Students discussing their mathematical ideas: the role of the teacher

Abstract

This article adds to current research on enhancing student discourse in mathematics teaching specifically in secondary schools but with equal relevance to elementary schools. Three mathematics teachers in secondary education were confronted with the question of how to encourage students to discuss their work with each other in the daily practice of their mathematical lessons. In response to this question the teachers devised three different approaches to encourage student discourse. One of the teachers chose to experiment with another setting to perform mathematical tasks that involved students working together on a group test. The second teacher experimented with a new kind of help when students were working on their maths tasks and asked for assistance. The third created a new setting in which the teacher (temporarily) did not provide mathematical hints and the students had to solve their own problems. The three teachers were very motivated, but they all had difficulties in not giving explanations themselves when supporting their students in their collaborative mathematical learning. They found that temporarily diminishing their product help stimulated discussion between students. It also became clear that the process of teacher reflection and follow-up discussions with the researcher/observers promoted changes of practice.

Pendekatan Kontekstual dengan Scaffolding untuk Meningkatkan Kemampuan Berpikir Kritis Matematis

“…Diskusi antar siswa dalam satu kelompok memiliki peranan penting dalam menjalani proses pembelajaran Scaffolding dengan pendekatan kontekstual ini. Guru harus dapat mendorong siswa untuk berdiskusi (Pijls & Dekker, 2011). Diskusi membantu pemahaman semua anggota kelompok sehingga mencapai ketuntasan penyelesaian soal-soal dalam LKS yang lebih cepat.…”

Implementing The Use of Magic Triangles for Developing Mathematical Reasoning Process in Delivering School Mathematics

“…All groups are guided together to use analogy reasoning, reasoning to use the same way to get number arrangement in magic triangles. The analogy reasoning consists of (1) making the sum list of four numbers (without repetition), and (2) selecting the appropriate four numbers that satisfied the rule.…”

“…Star states that reasoning is part of understanding when someone is solving a problem, and it can be said that reasoning is the capacity (a) in applying concepts, (b) in relating facts and concepts, and (c) in making decisions [5]. Stacey states that basic mathematical capability includes doing communication, implementing representation, designing strategy, using symbols, and reasoning argumentation [2].…”

“…It is predicted that many teachers tend to hesitate in delivering healthy and qualified mathematics learning. Stacey says that this kind of low motivation is named as Shallow Teaching Syndrome (STS) [2]. Stacey also identifying the phenomena of STS are (1) repetition of previous problems, (2) low procedural complexity, and (3) the absence of mathematical reasoning [2].…”

“…Stacey says that this kind of low motivation is named as Shallow Teaching Syndrome (STS) [2]. Stacey also identifying the phenomena of STS are (1) repetition of previous problems, (2) low procedural complexity, and (3) the absence of mathematical reasoning [2]. Repetitions are known by identifying teacher actions in which the teacher using the textbook, the materials, and the problems, without preliminary inspection.…”