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Scaffolding for mathematics teaching in inclusive primary classrooms: a video study

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Abstract

Scaffolding is an important tool for meeting the challenging needs of heterogeneous groups of students in inclusive classrooms. It is especially useful when supporting low achievers. A video study (funded by the Swiss National Science Foundation, Project Nr. 134652) of 36 inclusive classes, (3rd grade, aged 9 years), was conducted to examine how classroom teachers and special education teachers implemented a remedial mathematics program in a classroom setting. The program focused on the following facets of scaffolding: cognitive activation, stimulating discourse, handling errors productively, target orientation, and using manipulatives. The results show that 54 % of the teachers achieved a high competency for using manipulatives and target orientation, facets for which the program provided more detailed instructions. The teachers attained lower values for stimulating discourse, cognitive activation, and handling errors productively, where the program offered more general guidance. The special education teachers had lower rating scores than the classroom teachers, although the same scoring pattern as the teachers. This study shows that it is possible to encourage the use of scaffolding in inclusive classrooms. However, the disparate results for the different facets imply that scaffolding in classroom situations is a competency that cannot simply be adopted from a “program”, and more intensive teacher training programs seem to be necessary.

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References

  • Alexander, R. (2008). Towards dialogic teaching. Rethinking classroom talk (4th ed.). Cambridge: Dialogos.

    Google Scholar 

  • Andersson, U. (2010). Skill development in different components of arithmetic and basic cognitive functions: Findings from a 3-year longitudinal study of children with different types of learning disabilities. Journal of Educational Psychology, 102(1), 115–134.

    Article  Google Scholar 

  • Applebee, A. N., & Langer, J. A. (1983). Instructional scaffolding: Reading and writing as natural language activities. Language Arts, 60(2), 168–175.

    Google Scholar 

  • Beck, E., Baer, M., Guldimann, T., Bischoff, S., Brühwiler, C., Müller, P., & Vogt, F. (2008). Adaptive Lehrkompetenz: Analyse und Struktur, Veränderbarkeit und Wirkung handlungssteuernden Lehrerwissens [Adaptive teaching competence: Analysis and structure, changeability and effects of guiding teacher competence]. Münster: Waxmann.

    Google Scholar 

  • Campbell, P. F., & Malkus, N. N. (2014). The mathematical knowledge and beliefs of elementary mathematics specialist-coaches. ZDM - The International Journal on Mathematics Education, 46(2), 213–225.

    Article  Google Scholar 

  • Corno, L., & Snow, R. E. (1986). Adapting teaching to individual differences among learners. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd ed., pp. 605–629). New York: Macmillan.

    Google Scholar 

  • Freesemann, O. (2014). Schwache Rechnerinnen und Rechner fördern. Eine Interventionsstudie an Haupt-, Gesamt- und Förderschulen [Fostering students with learning difficulties in mathematics. An intervention study in middleschool]. Wiesbaden: Springer Spektrum.

    Google Scholar 

  • Fuchs, L. S., Fuchs, D., & Compton, D. L. (2012). The early prevention of mathematics difficulty: Its power and limitations. Journal of Learning Disabilities, 45(3), 257–269.

    Article  Google Scholar 

  • Fuchs, L. S., Powell, S. R., Hamlett, C. L., Fuchs, D., Cirino, P. T., & Fletcher, J. M. (2008). Remediating computational deficits at third grade: A randomized field trial. Journal of Research on Educational Effectiveness, 1(1), 2–32.

    Article  Google Scholar 

  • Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, O., & Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79, 1202–1242.

    Article  Google Scholar 

  • Hammond, J., & Gibbons, P. (2005). Putting scaffolding to work: The contribution of scaffolding in articulating ESL education. Prospect, 20(1), 6–30.

    Google Scholar 

  • Heward, W. L. (2003). Ten faulty notions about teaching and learning that hinder the effectiveness of special education. The Journal of Special Education, 36(4), 186–205.

    Article  Google Scholar 

  • Jones, N. D., & Brownell, M. T. (2014). Examining the use of classroom observations in the evaluation of special education teachers. Assessment for Effective Intervention, 39(2), 112–124.

    Article  Google Scholar 

  • Krammer, K. (2009). Individuelle Lernunterstützung in Schülerarbeitsphasen. Eine videobasierte Analyse des Unterstützungsverhaltens von Lehrpersonen im Mathematikunterricht [Teachers’ assistance of individual students in mathematics lessons: A video-based study]. Münster: Waxmann.

    Google Scholar 

  • Lepper, M. R., Drake, M. F., & O’Donnell-Johnson, T. (1997). Scaffolding techniques of expert human tutors. In K. Hogan & M. Pressley (Eds.), Scaffolding student learning. Instructional approaches and issues (pp. 108–144). Cambridge: Brookline Books.

    Google Scholar 

  • Lipowsky, F. (2004). Was macht Fortbildungen für Lehrkräfte erfolgreich? Befunde und mögliche Konsequenzen für die Praxis [What makes an in-service training successful for the teachers? Findings and possible implications for practice]. Die Deutsche Schule, 96, 462–479.

    Google Scholar 

  • Mazzocco, M. M. M., Devlin, K. T., & McKenney, S. J. (2008). Is it a fact? Timed arithmetic performance of children with mathematical learning disabilities (MLD) varies as a function of how MLD is defined. Developmental Neuropsychology, 33(3), 318–344.

    Article  Google Scholar 

  • Montague, M. (2011). Effective instruction in mathematics for students with learning difficulties. In C. Wyatt-Smith, J. Elkins & S. Gunn (Eds.), Multiple perspectives on difficulties in learning literacy and numeracy (pp. 295–313). doi:10.1007/978-1-4020-8864-3_14.

  • Moser Opitz, E. (2013). Rechenschwäche – Dyskalkulie: Theoretische Klärungen und empirische Studien an betroffenen Schülerinnen und Schülern [Learning disabilities in mathematics: Theoretical foundations and empirical studies] (2nd ed.). Bern: Haupt.

    Google Scholar 

  • Murphy, M. M., Mazzocco, M. M., Hanich, L. B., & Early, M. C. (2007). Cognitive characteristics of children with mathematics learning disability (MLD) vary as a function of the cutoff criterion used to define MLD. Journal of Learning Disabilities, 40(5), 458–478.

    Article  Google Scholar 

  • Nougaret, A. A., Scruggs, T. E., & Mastropieri, M. A. (2005). Does teacher education produce better special education teachers? Exceptional Children, 71(3), 217–229.

    Article  Google Scholar 

  • Pedrotty Bryant, D., Bryant, B. R., Gersten, R., Scammacca, N., & Chavez, M. M. (2008). Mathematics intervention for first- and second-grade students with mathematics difficulties: The effects of Tier 2 intervention delivered as booster lessons. Remedial and Special Education, 29(1), 20–32.

    Article  Google Scholar 

  • Pfister, M., Stöckli, M., Moser Opitz, E., & Pauli, C. (2015). Inklusiven Mathematikunterricht erforschen: Herausforderungen und erste Ergebnisse aus einer Längsschnittstudie [Investigating mathematics teaching in inclusive classrooms: Challenges and first results of a longitudinal study]. Unterrichtswissenschaft, 43(1), 53–67.

    Google Scholar 

  • Praetorius, A.-K. (2014). Messung von Unterrichtsqualität durch Ratings [Measuring teaching quality by ratings]. Münster: Waxmann.

    Google Scholar 

  • Rakoczy, K., & Pauli, C. (2006). Hoch inferentes Rating: Beurteilung der Qualität unterrichtlicher Prozesse [High-inference rating: Evaluating the quality of teaching processes]. In I. Hugener, C. Pauli, & K. Reusser (Eds.), Videoanalysen [Video analysis] (Vol. 15, pp. 206–233). Frankfurt am Main: DIPF.

    Google Scholar 

  • Rittle-Johnson, B. (2006). Promoting transfer: Effects of self-explanation and direct instruction. Child Development, 77(1), 1–15.

    Article  Google Scholar 

  • Smit, J., van Eerde, H. A. A., & Bakker, A. (2013). A conceptualisation of whole-class scaffolding. British Educational Research Journal, 39(5), 817–834.

    Article  Google Scholar 

  • Stöckli, M., Moser Opitz, E., Pfister, M., & Reusser, L. (2014). Gezielt fördern, differenzieren und trotzdem gemeinsam lernen – Überlegungen zum inklusiven Mathematik-unterricht [Remediation, differentiation and learning together – Reflections on inclusive mathematics teaching]. Sonderpädagogische Förderung heute, 59(1), 44–56.

    Google Scholar 

  • Stone, C. A. (1998). The metaphor of scaffolding: Its utility for the field of learning disabilities. Journal of Learning Disabilities, 31(4), 344–364.

    Article  Google Scholar 

  • United Nations (2006). Convention on the rights of persons with disabilities. Accessed 10 Nov 2014. http://www.un.org/esa/socdev/enable/rights/convtexte.htm.

  • van de Pol, J., Volman, M., & Beishuizen, J. (2010). Scaffolding in teacher-student interaction: A decade of research. Educational Psychological Review, 22, 271–296.

    Article  Google Scholar 

  • Williams, S. R., & Baxter, J. A. (1996). Dilemmas of discourse-oriented teaching in one middle school mathematics classroom. The Elementary School Journal, 97(1), 21–38.

    Article  Google Scholar 

  • Wißmann, J., Heine, A., Handl, P., & Jacobs, A. M. (2013). Förderung von Kindern mit isolierter Rechenschwäche und kombinierter Rechen- und Leseschwäche: Evaluation eines numerischen Förderprogramms für Grundschüler [Fostering students with mathematical disease and combined mathematical and reading disease: Evaluation of a numeric remedial program in primary schools]. Lernen und Lernstörungen, 2(2), 91–109.

    Article  Google Scholar 

  • Wood, D. (2001). Scaffolding, contingent tutoring and computer-supported learning. International Journal of Artificial Intelligence in Education, 12, 280–292.

    Google Scholar 

  • Wood, D., Bruner, J. S., & Ross, G. (1976). The role of tutoring in problem solving. Journal of Child Psychology and Psychiatry, 17, 89–100.

    Article  Google Scholar 

  • Woodward, J., & Brown, C. (2006). Meeting the curricular needs of academically low-achieving students in middle grade mathematics. Journal of Child Psychology and Psychiatry, 17, 89–100.

    Article  Google Scholar 

Download references

Acknowledgments

We thank the Swiss National Science Foundation for funding the research. We would like to thank our former students Pia Kessler and Noemi Lüscher for their great help with the video rating.

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Authors and Affiliations

  1. Institut für Erziehungswissenschaft, Universität Zürich, Hirschengraben 48, 8001, Zurich, Switzerland

    Mirjam Pfister & Elisabeth Moser Opitz

  2. Departement Erziehungswissenschaften, Universität Freiburg/Fribourg, Rue Faucigny 2, 1700, Fribourg, Switzerland

    Christine Pauli

Authors
  1. Mirjam Pfister
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  2. Elisabeth Moser Opitz
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  3. Christine Pauli
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Correspondence to Mirjam Pfister.

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Pfister, M., Moser Opitz, E. & Pauli, C. Scaffolding for mathematics teaching in inclusive primary classrooms: a video study. ZDM Mathematics Education 47, 1079–1092 (2015). https://doi.org/10.1007/s11858-015-0713-4

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