How Do Mathematics Teachers Use Scaffolding During Their Lessons in Lower Secondary Schools?
Author(s):
Roar Bakken Stovner (presenting / submitting)
Conference:
ECER 2017
Format:
Paper (Copy for Joint Session)

Session Information

24 SES 06 JS, Cultural Approach in Mathematics Education

Joint Paper Session NW 24 and NW 27

Time:
2017-08-23
15:30-17:00
Room:
K6.04
Chair:
Florence Ligozat

Contribution

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.

Method

Our analyses draw on recorded videos from mathematics instruction in Norwegian lower secondary classrooms. The data consists of 196 videos of 49 teachers from different schools, all teaching a class of 13-14 years old students across four consecutive lessons (45-60 minutes each). To represent the full variety of Norwegian schools, we sampled both urban and rural schools in several Norwegian districts, including schools with high and low gains on national tests in numeracy. The videos were collected in the school year August 2014 to June 2015 and were captured with two video cameras, one focusing on the teacher and one focusing on the class. The videos were coded using an observational coding manual called Protocol for Language Arts Teaching Observation (PLATO), which has been modified to analyze mathematics instruction as well (Cohen, Grossman, Borko, Loeb, & Shavelson, 2013). We used an existing coding manual to i. enable comparisons with other studies, ii. make interpretations explicit and reproducible and iii. because the manual has been validated in several large-scale studies (e.g. Kane, 2012). To check for inter- and intra-rater reliability, no teacher is coded by only one coder and 10% of the material is coded by two coders. For the present analysis, we used only two PLATO-codes, namely Feedback and Modelling. Four levels of feedback are coded: the teacher 1) gives no feedback 2) only gives perfunctory feedback like “good”, “correct”, etc. 3) gives procedural feedback on how to complete the task or 4) gives substantial feedback focusing on the underlying skills. Similarly, the four levels of modelling are: the teacher 1) does not model 2) models incompletely or only to some students 3) models the task completely 4) models the meta-cognitive skills used in completing the task. With this coding, we obtain a summary view of which teachers assist students through either modelling or feedback or both. Looking across all the coded classrooms, a purposive stratified sample of some teachers will be described in more detail. The sample is chosen to give a range of modelling- and feedback-practices and a range of student achievement gains on the national test in numeracy. A display of the modelling- and feedback-practices of these teachers will be discussed, and we will look for persistent differences in modelling and feedback in classes with different achievement gains.

Expected Outcomes

Our preliminary findings show interesting patterns in the data that we will discuss and exemplify in our presentation. Regarding step two of scaffolding, responsiveness, a preliminary finding is that Norwegian mathematics teachers generally give students extensive assistance with procedures, clearly modelling procedures and giving feedback on them. We also found that Norwegian teachers almost never assist students with misconceptions or meta-cognitive processes. This is evident in the codes for both feedback and modelling, showing that teachers generally give only perfunctory or procedural feedback and that very few teachers model the thought processes needed to complete a task. Regarding step three of scaffolding, fading, it seems that each teachers’ instructional assistance is fairly constant, and we found no proof of fading through the PLATO codes alone. For example, a teacher who in the beginning of the first lesson is observed to say “good”, “correct” or give procedural explanations when students have made mistakes, is highly likely to give such feedback throughout all four lessons and to all students. Conversely, also teachers who give careful feedback about students’ ideas, are likely to do this across all four lessons. These findings show that scaffolding is a skill not yet enacted by Norwegian teachers and that teachers’ assistance stays fairly constant throughout a medium-long timescale of four lessons. Further analyses might discover some teachers who successfully enact scaffolding, revealing clues to how they accomplish it. The final results from this study should inform future professional development and teacher education programs and uncover new directions for research on mathematics instruction.

References

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

Author Information

Roar Bakken Stovner (presenting / submitting)
University of Oslo, Norway

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