24 SES 06 JS, Cultural Approach in Mathematics Education
Joint Paper Session NW 24 and NW 27
Improving students’ mathematical outcomes is on the forefront of many European governments’ educational agendas (Kunnskapsdepartementet, 2014; Nath & Border, 2013; OECD, 2016; Silver, 1998) and teachers’ instructional practices in mathematics classrooms has received much attention since it is an important factor for student learning (Chetty, Friedman, & Rockoff, 2011; Hattie, 2008; Seidel & Shavelson, 2007). One central instructional practice introduced to aid students’ learning is scaffolding, “the process that enables a child or novice to solve a problem, carry out a task, or achieve a goal which would be beyond his unassisted efforts” (Wood, Bruner, & Ross, 1976, p. 90). The current empirical research consists of either case-studies, giving existence proofs of effective scaffolding in mathematics, or experimental studies, showing that scaffolding practices can be successfully implemented in schools (Bakker, Smit, & Wegerif, 2015). What remains an unanswered question, is how mathematics teachers currently scaffold the learning content in their everyday instruction. In the present study, we contribute to the understanding of this question by investigating everyday scaffolding practices enacted by Norwegian mathematics teachers captured through video observation.
The idea of scaffolding was initially used only about dyadic adult-child interactions (e.g. Wood et al., 1976), but has recently been used to analyze whole-class interactions in mathematics classrooms as well (Smit & van Eerde, 2013). Whether in a dyadic- or group-setting, scaffolding has three characteristic steps, following (Bakker et al., 2015): i. diagnosis (finding out what the students can do alone or with scaffolds), ii. responsiveness (adaptively giving assistance) and iii. fading or handover to independence (withdrawing assistance). These three steps can be used for cognitive scaffolding (enabling students to solve problems without the teacher’s help), social scaffolding (establishing norms for productive classroom interactions) or affective scaffolding (increasing students’ self-efficacy or motivation). Of special interest to me is cognitive scaffolding learning and Anghileri (2006) argue that two central components for mathematics learning is modelling and feedback. Thus, the aim of our study is to describe cognitive scaffolding practices in Norwegian mathematics classrooms by identifying how teachers assist students in completing mathematical tasks through modelling or feedback and how the teachers fade this assistance within the course of four lessons.
Anghileri, J. (2006). Scaffolding practices that enhance mathematics learning. Journal of Mathematics Teacher Education, 9(1), 33–52. https://doi.org/10.1007/s10857-006-9005-9 Bakker, A., Smit, J., & Wegerif, R. (2015). Scaffolding and dialogic teaching in mathematics education: introduction and review. ZDM, 47(7), 1047–1065. https://doi.org/10.1007/s11858-015-0738-8 Chetty, R., Friedman, J. N., & Rockoff, J. E. (2011). The Long-Term Impacts of Teachers: Teacher Value-Added and Student Outcomes in Adulthood (Working Paper No. 17699). National Bureau of Economic Research. Retrieved from http://www.nber.org/papers/w17699 Cohen, J., Grossman, P., Borko, H., Loeb, S., & Shavelson, R. J. (2013). Practices that cross disciplines?: A closer look at instruction in elementary math and English language arts. Stanford University. Retrieved from http://purl.stanford.edu/sm582yp3336 Hattie, J. (2008). Visible Learning: A Synthesis of Over 800 Meta-Analyses Relating to Achievement. Routledge. Kane, T. J. |Staiger. (2012). Gathering Feedback for Teaching: Combining High-Quality Observations with Student Surveys and Achievement Gains. Research Paper. MET Project. Bill & Melinda Gates Foundation. Retrieved from https://eric.ed.gov/?id=ED540960 Kunnskapsdepartementet. (2014). Rapport fra ekspertgruppa for realfagene. Kunnskapsdepartementet. Retrieved from https://www.regjeringen.no/globalassets/upload/kd/vedlegg/rapporter/rapport_fra_ekspertgruppa_for_realfagene.pdf Nath, C., & Border, P. (2013). STEM education for 14-19 year olds. Parliamentary Office of Science and Technology, POST-PN-430. Retrieved from http://researchbriefings.parliament.uk/ResearchBriefing/Summary/POST-PN-430 OECD. (2016). Equations and Inequalities. Paris: OECD Publishing. Retrieved from http://dx.doi.org/10.1787/9789264258495-en Seidel, T., & Shavelson, R. J. (2007). Teaching Effectiveness Research in the Past Decade: The Role of Theory and Research Design in Disentangling Meta-Analysis Results. Review of Educational Research, 77(4), 454–499. https://doi.org/10.3102/0034654307310317 Silver, E. A. (1998). Improving Mathematics in Middle School: Lessons from TIMSS and Related Research. U.S. Government Printing Office, Superintendent of Documents, Mail Stop: SSOP, Washington, DC 20402-9328. Retrieved from https://eric.ed.gov/?id=ED417956 Smit, J., & van Eerde, D. (2013). What counts as evidence for the long-term realisation of whole-class scaffolding? Learning, Culture and Social Interaction, 2(1), 22–31. https://doi.org/10.1016/j.lcsi.2012.12.006 Wood, D., Bruner, J. S., & Ross, G. (1976). The Role of Tutoring in Problem Solving*. Journal of Child Psychology and Psychiatry, 17(2), 89–100. https://doi.org/10.1111/j.1469-7610.1976.tb00381.x
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