Secondary students’ proof constructions in mathematics: The role of written versus oral mode of argument representation

Abstract

Prior research showed that many secondary students fail to construct arguments that meet the standard of proof in mathematics. However, this research tended to use survey methods and only consider students presenting their perceived proofs in written form. The limited use of observation methods and the lack of consideration of students presenting their perceived proofs orally—in tandem with their written proofs for the same claims—might have resulted in a skewed picture of the potential of students’ constructed proofs, and this raises concern about the validity of research findings. The research reported in this article substantiates this concern. Using data from a design experiment in two secondary mathematics classrooms (14–15‐year‐olds), I explored the role of the written versus the oral mode of argument representation in students’ proof constructions. Findings from the comparison between the written arguments (perceived proofs) that the students produced during small group work and the oral arguments that the students presented in front of the class for the same claims showed that the oral mode of representation is more likely than the written mode to be associated with the construction of arguments that meet the standard of proof. Thus if a study had analysed students’ written arguments only (as in survey research), it would have reported a less favourable picture of the potential of students’ constructed proofs than another study that would focus only on students’ oral arguments (as in observational research). Implications for methodology, research and practice are discussed in light of these findings.

The impact of high stakes oral performance assessment on students’ approaches to learning: a case study

“…The research questions were motivated by the lack of insight into the reasons why a change in summative assessments may result in a change in students' approaches to learning (Scouller, 1998) and by the very uniform assessment diet that mathematics has in the UK at least. We chose oral performance assessment as there is evidence that this dialogic form of assessment may help students express their relational understanding, especially in STEM subjects (Schoultz et al, 2001;Stylianides, 2019). Moreover, Brown et al (2013) suggest that uniform assessment diets lead to reproductive learning, therefore, contributing variety to students' uniform assessment diet may help fostering deep learning approaches in mathematics.…”

“…The study on students' proof production conducted by Stylianides (2019) echoes these findings. In the school context, Stylianides (2019) found that students were more likely to produce arguments that met the standard of proof when working in a dialogic manner with interlocutors rather than when working in a written form by themselves.…”

Posing New Researchable Questions as a Dynamic Process in Educational Research

“…The three studies in the area of students' justification schemes that we discussed in this part of the paper (Dawkins & Karunakaran, 2016;Stylianides, 2019;Weber et al, 2020) illustrate the idea that the conceptual terrain in this research area becomes more complex with advancements in research knowledge about the factors that can influence students' performance on proof construction tasks. Also, as the field's knowledge of new potentially influential factors grows, there is a consequential expansion of new researchable questions that can guide researchers' investigations towards a more refined, and presumably more accurate, body of research knowledge about students' justification schemes.…”

“…In this part, we will discuss briefly three recent studies that are relevant to the investigation of students' justification schemes (Dawkins & Karunakaran, 2016;Stylianides, 2019;Weber, Lew, & Mejia-Ramos, 2020), and we will consider how each of them can take RQ 2 to a new direction, thus giving rise to new researchable questions. We will label the new research questions as RQ 3a-c so as to indicate their conceptual (rather than actual) evolution from RQ 2 .…”

Profil Argumentasi Mahasiswa Dalam Melakukan Pembuktian Pada Topik Analisis Kompleks

“…Penguatan kemampuan dalam melakukan pembuktian, merupakan salah satu isu utama pembelajaran matematika.Hal ini disebabkan oleh kenyataan bahwa kompetensi dalam melakukan pembuktian pernyataan matematis adalah salah satu karakteristik utama mahasiswa matematika.Namun demikian, kajian pada bagaimana meningkatkan kemampuan siswa dalam melakukan pembuktian memang masih sangat sedikit [6].Pada saat yang bersamaan pembuktian merupakan topik yang sulit untuk dipelajari dan juga dibelajarkan [7].Padahal, kemampuan berargumentasi termasuk kemampuan dalam melakukan justifikasi maupun penyangkalan merupakan kemampuan yang harus muncul dalam setiap proses pembuktian. Kemampuan semacam inilah, lebih familiar disebut kemampuan berfikir tingkat tinggi (higher order thinking skill) [8] yang sangat dibutuhkan mahasiswa.…”