Exploring the impact of changes in my practice on one pupil’s learning in mathematics. Joseph – A case study

Authors

  • Anne T. Mulligan Middlesex University, London

DOI:

https://doi.org/10.18778/2450-4491.06.12

Keywords:

action research, generalising, collaborative environment, strategies

Abstract

This case study emerged from Action Research involving Year 2 pupils. The purpose of the research was to examine the effect that changing my practice had on my pupils’ learning in mathematics. I focused on Joseph, a higher attaining pupil and explored how his behaviour changed as I began to change aspects of my teaching. My research questions focused on tasks I provided for pupils, strategies they used to find solutions and my use of questioning to challenge their thinking. The data came from lesson observations, transcripts, samples of pupils’ work and notes from my research diary. Qualitative methods such as theme and comparative analysis were employed to analyse the data using a grounded theory approach. This case study does not claim that because one pupil experienced these changes they were experienced by all. It shows the changes that are possible when an environment of collaborative problem solving is created.

Author Biography

Anne T. Mulligan, Middlesex University, London

Ph.D., Senior Lecturer at the Middlesex University in London, teaching primary mathematics and geography on the Initial Teacher Education programs. With over 20 years of experience in teaching in the primary classroom, including 4 years as a Deputy Head Teacher, Anne’s areas of interest include problem-solving and anxiety in mathematics.

References

Altrichter R., Feldman A., Posch P., Somekh B. (2008) Teachers Investigate their Work (2 ed.), London, Routledge.
Google Scholar

Anghileri J. (1989) An Investigation of Young Children’s Understanding of Multiplication, “Educational Studies in Mathematics”, 20: 367–385.
Google Scholar

Bassey M. (1999) Case study research in educational settings, Open University Press.
Google Scholar

Carpenter T. P., Ansell E., Franke M. L., Fennema E., Weisbeck L. (1993) Models of Problem Solving: A Study of Kindergarten Children’s Problem-Solving Processes, “Journal for Research in Mathematics Education”, 24: 428–444.
Google Scholar

Carpenter T. P., Levi L. (2000) Developing conceptions of algebraic reasoning in the primary grades, Res. Rep. 00-2.Univ. Madison, WI: National Centre for Improving Student Learning and Achievement in Mathematics and Science.
Google Scholar

Carpenter T. P., Moser J. M. (1984) The Acquisition of Addition and Subtraction Concepts in Grades One through Three, “Journal for Research in Mathematics Education”, 15: 179–202.
Google Scholar

Cohen L., Manion L., Morrison K. (2005) Research Methods in Education, London, Routledge Falmer.
Google Scholar

Corbin J., Strauss A. (2008) Basics of Qualitative Research (3 ed.), London, Sage Publications Ltd.
Google Scholar

Denscombe M. (2005) The Good Research Guide, Maidenhead, Open University Press.
Google Scholar

Gerring J. (2007) Case study research: principles and practices, Cambridge University Press.
Google Scholar

Goos M., Galbraith P., Renshaw P. (2004) Establishing a community of practice in a secondary mathematics classroom in: B. Allen, S. Johnston-Wilder (eds.), Mathematics Education: Exploring the Culture of Learning, Falmer Pr.
Google Scholar

Herbert A., Feldman A., Posch P., Somekh B. (2008) Teachers Investigate Their Work: An Introduction to Action Research Across the Professions, 2nd Edition, New York, Routledge.
Google Scholar

Hewitt D. (1994) Train spotters’ paradise, “Teaching Mathematics”: 47–51.
Google Scholar

Kaput J., Blanton M. (1999) Algebraic reasoning in the context of elementary mathematics: making it implementable on a massive scale, https://files.eric.ed.gov/fulltext/ED441663.pdf
Google Scholar

Kilpatrick M. (2003) Why did you say right angles?, The place of questioning in mathematics, ACE Papers,https://researchspace.auckland.ac.nz/bitstream/handle/2292/25116/ACE_Paper_5_Issue_12.pdf?sequence=1
Google Scholar

Macdonald B., Walker R. (1974) Case-study and The Social Philosophy of Educational Research, “Cambridge Journal of Education”, 5 (1): 2–11.
Google Scholar

Martino A. M., Maher C. A. (1999) Teacher Questioning to Promote Justification and Generalization in Mathematics: What Research Practice Has Taught Us, “The Journal of Mathematical Behavior”, 18: 53–78.
Google Scholar

Mason J. (1999) Learning and doing mathematics, (2 ed.), York, QED.
Google Scholar

Mercer N., Sams C. (2006) Teaching children how to use language to solve maths problems, “Language and Education”, 20 (6): 507–528.
Google Scholar

Mitchelmore M. C. (2002) The role of abstraction and generalisation in the development of mathematical knowledge, “Mathematics Education for a Knowledge-Based Era”, 2: 157–167.
Google Scholar

Mulligan J., Watson J. (1998) A developmental multimodal model for multiplication and division, “Mathematics Education Research Journal”, 10: 61–86.
Google Scholar

Nicholls J. G., Cobb P., Wood T., Yackel E., Patashnick M. (1990) Assessing students’ theories of success in mathematics: Individual and classroom differences, “Journal for Research in Mathematics Education”, 21: 109–122.
Google Scholar

Nolas Sevasti-Melissa (2011) Grounded theory in: Frost Nollaig (ed.), Qualitative Research Methods in Psychology: Combining Core Approaches, Maidenhead, Open University Press: 16–43.
Google Scholar

Rojas-Drummond S., Mercer N. (2003) Scaffolding the development of effective collaboration and learning, “International Journal of Educational Research”, 39:99–111.
Google Scholar

Rowley J. (2002) Using case studies in research, “Management Research News”, 25: 16–27.
Google Scholar

Secada W. G., Fuson K. C., Hall J. W. (1983) The Transition from Counting-all to Counting-on in Addition, “Journal for Research in Mathematics Education”, 14: 47–57.
Google Scholar

Simons H. (1996) The paradox of case study, “Cambridge Journal of Education”, 26. Stake R. E. (1978) The Case Study Method in Social Inquiry, “Educational Researcher”,7: 5–8.
Google Scholar

Stake R. E. (1995) The art of case study research, Sage Publications, Inc.
Google Scholar

Steinberg R. M. (1985) Instruction on Derived Facts Strategies in Addition and Subtraction, “Journal for Research in Mathematics Education”, 16: 337–355.
Google Scholar

Sullivan P., Warren E., White P. (2000) Students’ responses to content specific openended mathematical tasks, “Mathematics Education Research Journal”, 12: 2–17.
Google Scholar

Tobin K. (1987) The Role of Wait Time in Higher Cognitive Level Learning, “Review of Educational Research”, 57: 69–95.
Google Scholar

Wegerif R., Littleton K., Dawes L., Mercer N., Rowe D. (2004) Widening access to educational opportunities through teaching children how to reason together, “Westminster Studies in Education”, 27 (2): 143–156.
Google Scholar

Yin R. K. (2009) Case study research: Design and methods, 4th ed., Thousand Oaks, Sage Publications, Inc.
Google Scholar

Zazkis R., Liljedahl P., Chernoff E. J. (2008) The role of examples in forming and refuting generalizations, “ZDM Mathematics Education”, 40: 131–141.
Google Scholar

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Published

2018-10-19

How to Cite

Mulligan, A. T. (2018). Exploring the impact of changes in my practice on one pupil’s learning in mathematics. Joseph – A case study. Nauki O Wychowaniu. Studia Interdyscyplinarne, 6(1), 143–160. https://doi.org/10.18778/2450-4491.06.12