Analysis of the cognitive unity or rupture between conjecture and proof when learning to prove on a grade 10 trigonometry course

Fiallo, Jorge; Gutiérrez, Ángel

doi:10.1007/s10649-017-9755-6

Cited by 27 publications

(21 citation statements)

References 13 publications

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“…Many studies have investigated the affordances of DGEs, which include dragging and measuring modalities that lead to the production and testing of conjectures by generating various diagrams (Arzarello et al 2002;Olivero and Robutti 2007). Some researchers argue that bridging what can appear to students as a 'gap' between argumentation and proving (especially the 'gap' between empirical investigation/conjecturing and deductive proving) is helped if students experience 'cognitive unity' between conjecturing and proving (Boero et al 1996;Fiallo and Gutiérrez 2017).…”

mentioning

confidence: 99%

Interplay between Paper-and-Pencil Activity and Dynamic-Geometry-Environment Use during Generalisation and Proving

Komatsu

Jones

2020

Digit Exp Math Educ

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Digital tools have a potential to change significantly the form of mathematical learning taking place in classrooms, with research pointing to various affordances in comparison with physical tools such as paper-and-pencil environments. Nevertheless, there is a scarcity of research that has examined in-depth the interrelated roles these two types of tools fulfil in mathematics learning. This issue of interrelated roles is important because, when digital tools are incorporated into classrooms, students usually also have notebooks and worksheets within which they carry out actions complementary to their use of digital tools. In this article, we focus on the use of dynamic geometry environments (DGEs) in conjecturing and proving, and, in particular, we examine the interplay between students' paper-and-pencil activity and their use of a DGE during the producing and proving of a generalisation of a statement. We analyse a series of lessons involving secondary school students (aged 14-15, Grade 9) and show that, while DGE use supported the students in generalising a statement, they were initially unable to prove the generalisation while using the DGE, but subsequently succeeded through their paper-and-pencil activity. Our research illustrates the affordance of paper-andpencil environments to support students in working on different representations, and thus highlights how the interplay between paper-and-pencil activity and DGE use can be important for the progress of conjecturing and proving. We also show the roles taken by the teacher in supporting the students' work, and point to the need for further research into the back-and-forth use of digital and physical tools. Keywords Digital tool. Physical tool. Dynamic geometry environment. Paper-and-pencil activity. Generalisation and proof. Teacher role It is now well known that digital tools provide relative affordances in comparison with those provided by physical tools, such as paper-and-pencil environments and concrete

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confidence: 99%

Interplay between Paper-and-Pencil Activity and Dynamic-Geometry-Environment Use during Generalisation and Proving

Komatsu

Jones

2020

Digit Exp Math Educ

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“…Regarding reasoning and proof, [19] examined high school students' plausible methods for dividing a square into two equal areas; the research findings indicated that the use of Cabri Geometry provided students with methods of initially formulating a conjecture and subsequently developing an argument to support it. Reference [20] analyzed methods adopted by students to prove trigonometry theorems. Based on students' proofs, the researchers found that Cabri Geometry helped the students to discover and verify conjectures.…”

Section: A Dgsmentioning

confidence: 99%

Predicting the Determinants of Dynamic Geometry Software Acceptance: A Two-Staged Structural Equation Modeling — Neural Network Approach

Chen¹

2020

IJIET

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“…First, the ineffectiveness of instruction in trigonometry learning (Tallman & Frank, 2020). Second, the curriculum does not highlight how students relate the different representations of trigonometric concepts and minimize the use of textbooks that emphasize rote and procedures (Fiallo & Gutiérrez, 2017). The priority is therefore to minimize student errors by designing learning that stimulates students to understand the concept of trigonometry (Mesa & Herbst, 2011).…”

Section: Pre-service Teachers' Knowledge On Trigonometrymentioning

confidence: 99%

Exploration of pre-service teachers’ pedagogical content knowledge in mathematics learning in senior high school based on gender and academic skills

Ma’rufi

Ikram

Ilyas

2020

Journal for the Education of Gifted Young Scientists

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In Indonesia, pre-service mathematics teacher education is strictly supervised so that Pedagogical Content Knowledge (PCK) becomes an important aspect to build the quality of learning. This study aimed to explore pre-service mathematics teachers' PCK based on gender and academic skills. To obtain rich and in-depth data, a qualitative approach was used. A total of 70 subjects aged between 19-21 years old participated in this study. There were two subjects selected based on their academic skills and gender. Using a grounded theory approach, we conducted a preliminary analysis, open coding, axial coding to obtain the three PCK components, namely Knowledge of Subject Matter (KSM), Knowledge of Pedagogy (KP), and Knowledge of Student (KS). Research findings revealed that the pre-service teachers' pedagogical content knowledge in terms of knowledge of subject matter was categorized as good in mathematics learning. As for their knowledge of pedagogy, the male subjects presented the concepts by employing the expository strategy, the female subjects with high skills used the guided discovery, and the female subjects with average skill also employed the strategy of expository. In the aspect of knowledge of students, the subjects with average skills overcame students' misconception by explaining the procedures and using the strategy of asking, but the subjects with high academic skills did not only implement the two previous strategies but also used their reasoning behind every procedure of problem-solving that they carried out. These findings can be used as recommendations for the development of mathematics learning.

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Analysis of the cognitive unity or rupture between conjecture and proof when learning to prove on a grade 10 trigonometry course

Cited by 27 publications

References 13 publications

Interplay between Paper-and-Pencil Activity and Dynamic-Geometry-Environment Use during Generalisation and Proving

Interplay between Paper-and-Pencil Activity and Dynamic-Geometry-Environment Use during Generalisation and Proving

Predicting the Determinants of Dynamic Geometry Software Acceptance: A Two-Staged Structural Equation Modeling — Neural Network Approach

Exploration of pre-service teachers’ pedagogical content knowledge in mathematics learning in senior high school based on gender and academic skills

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