Model 2: The likelihood of weak numeracy assessment performance 107

Fixed characteristics

We identified five fixed characteristics that were associated with weak performance in the numeracy assessment. In order of predictive power these are:

1. Not having English as first language, especially for some ethnic groups 2. Having a (self-assessed) learning difficulty

3. Neither parent staying in education beyond the age of 16 4. Being female

5. Being aged 16 to 24 or 55 and older

Although this model has a number of similarities with the literacy model, there are some distinctive features.

Firstly, language is less of a factor (although still sufficiently strong to be the lead predictor in the model) and secondly, some minority ethnic groups (e.g. Indian and the ‘White other’ and ‘other’ categories) perform at the same standard as the majority White British group once differences in first language status are controlled for. In the literacy model, all these groups were more likely to perform weakly on the assessment, even controlling for language status.

Probably the most striking feature of the model is the inclusion of gender. Women were much more likely than men to be categorised below Entry Level 3 in the numeracy assessment. Another feature is the slightly u-shaped age effect in which both the oldest and youngest generations performed relatively weakly on the assessment.

Application of this five-term regression model allowed us to create three groups with different base likelihoods of weak numeracy assessment performance:

Group 1: 4-18 per cent (mean = 14 per cent) Group 2: 18-26 per cent (mean = 22 per cent) Group 3: 26-87 per cent (mean = 36 per cent)

108

Model fit (fixed characteristics only)

The total explanatory power was 11.9 per cent, lower than for the literacy model (17.1 per cent). This is allocated as follows: ethnic group/language (4.8 per cent), learning difficulty status (2.7 per cent), parental education (2.7 per cent), gender (1.1 per cent), age-band (0.6 per cent). There are no obvious problems with model fit.

Acquired characteristics

We identified five acquired characteristics that were associated with weak performance in the numeracy assessment. In order of predictive power these are:

1. No Maths GCSE/equivalent A*-C

2. Highest qualification is rated at Level 2 or below 3. Infrequent or zero computer use

4. Working in particular industry sectors (although the patterning is unclear)

5. Working in lower supervisory or semi-routine and routine occupations (or long-term unemployed)

The association between highest qualification and numeracy is high. Holding any qualifications at all is a significant advantage over holding none and holding Level 3 qualifications and above is a significant advantage over holding lower qualifications. A degree is particularly valuable in this context.

As expected, holding a qualification relevant to numeracy (a Level 2 maths qualification) is associated with better performance on the assessment, even controlling for general qualification level.

In terms of work, there appears to be a moderate divide between “white collar” and “blue collar” occupations, just as there was with literacy. Working in routine occupations in particular is associated with weaker performance on the numeracy assessment, beyond that expected given educational level. However, while with literacy there was no strong distinction between “white collar” categories, here we find that those in the higher professional or managerial occupations score significantly better than those in other “white collar” work. This either suggests that senior “white collar” work helps individuals retain numeracy skills or that a high standard of numeracy is one of the keys to seniority.

As with literacy, the sample size per industry sector is often small so specific conclusions -

beyond the bland observation that industry sector seems to matter – are hard to find. Working in the ‘education’, ‘public sector administration’ and ‘finance’ sectors appears to lessen the odds of weak assessment performance. The first two were also associated with strong literacy skills but the addition of ‘finance’ makes intuitive sense.

As with literacy, those using computers frequently tended to achieve a higher assessment score than others, controlling for educational and work status.

Basic skills training in maths or numeracy was not an influential factor and was excluded from the model. This mirrors the literacy model and might be explained in the same way, namely that the impact of such training may be to bring students up to the average for their particular

Chapter 6: Understanding the relationship between skills and personal characteristics

109 combination of personal characteristics. However, it requires longitudinal data or formal

experimental data to make any firm quantifying statements about the ‘impact’ of such training. Fixed and acquired characteristics model fit

Addition of these acquired variables nearly doubles the explanatory power of the model from 11.9 per cent to 29.5 per cent. In the full model, this is allocated as follows: ‘fixed’

characteristics (10.6 per cent), whether has Level 2 maths qualification (5.7 per cent), highest qualification (4.8 per cent), computer use (3.3 per cent), industry sector (2.8 per cent), and occupational category (2.3 per cent). There are no obvious problems with model fit.

Differences between base groups

With literacy, we saw that the higher the likelihood of weak assessment performance in each base group, the more important the acquired characteristics are. However, there is much less variation with numeracy. The explanatory power of the final model varied only from 22 per cent to 29 per cent (group 1: 22 per cent; group 2: 22 per cent; group 3: 29 per cent; for literacy, the range was 12-42 per cent).

Only the education and computer use variables were significant for group 1 (those with the lowest likelihood of having weak numeracy). This is a close fit with what was observed for literacy, albeit with an extra penalty if the individual had never used a computer.

For groups 2 and 3 (with medium / high probability of having weak numeracy), the balance shifts so that education and work have more equal weight in terms of predictive power. It is also noticeable that, for group 2, holding a Level 2 maths qualification matters a lot more than overall highest qualification. For group 1, highest qualification carries more weight.

The importance of frequent computer use is also a distinctive feature of the group 2 model, with much stronger penalties associated with infrequent or zero use. The reason for this is unclear. There was some indication that having a limiting disability or illness is an additional drawback for group 3 but the penalty associated with this was not strong.

Finally, basic skills training was not a significant factor for any group.