1. How good at mathematics do students need to be on entry to primary school initial teacher education?
Dr. Lorraine Harbison1
Dr. Joseph Harbison2
Church of Ireland College of Education, Dublin 1
Trinity College Dublin 2

4. Aspects of mathematics knowledge important for teachers
Subject matter content knowledge
Pedagogical content knowledge
Curricular knowledge
(Shulman 1986, Delaney 2012)
(2) and (3) fall within remit of teacher training
(1) is assumed in secondary school graduates

5. Leaving Certificate (Ireland)
Taken by secondary school students at completion of 5 or 6 years secondary education
Mathematics is compulsory
Higher, Ordinary and Foundation Level
ITE: Minimum Pass in Ordinary Level Required

6. Leaving Certificate Grades & Central Applications Office Points
Higher Level
Ordinary Level A1
100 60 A2 90 50 B1 85 45 B2 80 40 B3 75 35 C1 70 30 C2 65 25 C3 20 D1 55 15 D2 10 D3 5

7. Questions.
Are leaving cert. results a good indicator of primary school mathematical knowledge?
Is there a threshold to indicate competence in primary mathematics?
Are proposed thresholds (a pass or C3 in honours mathematics or equivalent) were introduced how would it effect current recruitment?

8. Not that easy
Assumption that passing Leaving Cert. = having mathematics skill appropriate to ITE is not automatic
Several steps to validate this assumption
Kane et al 2004

9. Not that easy Participants’ observed performance on test items
Specific score
Test domain
Required knowledge, skills and judgment domain
Practice domain
Certification
Kane 2004

10. Not that easy.
Leaving Cert exam Leaving Cert result Overall Mathematical Knowledge Knowledge relevant for primary school teaching Ability to use or apply this knowledge Admission to ITE

11. Competence in Primary School Mathematics
SIGMA-T Standard Attainment test Level 5
Typically administered in 6th class (Final year in Primary School, years)
119 questions

12. Methods
Over 3 years, 1st year ITE Students in CICE completed SIGMA T Level 5 in their first term.
Leaving Cert. (LC) results obtained by the students, typically obtained in the preceding 6 months, converted into CAO points to allow standardisation of Higher and Ordinary grades.
Mean and SD of SIGMA-T and LC results obtained and arbitrary SATS ‘pass mark’ derived from results, ‘Grading on a curve’:
‘Pass mark’ = mean -1 standard deviation.

13. Results 95 Students (88 female)
LC results range: D2 (ordinary) to B2 (higher)
SIGMA-T score range: 39 (32.8%) to 111 (93.3%)
Mean SIGMA T: 84.6 (71.1%)
Standard Deviation: 13.9
SAT ‘Pass mark’ >70 (58.8%)

14. Correlation
Leaving Cert (CAO) Score
SAT Score
r=0.59, p<0.001

15. Results 17 (18%) Students SIGMA-T ≤ 70
16 of these had a Leaving Cert score <45

16. Grade
Higher Level
Ordinary Level A1
100 60 A2 90 50 B1 85 45 B2 80 40 B3 75 35 C1 70 30 C2 65 25 C3 20 D1 55 15 D2 10 D3 5

17. Results 17 (18%) Students SIGMA-T ≤ 70
16 of these had a Leaving Cert score <45
31 (33%) other students LC score also <45
Mean SIGMA-T: 87.6
Only 15 (15.3%) students LC score ≥60
Mean SIGMA-T: 95.8

18. What about?
Male Female n 7 88 Mean LC Score p=0.06* Mean SAT score p=0.03* Top 2 in LC and top 8 scorers in SATs were female *Student’s t test.

19. Conclusion
Correlation between Leaving Cert. results and SATs is moderate.
No obvious threshold level for Leaving Cert. to clearly define competence in primary school mathematics.
Difference between mathematics competence between males and females significant but modest.