Threshold Concepts Vs. Tricky Topics - Exploring the Causes of Student´s Misunderstandings with the Problem Distiller Tool

Sara Cruz, José Alberto Lencastre, Clara Coutinho, Gill Clough, Anne Adams

2016

Abstract

This paper presents a study developed within the international project JuxtaLearn. This project aims to improve student understanding of threshold concepts by promoting student curiosity and creativity through video creation. The math concept of 'Division', widely referred in the literature as problematic for students, was recognised as a 'Tricky Topic' by teachers with the support of the Tricky Topic Tool and the Problem Distiller tool, two apps developed under the JuxtaLearn project. The methodology was based on qualitative data collected through Think Aloud protocol from a group of teachers of a public Elementary school as they used these tools. Results show that the Problem Distiller tool fostered the teachers to reflect more deeply on the causes of the students’ misunderstandings of that complex math concept. This process enabled them to develop appropriate strategies to help the students overcome these misunderstandings. The results also suggest that the stumbling blocks associated to the Tricky Topic ‘Division’ are similar to the difficulties reported in the literature describing Threshold Concepts. This conclusion is the key issue discussed in this paper and a contribution to the state of the art.

References

  1. Adams, A., Rogers, Y., Coughlan, T., Van-der-Linden, J., Clough, G., Martin, E., & Collins, T. (2013). Teenager needs in technology enhanced learning. Workshop on Methods of Working with Teenagers in Interaction Design, CHI 2013, Paris, France.
  2. Adams, A. & Clough, G. (2015). The E-assessment burger: Supporting the Before and After in EAssessment Systems. Interaction Design and Architecture(s) Journal - IxD&A, N.25, 2015, pp. 39- 57.
  3. Arends. R. I. (2008). Aprender a ensinar. Lisboa: McGrawHill.
  4. Clough, G., Adams, A., Cruz, S., Lencastre, J.A., & Coutinho, C. (2015). I just don't understand why they don't understand: Bridging the gaps in student learning. British Journal of Educational Technology. Submitted for evaluation.
  5. Bardin, L. (2013). Análise de conteúdo. Lisboa: Edições 70.
  6. Barradell, S., & Kennedy-Jones, M. (2013). Threshold concepts, student learning and curriculum: making connections between theory and practice. Innovations in Education and Teaching International, pp. 1-10.
  7. Bívar, A., Grosso, C., Oliveira, F., & Timóteo, M. C. (2012). Metas curriculares do ensino básico - matemática. Lisboa: Ministério da Educação e Ciência.
  8. Bogdan, R., & Biklen, S. (1994). Investigação Qualitativa em Educação. Uma introdução à teoria e aos métodos. Porto Editora: Porto.
  9. Brocardo, J., & Serrazina, L. (2008). O sentido do número no currículo de matemática. O sentido do número: Reflexões que entrecruzam teoria e prática, pp. 97- 115.
  10. Cascalho, J. M., Teixeira, R. E. C., & Ferreira, R. F. M. (2014). Cálculo mental na aula de matemática: explorações no 1. º ciclo do Ensino Básico.
  11. Coutinho, C. P. (2013). Metodologia de investigação em ciências sociais e humanas. Coimbra: Almedina.
  12. Cousin, G. (2006) An Introduction to Threshold concepts. Planet, 17, Available at http://www.sddu.leeds.ac.uk/uploaded/learningteaching-docs/teachtalk/5-12- 2008/cousin_threshold_concepts.pdf.
  13. Correa, J., Nunes, T., & Bryant, P. (1998). Young children's understanding of division: The relationship between division terms in a non-computational task. Journal of Educational Psychology, 90, pp. 321-329.
  14. Fernandes, D. R., &, Martins, F. M. (2014). Reflexão acerca do ensino do algoritmo da divisão inteira: proposta didática. Educação e Formação, (Vol. 9), pp.174-197.
  15. Fielder, S. (2007) The Teaching Assistants' Guide to Numeracy. London: Athenacum Press Ltd, Gateshead.
  16. Flores, R., Koontz, E., Inan, F. A., & Alagic, M. (2015). Multiple representation instruction first versus traditional algorithmic instruction first: Impact in middle school mathematics classrooms. Educational Studies in Mathematics, 89(2), pp. 267-281.
  17. Greer, B. (2012). Inversion in mathematical thinking and learning. Educational Studies in Mathematics, 79(3), pp. 429-438.
  18. Harlow, A., Scott, J., Peter, M., & Cowie, B. (2011) "Getting stuck" in Analogue Electronics: Threshold concepts as an Explanatory Model. European Journal of Engineering Education, (Vol. 36, 5), pp. 435-447.
  19. Hoppe, H. U., Erkens, M., Clough, G., Daems, O., & Adams, A. (2013) Using Network Text Analysis to Characterise Teachers' and Students' Conceptualisations in Science Domains. In Learning Analytics and Knowledge.
  20. Kenney, R., Shoffner, M., & Norris, D. (2014). Reflecting on the Use of Writing to Promote Mathematical Learning: An Examination of Preservice Mathematics Teachers' Perspectives. The Teacher Educator, 49(1), pp. 28-43.
  21. Kornilaki, E., & Nunes, T. (2005). Generalising principles in spite of procedural differences: Children's understanding of division. Cognitive Development, 20, pp. 388-406.
  22. Loertscher, J., Green, D., Lewis, J. E., Lin, S., & Minderhout, V. (2014). Identification of threshold concepts for biochemistry. CBE-Life Sciences Education, 13(3), pp. 516-528.
  23. Loertscher, J., Green, D., Lewis, J. E., Lin, S., & Minderhout, V. (2014). Identification of threshold concepts for biochemistry. CBE-Life Sciences Education, 13(3), pp. 516-528.
  24. Lucas, U. & Mladenovic, R. (2007) The potential of threshold concepts: an emerging framework for educational research and practice. London Review of Education, 5(3), pp. 237-248.
  25. Machiocha, A. (2014). Teaching research methods: threshold concept. In 13th European conference on research methods for business and management, London.
  26. Mendes, F. (2013). A aprendizagem da divisão: um olhar sobre os procedimentos usados pelos alunos. Da Investigação às Práticas, 3(2), pp. 5-30.
  27. Meyer, J. & Land, R. (2003) Threshold concepts and troublesome knowledge: linkages to ways of thinking and practising within the disciplines. In Rust, C. (Ed.) Improving student Learning - Theory and Practice Ten Years on. Oxford, Oxford Centre for Staff and Learning Development (OCSLD), pp.412-424.
  28. Meyer, J. & Land, R. (2006) Overcoming barriers to student understanding: Threshold concepts and Troublesome Knowledge. In Meyer, J. & Land, R. (Eds.) Overcoming Barriers to Student Understanding: Threshold concepts and Toublesome Knowledge. London and New York, Routledge, pp.19- 32.
  29. Meyer, J. H., Knight, D. B., Callaghan, D. P., & Baldock, T. E. (2015). An empirical exploration of metacognitive assessment activities in a third-year civil engineering hydraulics course. European Journal of Engineering Education,40(3), pp. 309-327.
  30. Montague, M. (2003). Teaching Division to Students With Learning Disabilities: A Constructivist Approach, Exceptionality: A Special Education Journal, 11:3, pp. 165-175.
  31. National Council of Teachers of Mathematics (NCTM 2008). Princípios e Normas para a Matemática Escolar. APM: Lisboa.
  32. Northcote, M. T. (2014). Threshold Concepts and Attitudes in Mathematics Education: Listening to Students' Past, Present and Projected Stories. Education Conference Papers. Paper 15.
  33. Nunes, T., Bryant, P., Evans, D., & Barros, R. (2015). Assessing Quantitative Reasoning in Young Children. Mathematical Thinking and Learning, 17(2- 3), pp. 178-196.
  34. Squire, S., & Bryant, P. (2002a). The influence of sharing on children's initial concept of division. Journal of Experimental Child Psychology, 81, pp. 1-43.
  35. Squire, S., & Bryant, P. (2002b). From sharing to dividing: Young children's understanding of division. Developmental Science, 5(4), pp. 452-466.
  36. Unlu, M., & Ertekin, E. (2012). Why do pre-service teachers pose multiplication problems instead of division problems in fractions? Procedia-Social and Behavioral Sciences, 46, pp. 490-494.
  37. Van Someren, M. W., Barnard, Y., & Sandberg, J. (1994). The Think Aloud Method: A Practical Guide to Modeling Cognitive Processes. London: Academic Press.
  38. Zhao, N., Valcke, M., Desoete, A., Burny, E., & Imbo, I. (2014). Differences between Flemish and Chinese primary students' mastery of basic arithmetic operations. Educational Psychology, 34(7), pp. 818- 837.
Download


Paper Citation


in Harvard Style

Cruz S., Lencastre J., Coutinho C., Clough G. and Adams A. (2016). Threshold Concepts Vs. Tricky Topics - Exploring the Causes of Student´s Misunderstandings with the Problem Distiller Tool . In Proceedings of the 8th International Conference on Computer Supported Education - Volume 1: CSEDU, ISBN 978-989-758-179-3, pages 205-215. DOI: 10.5220/0005908502050215


in Bibtex Style

@conference{csedu16,
author={Sara Cruz and José Alberto Lencastre and Clara Coutinho and Gill Clough and Anne Adams},
title={Threshold Concepts Vs. Tricky Topics - Exploring the Causes of Student´s Misunderstandings with the Problem Distiller Tool},
booktitle={Proceedings of the 8th International Conference on Computer Supported Education - Volume 1: CSEDU,},
year={2016},
pages={205-215},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005908502050215},
isbn={978-989-758-179-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 8th International Conference on Computer Supported Education - Volume 1: CSEDU,
TI - Threshold Concepts Vs. Tricky Topics - Exploring the Causes of Student´s Misunderstandings with the Problem Distiller Tool
SN - 978-989-758-179-3
AU - Cruz S.
AU - Lencastre J.
AU - Coutinho C.
AU - Clough G.
AU - Adams A.
PY - 2016
SP - 205
EP - 215
DO - 10.5220/0005908502050215