Non Routine Mathematical Problem Solving with Lower Achieving Children


  • Cheryl Greene


Mathematics, Problem Solving, Lower-Achieving, Non-Routine Problems


This article discusses aspects of a research study which was carried out with twenty-four fourth class pupils in a school designated as disadvantaged in Dublin. The study focused on the strategies children used to solve non-routine mathematical problems, without having prior formal instruction on problemsolving strategies. Within the class were a high number of children performing below the twentieth percentile in mathematics. However, the study found that these lower-achieving children performed beyond expectations on non-routine problems and at times even outperformed their higher-achieving peers.


DeCorte, E. (1995) Fostering Cognitive Growth: A Perspective from Research on Mathematics Learning and Instruction, Educational Psychologist, Vol. 30 (1), pp. 37-46.

Department of Education and Science (DES) (2005) Literacy and Numeracy in Disadvantaged Schools: Challenges for Teachers and Learners, Dublin: The Stationery Office.

Duncan, A. (1992) What Primary Teachers Should Know About Maths, London: Hodder and Stoughton.

English, L.D. (1993) Children’s Construction of Mathematical Knowledge in Solving Novel Isomorphic Problems in Concrete and Written Form, Retrieved January 22, 2007, from

Foster, A. and Ankers, L. (2004) Can Do Problem-Solving: Teacher’s Book, Cheltenham: Nelson Thornes Ltd.

Ireland (1999) Primary School Curriculum: Mathematics, Dublin: The Stationery Office.

Jones, C. (2003) Problem Solving-what is it? Australian Primary Mathematics Classroom, Vol. 8 (3), pp. 25-28.

Lester, F.K. (1994) Musings About Mathematical Problem-Solving Research: 1970-1994, Journal for Research in Mathematics Education, Vol. 25 (6), pp. 660-675.

Roh, K.H. (2003) Problem-Based Learning in Mathematics, Retrieved 24 October, 2006, from

Schoenfeld, A.H. (1992) Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics. In Grouws, D. (ed.) Handbook of Research in Mathematics Teaching and Learning, New York: Macmillan.

Surgenor P., Shiel, G., Close, S. and Millar, D. (2006) Counting on Success: Mathematics Achievement in Primary Schools, Dublin: Educational Research Centre.

Trafton, P.R. and Midgett, C. (2001) Learning Through Problems: A Powerful Approach to Teaching Mathematics, Teaching Children Mathematics, Vol. 7 (9), pp.532-536.

Wheatley, G.H. (1983) Problem Solving Makes Math Scores Soar, Educational Leadership, December 1983/January 1984, pp. 52-53.

Windsor, K. (2003) Primary Problems Solved Without Sheets, Mathematics Teaching, No.184, pp. 27-29.




How to Cite

Greene, C. (2021). Non Routine Mathematical Problem Solving with Lower Achieving Children. REACH: Journal of Inclusive Education in Ireland, 22(1), 13–23. Retrieved from