Formulating a conjecture through an identification of robust invariants with a dynamic geometry system

Anwar, Lathiful; Mali, Angeliki; Goedhart, Martin

doi:10.1080/0020739x.2022.2144517

Cited by 2 publications

(2 citation statements)

References 32 publications

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“…This might have influenced PMTs' understanding of how to instantiate the definitions, axioms, and theorems, for instance, in order to deduce a conclusion from given assumption(s). Additionally, conjecturing through constructing and dragging by using GeoGebra might have affected students' understanding of a conditional statement, particularly the logical status of premises and conclusions (Anwar et al, 2022;Baccaglini-Frank & Mariotti, 2010). Further, we are aware that the statements in this paper were translations of students' utterances from Bahasa Indonesia into English, and those translations might not fully represent the meaning of the Indonesian words to the reader.…”

Section: Discussionmentioning

confidence: 98%

Learning trajectory of geometry proof construction: Studying the emerging understanding of the structure of Euclidean proof

Anwar

Goedhart

Mali

2023

EURASIA J Math Sci Tech Ed

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This paper presents a learning trajectory of geometry proof (LTGP) for Indonesian prospective mathematics teachers (PMTs) during their first year of studies at an Indonesian university. The trajectory aims at PMTs’ progression of their understanding of the structure of proof and their proof construction abilities. We designed and implemented teaching materials with geometry problems based on the use of the flow-chart proof format and the model of understanding of proof structure from Miyazaki et al. (2017). We present an analysis of data from pre- and post-tests of proof construction problems, written answers to proof problems during intervention with 60 PMTs, and individual interviews with eight PMTs. We found that the intervention supports PMTs’ understanding of the structure of proof and their proof construction abilities. Our findings contribute to knowledge about teaching strategies to support students in their understanding and construction of a proof. From our findings, we suggest the use of the flow-chart proof format together with other more formal proof formats in creating, reading, and rewriting proof of geometric propositions and the use of open problems to encourage students to think forward and backwards interactively to help students plan for proof construction.

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Section: Discussionmentioning

confidence: 98%

Learning trajectory of geometry proof construction: Studying the emerging understanding of the structure of Euclidean proof

Anwar

Goedhart

Mali

2023

EURASIA J Math Sci Tech Ed

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“…Teachers often used learning videos downloaded through YouTube and/or created by the teacher as media to introduce the problem and visualisation representing the mathematical concepts. To support the teacher's explanation in the created video, some teachers used a certain software/application tool, GeoGebra, as this app has excellent features such as construction dan dragging tools to help students understand the concepts (Anwar et al, 2022). Some teachers preferred to use ready instructional videos because it was more effective than those made by teachers.…”

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confidence: 99%

Teachers’ Perception of Teaching and Learning During to Post Covid-19 Pandemic Era: A Case of Indonesian Mathematics Teachers

2023

JHETP

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This study explores secondary school mathematics teachers' perceptions of teaching and learning during to post the COVID-19 Pandemic. The Quantitative data were collected through a survey of 45 secondary school mathematics teachers (34 females and 11 males). Moreover, the qualitative data were collected through semi-structured interviews with four secondary school mathematics teachers (2 females and two males). The quantitative data were analysed statistically. Moreover, thematic analysis was used to analyse the qualitative data. The quantitative results indicate a significant connection between teachers' difficulties in teaching and learning and their profiles: their school type, academic degree, and professional qualification. The secondary mathematics teachers of public schools faced more obstacles than the teachers of private schools. The qualitative analysis showed that five main instructional aspects might affect teaching and learning success during the pandemic era: learning modes, learning activities, learning media, learning tools, assessment, and time consumption.

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Formulating a conjecture through an identification of robust invariants with a dynamic geometry system

Cited by 2 publications

References 32 publications

Learning trajectory of geometry proof construction: Studying the emerging understanding of the structure of Euclidean proof

Learning trajectory of geometry proof construction: Studying the emerging understanding of the structure of Euclidean proof

Teachers’ Perception of Teaching and Learning During to Post Covid-19 Pandemic Era: A Case of Indonesian Mathematics Teachers

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