Since retirement, I am engaged in PhD supervision and research in the development of algebraic thinking in the Numeracy Development Project.
 

Research interests

• Teaching and learning of mathematics in primary schools (age 5 - 14)
• Professional development of teachers
• Evaluating professional development programmes in mathematics education
• Ways of increasing the achievement of low income, ethnically different students
• Understanding decimal fractions
• Young children's understanding of measurement
• Teaching students with learning difficulties
• Young children’s understanding of compensation and covariance in part/whole relations.
• Use of language for mathematical concepts
   

Some Current and Recent Theses Supervised

• Nicky Knight (EdD) Sustaining Changed Teacher Practice in Numeracy
• Kate Niederer (PhD) Self Esteem of Gifted Children
• Fiona Ell (PhD) Learning about Multiplication: An Interpretation of a Transition
• Barbara Miller-Reilly (PhD) Evaluation of Three Programmes in Bridging Mathematics.
• Sanka Bambarawana Liyanage (PhD) A Framework for Informal Assessment Questions Used by Secondary School Mathematics Teachers.
• Lim Eng Leong (PhD) The Deca-Based Approach: A Mathematical Program to Learn and Apply Two-Digit Numbers
• Tamsin Meaney (PhD) Mathematics Curriculum Development for Indigenous Groups
• Norma Black (Med) Multiplication and Division through Counting Patterns
• Pamela Perger (MA) Pasifika Students’ Perspectives on Factors that Contribute to Achievement in Mathematics at Year 7
• Angela Scroggins (Med) Differences In Teaching Practices between Highest and Lowest Strategy Teaching Groups
• Evaline Ha'angana (MEd) Poto'i Fika 'I he Longa'i Fanau Tonga: Early Childhood Mathematics in Tongan Children.
• Sangmi Yun (MA) Language Differences in Geometry: Comparisons between Korean and New Zealand Mathematics Textbooks
• Hannah Vettiveerarasa (MEd) Helping adult students' understand fractions.
• Anne Buzeika (MEd) Children Using Invented Algorithms for Multi-digit Computation.
• Fiona Ell (MA) School-initiated Mathematics in the Home.
   

Some Recent Publications

• Irwin, K. C. & others. Evaluations of the New Zealand Numeracy Project: 2006, 2005, 2004, 2003, 2002. (under different titles) Wellington: Ministry of Education. Available through http://www.nzmaths.co.nz/
• Irwin, K. C. & Britt, M. S. (2005). The algebraic nature of students’ numerical manipulation in the New Zealand Numeracy Project. Educational Studies in Mathematics, 58(2), 169-188.
• Irwin, K. C. & Irwin, R. J. (2005). Assessing development of numeracy in students from different socio-economic areas: A Rasch analysis Educational Studies in Mathematics, 58(3), 283-298.
• Irwin, R. J. & Irwin, K. C. (2005). Attitude towards mathematics of 11- year-olds: Analysis of a questionnaire and its relation to mathematical achievement. In R. Waugh (Ed.), On the forefront of educational psychology. (pp. 107-116) New York: Nova Science Publishers
• Irwin, K. C, Vistro-Yu, C & Ell, F. (2004). Understanding of linear measurement: A comparison of Filipino and New Zealand children. Mathematics Education Research Journal, 16(2), 3-24.
• Irwin, K. C. (2001). Using everyday knowledge of decimals to enhance understanding. Journal for Research in Mathematics Education, 32, (399-421).
• Britt, M. S., Irwin, K. C. & Ritchie, G. (2001). Professional conversations and professional growth. Journal of Mathematics Teacher Education, 4, (29-53).
• Ferrer, B., Hunter, B., Irwin, K. C., Sheldon, M., Thompson, C. & Vistro-Yu, C. (2001). By the unit or by the square unit? Mathematics Teaching in the Middle School,7(3), (132-139).
• Stacey, K., Helme, S., Steine, V., Baturo, A., Irwin, K., & Bana, J. (2001) Preservice teachers’ knowledge of difficulties in decimal numeration. Journal of Mathematics Teacher Education, 4, 205-255.
• Irwin, K. C. (1996). Children's understanding of the principles of compensation and covariation in part-whole relationships. Journal for Research in Mathematics Eduction, 27, 25-40.

Some research contracts held

• Ministry of Education, evaluation of aspects of the Numeracy Development Project, mostly for older students (2002 - 2007)
• ASIA: New Zealand fund for an exchange in mathematics and science education between the School of Education and Mathematics Education Unit and Ateneo de Manila University in the Philippines.