1. Between-school Variance in Achievement
Variance in achievement can be partitioned into between- and within-school variance.
Between-school variance is expressed as a percentage of the total variance in achievement.
Large between-school variance (relative to within-school variance) can be interpreted as an indicator of a more heterogeneous school system.
Sampling in PISA induces an intra-cluster correlation (ICC) between students in each school, since students in a school tend to be similar to one another

2. Between-school Variance in Science (OECD countries)

3. Between-school Variance in Mathematics (OECD Countries)

4. Between-school Variance in Reading Literacy (OECD Countries)

5. School-level score point difference associated with one-unit increase in school mean ESCS

6. Between-school variance in science explained by ESCS (selected countries)
Multi-level modelling to explain between- and within-school variance in achievement
Finding in earlier PISA studies – most between-school variance explained by school scoio-economic status, variables such as school size, gender composition, and school type (whether secondary, community/comprehensive or vocational) were dropped from our multi-level models because so much between school variance was explained by scoioeconomic status – whether it was

7. Explaining Performance in Science – Student-level variables
Gender
Socio-economic status (JC fee-waiver)
Number of books in the home
Home educational resources (more resources better)
Absence from school (frequent absenteeism associated with lower scores)
Grade level (Students in lower grade levels do less well)
Study of science (those who don’t study science do less well)
Gender – small negative difference in favour of females.

8. Conclusion
Relative to other countries, differences in performance between schools in Ireland are moderate.
Nevertheless, there is an association between school-level socioeconomic status and school-level achievement, which is also in the moderate range.
Further, school-level socio-economic status seems to account for the ‘effects’ of other school variables such as school type, school size, and school gender composition.

9. Conclusion
Variables such as home educational resources, parent-student interaction, attendance at school, engagement in science, extent of bullying, involvement in paid work etc. would seem to be candidates for change.
Care needs to be exercised in interpreting associations between attitudinal variables and achievement, particularly between self-efficacy and science performance.

10. Conclusion
Associations between curriculum and PISA are worth examining in more detail, particularly in the case of mathematics.
In the case of science, more work is needed in examining the how reading ability interacts with scientific knowledge in explaining performance.

11. Conclusion
Another issue worth examining in more detail is the performance of students not taking Junior Certificate science vs. those taking Ordinary level.
Finally, differences in knowledge of science among male and female students are worth exploring in greater detail.