9.54 (s.d 6.976) for 7-year-olds; 9.776 (s.d 7.15) for 8-year-olds; 10.007 (s.d 6.74) for 9-year-olds; 19.41 (s.d 1.35) for 10-year-olds; and 19.28 (s.d 7.1) for 11-year-olds.