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Metacognitive and discursive activities – an intellectual kernel of classroom discussions in learning mathematics
Elmar Cohors-Fresenborg
To cite this version:
Elmar Cohors-Fresenborg. Metacognitive and discursive activities – an intellectual kernel of classroom discussions in learning mathematics. Eleventh Congress of the European Society for Research in Mathematics Education, Utrecht University, Feb 2019, Utrecht, Netherlands. �hal-02435264�
Metacognitive and discursive activities – an intellectual kernel of classroom discussions in learning mathematics
Elmar Cohors-Fresenborg
University of Osnabrueck, Department of Mathematics, Osnabrueck, Germany; [email protected] Keywords: Classroom discussions, instructional quality, metacognition.
Theoretical background
Although metacognition is widely regarded as a promoter of sustainable learning processes (Dignath & Büttner, 2009), little is known about the implementation of metacognition and the mode of its functioning in classroom communications (Lingel, Neuenhaus, Artelt, & Schneider, 2014).
When metacognition during classroom discussions is in the scope of interest, its conceptualization must refer to a broader scope of activities than in the case of problem solving. It cannot be restricted to metacognitive processes understood as cognition about one’s own or others cognition, but should take into account also cognition about the inputs, subjects and results of cognition (calculation, ver- bal or written information, argumentations, questions). According to this conceptualization, the ob- jectives of metacognition in learning mathematics are, for example, to plan the use of mathematical tools, methods, and representations to justify an argumentation or to explain an idea; to control and evaluate the accurateness of argumentations, the adequateness of external (e.g. formal) or internal representations of mathematical concepts, the correctness of the use of tools and procedures; to re- flect on the ways of reasoning, defining or proving, and on similarities and differences in concep- tions and arguments. The learning process in a class can lead to a deep understanding of concepts, representations and tools only if the planning, monitoring and reflection related to them are elabo- rated, take students’ ways of thinking into consideration, and build a coherent discourse. Therefore, the class discussion must feature discursivity. Discursivity means activities carried out to support the coherence and precision of a discussion. On the contrary, negative discursivity means activities with a negative influence on understanding what is meant (Cohors-Fresenborg & Kaune, 2007).
A rating system for evaluating metacognitive-discursive instructional quality
During the last three years1, we worked on the design of a rating system for evaluating metacogni- tive-discursive instructional quality in different school subjects. The rating procedure consists of two levels: first an extended version of the category system developed by Cohors-Fresenborg and Kaune (2007) is used to categorize metacognitive and discursive activities in students’ and teacher’s utterances; then, seven high inference rating scales are used for a global rating of the instructional quality of these activities in the given lesson (Nowińska, 2016). Each scale consists of an item (guiding question) focusing rater’s attention on aspects to be evaluated, and of 3-5 answers describ- ing in detail how these aspects are reflected in the discussion. The two-level rating procedure was tested and evaluated in the DFG-project, based on 24 videotaped lessons (6 teachers/classes à 4 les- sons, grade 6 and 7). For 6 out of 7 rating scales, the generalizability studies indicate a high inter-
1 A research project supported by the DFG (German Science Foundation) under the reference CO 96/8-1.
rater reliability and a relatively high stability of the evaluated aspects across lessons (g-coefficients
>0.78); only 3 lessons per class/teacher would be needed to get reliable and generalizable (over the lessons) assessments of the 6 aspects of the instructional quality (Nowińska & Praetorius, 2017).
Some Insights from the Qualitative Lessons Analysis
When analyzing lessons an interesting type was observed in the case of some teachers/classes: there are many metacognitive, discursive, and only few negative discursive activities; but the class dis- cussions are only on the surface of the underlying problems. If the mathematical content becomes a little bit more substantial, then the inability of the teacher and the students for elaborate metacogni- tive mathematical activities breaks through, and indicates the lack of metacognitive-discursive edu- cation of this class. Now, the classroom discussion shows a lot of metacognitive activities, but also lots of negative discursivity. Consequently, the global rating of the metacognitive-discursive in- structional quality leads to many low marks: the metacognitive activities are not elaborate, do not build a coherent discourse, and therefore the students do not learn something substantial in this class. This observation is contrary to our hidden theory underlying the invention and use of the pri- mary version of the category system (Cohors-Fresenborg & Kaune, 2007), as it was represented in this paper. The new observation can explain the low correlations between observed metacognition and learning achievements as sometimes reported in the literature. We assume that high ratings achieved with the two-level rating system are needed for a deep understanding of mathematics, and that such ratings can be regarded as an indicator for an intellectual kernel of classroom discussions in learning mathematics.
References
Cohors-Fresenborg, E., & Kaune, C. (2007). Modelling classroom discussions and categorising discursive and metacognitive activities. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (pp.
1180–1189). Larnaca, Cyprus: University of Cyprus and ERME.
Dignath, C., & Büttner, G. (2009). Components of fostering self-regulated learning among students:
A meta-analysis on intervention studies at primary and secondary school level. Metacognition and Learning, 3, 231–264.
Lingel, K., Neuenhaus, N., Artelt, C., & Schneider, W. (2014). Der Einfluss des metakognitiven Wissens auf die Entwicklung der Mathematikleistung am Beginn der Sekundarstufe I [The influ- ence of metacognitive knowledge on the development of mathematical performance at the be- ginning of lower secondary education]. Journal für Mathematikdidaktik, 35, 49–77.
Nowińska, E. (2016). The design of a high inference rating system for an evaluation of metacognitiv-discursive teaching and learning quality. In S. Zehetmeier, B. Rösken-Winter, D.
Potari, & M. Ribeiro (Eds.), Proceedings of the ERME Topic Conference on Mathematics Teach- ing, Resources and Teacher Professional Development (pp. 46–55) Berlin, Germany: ERME.
Nowińska, E. & Praetorius, A.-K. (2017). Evaluation of a rating system for the assessment of meta- cognitive-discursive instructional quality. In T. Dooley & G. Gueudet (Eds.), Proceedings of the
Tenth Congress of the European Society for Research in Mathematics Education (pp. 3121–
3128). Dublin, Ireland: DCU Institute of Education and ERME.
