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

• Authors: Anne T. Mulligan

Title variants

Badanie wpływu zmiany sposobu nauczania matematyki na jednego z moich uczniów. Joseph – studium przypadku

• Languages of publication: EN

Abstracts

EN

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.

PL

Analizowane studium przypadku powstało w ramach badania w działaniu obejmującego uczniów szkoły podstawowej, w wieku 6 i 7 lat. Celem tego badania było zmierzenie wpływu zmian moich praktyk nauczania matematyki na moich uczniów. W moich badaniach skupiłam się na uczniu o imieniu Joseph, który osiągał bardzo dobre wyniki w szkole, i zbadałam, jak jego zachowanie zmieniło się pod wpływem zmiany sposobu mojego nauczania. Moje pytania badawcze koncentrowały się na zadaniach, które przygotowywałam dla uczniów. Ponadto skupiłam się na strategiach używanych przez moich uczniów do znalezienia rozwiązań. W pytaniach badawczych skoncentrowałam się na moim sposobie zadawania pytań, aby pobudzić uczniów do myślenia. Dane, wykorzystywane w badaniach, pochodziły z obserwacji lekcji, transkrypcji prac uczniów i notatek z moich badań. Metody jakościowe, takie jak analiza tematyczna i analiza porównawcza, zostały wykorzystane do analizy danych przy zastosowaniu podejścia metodologii teorii ugruntowanej. To studium przypadku nie dowodzi zmiany, z uwagi na fakt, że doświadczył tych zmian jeden uczeń, nie wpływaliśmy poprzez zmianę na wszystkich uczniów. To studium przypadku pokazuje zmiany, które są możliwe, gdy współtworzone jest środowisko wspólnego rozwiązywania problemów.

Keywords

EN

action research; generalising; collaborative environment; strategies

PL

badanie w działaniu; uogólnienie; współtworzone środowisko; strategie; badanie w działaniu; uogólnienie; współtworzone środowisko; strategie

• Publisher: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
• Journal: Nauki o Wychowaniu. Studia Interdyscyplinarne
• Year: 2018
• Volume: 6
• Issue: 1
• Pages: 143-160

Dates

published

2018-06-30

Contributors

author

Anne T. Mulligan

• Middlesex University, London

References

• Altrichter R., Feldman A., Posch P., Somekh B. (2008) Teachers Investigate their Work (2 ed.), London, Routledge.
• Anghileri J. (1989) An Investigation of Young Children’s Understanding of Multiplication, “Educational Studies in Mathematics”, 20: 367–385.
• Bassey M. (1999) Case study research in educational settings, Open University Press.
• 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.
• 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.
• 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.
• Cohen L., Manion L., Morrison K. (2005) Research Methods in Education, London, Routledge Falmer.
• Corbin J., Strauss A. (2008) Basics of Qualitative Research (3 ed.), London, Sage Publications Ltd.
• Denscombe M. (2005) The Good Research Guide, Maidenhead, Open University Press.
• Gerring J. (2007) Case study research: principles and practices, Cambridge University Press.
• 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.
• 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.
• Hewitt D. (1994) Train spotters’ paradise, “Teaching Mathematics”: 47–51.
• 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
• 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
• Macdonald B., Walker R. (1974) Case-study and The Social Philosophy of Educational Research, “Cambridge Journal of Education”, 5 (1): 2–11.
• 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.
• Mason J. (1999) Learning and doing mathematics, (2 ed.), York, QED.
• Mercer N., Sams C. (2006) Teaching children how to use language to solve maths problems, “Language and Education”, 20 (6): 507–528.
• 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.
• Mulligan J., Watson J. (1998) A developmental multimodal model for multiplication and division, “Mathematics Education Research Journal”, 10: 61–86.
• 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.
• Nolas Sevasti-Melissa (2011) Grounded theory in: Frost Nollaig (ed.), Qualitative Research Methods in Psychology: Combining Core Approaches, Maidenhead, Open University Press: 16–43.
• Rojas-Drummond S., Mercer N. (2003) Scaffolding the development of effective collaboration and learning, “International Journal of Educational Research”, 39:99–111.
• Rowley J. (2002) Using case studies in research, “Management Research News”, 25: 16–27.
• 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.
• 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.
• Stake R. E. (1995) The art of case study research, Sage Publications, Inc.
• Steinberg R. M. (1985) Instruction on Derived Facts Strategies in Addition and Subtraction, “Journal for Research in Mathematics Education”, 16: 337–355.
• Sullivan P., Warren E., White P. (2000) Students’ responses to content specific openended mathematical tasks, “Mathematics Education Research Journal”, 12: 2–17.
• Tobin K. (1987) The Role of Wait Time in Higher Cognitive Level Learning, “Review of Educational Research”, 57: 69–95.
• 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.
• Yin R. K. (2009) Case study research: Design and methods, 4th ed., Thousand Oaks, Sage Publications, Inc.
• Zazkis R., Liljedahl P., Chernoff E. J. (2008) The role of examples in forming and refuting generalizations, “ZDM Mathematics Education”, 40: 131–141.

Identifiers

DOI

10.18778/2450-4491.06.12