Action Proof: Analyzing Elementary School Students Informal Proving Stages through Counter-examples

Abstract

Both female and male elementary school students have difficulty doing action proof by using manipulative objects to provide conjectures and proof of the truth of a mathematical statement. Counter-examples can help elementary school students build informal proof stages to propose conjectures and proof of the truth of a mathematical statement more precisely. This study analyzes the action proof stages through counter-examples stimulation for male and female students in elementary schools. The action proof stage in this study focuses on three stages: proved their primitive conjecture, confronted counter-examples, and re-examined the conjecture and proof. The type of research used is qualitative with a case study approach. The research subjects were two of the 40 fifth-grade students selected purposively. The research instrument used is the task of proof and interview guidelines. Data collection techniques consist of Tasks, documentation, and interviews. The data analysis technique consists of three stages: data reduction, data presentation, and concluding. The analysis results show that at the stage of proving their primitive conjecture, the conjectures made by female and male students through action proofs using manipulative objects are still wrong. At the stage of confronted counter-examples, conjectures and proof made by female and male students showed an improvement. At the stage of re-examining the conjecture and proof, the conjectures and proof by female and male students were comprehensive. It can be concluded that the stages of proof of the actions of female and male students using manipulative objects through stimulation counter-examples indicate an improvement in conjectures and more comprehensive proof.

A learning trajectory of integer addition and subtraction using the kempreng game context

“…The second characteristic is the involvement of the subtraction-as-addition strategy in operating integer addition and subtraction, as in the study (Paliwal & Baroody, 2020). The third characteristic is a visual representation and physical activity involvement in operating integer addition and subtraction as in the previous study (e.g., Amir & Amir, 2021;Amir, 2022).…”

“…Moreover, the traditional kempreng game has stages in visually representing and physical activity in operating integers (Susanti, 2020). It is because primary students find it easier to understand and operate integers through informal visual representations (not symbolic representations) (Amir & Amir, 2021;Amir, 2022). Hence, our research aims to produce LT through the context of the traditional kempreng game on integer addition and subtraction material for primary students.…”

Primary Students’ Math Literacy in terms of Higher Order Thinking Skill

“…It can be seen that there are still some students who provide argumentative answers without attaching problem-solving strategies that are still wrong. This is because students are still not thorough and are still not familiar with problems accompanied by answer arguments (Amir & Amir, 2021;Brown, 2017;Chu et al, 2017). Math literacy can be said to be good if it can analyze, reason, and communicate mathematical knowledge and skills effectively and can solve and interpret mathematical solutions (Armstrong et al, 2018;Lara-Porras et al, 2019).…”