



 The NumberSense MMR™ Framework Validation  



Validation of the NumberSense MMR™ 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 in England, Wales, Scotland and Europe (Englishspeaking 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 as the data did not contain a truly continuous age variable.




Number Relationship 

Standardised Coefficients
beta 
t 
p 




Number Magnitude 
0.313 
12.92 
p < 0.001 
Number Meaning 
0.091 
3.784 
p < 0.001 
Age 
0.48 
2.46 
p < 0.014 
Table 1. Multiple Regression Analysis



The ANOVA analysis in Table 2 shows participants' 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 7years olds; 18.99 (s.d 1.76) for 8years olds; 19.3 (s.d 1.39) for 9years olds; 14.038 (s.d 5.198) for 10years olds; and 14.54 (s.d 1.66) for 11years olds.
The Tamhane2 post hoc tests showed that there were no significant differences between age 7 and 8 year olds, 8 and 1 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.




Factor 
p 
mean 
s.d 





Number Meaning 
F(4,2381)=13.26 
p = 0.001 


Age 7 


18.65 
2.113 
Age 8 


18.99 
1.76 
Age 9 


19.3 
1.39 
Age 10 


14.038 
>5.198 
Age 11 


14.54 

Number Magnitude 
F(4,2381)=24.467 
p = 0.001 


Age 7 


12.18 
4.74 
Age 8 


11.78 
4.75 
Age 9 


12.87 
5.177 
Age 10 


14.038 
6.63 
Age 11 


14.54 
5.48 
Number Relationship 
F(4,2381)=12.86 
p = 0.001 


Age 7 


9.54 
6.976 
Age 8 


9.776 
7.15 
Age 9 


10.007 
6.74 
Age 10 


19.41 
1.35 
Age 11 


19.28 
7.1 
Table 2. ANOVA Variance analysis with Age and dependent variables 


The Tamhane2 post hoc tests showed that there were no significant differences between age 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.
The Tamhane2 post hoc tests showed that there were no significant differences between age 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, 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.
Therefore, this shows that there is a large difference in Number Meaning between 7 year olds and older children and for age 9 there may have been a tendency for ceiling effect. Similarly, for Number Magnitude and Number Relationship, the biggest difference was between age 7 to 9 years and 10 to 11 years.






 The NumberSense MMR™ Framework Validation 


