Deductive or Inductive? Prospective Teachers’ Preference of Proof Method on an Intermediate Proof Task

Siswono, Tatag Yuli Eko; Hartono, Sugi; Kohar, Ahmad Wachidul

doi:10.22342/jme.11.3.11846.417-438

Cited by 12 publications

(14 citation statements)

References 29 publications

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“…The results of the study could be summarized that the deductive method and online exercises were effective in developing students' learning achievement of mathematic relations. The results of the study confirm the benefits of the deductive learning management in math education as found in the previous studies (e.g., Atta et al, 2015;Ayalon & Even, 2008;Rahmah, 2017;Singh, 2017;Sriplaeg, 2022;Siswono et al, 2020). At this point, apart from developing students' knowledge of the area (Singh, 2017), mathematical problem-solving (Rahmah, 2017), and solving intermediate proof tasks (Siswono et al, 2020), the deductive learning management was also capable of improving students' knowledge of mathematical relation.…”

Section: Discussionsupporting

confidence: 89%

“…They are also allowed to test their understanding of the concept via exercises that could ensure their development of skills and abilities. The benefits of the deductive method in teaching mathematics could be seen in several studies (e.g., Atta et al, 2015;Ayalon & Even, 2008;Rahmah, 2017;Singh, 2017;Sriplaeg, 2022;Siswono et al, 2020).…”

Section: ) Application Stagementioning

confidence: 96%

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Developing Grade 10 Student Learning Achievement of Relation Using Deductive Learning Management with Online Exercises

Reangnok

Poonputta

2022

JEI

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The purposes of the study were 1) to investigate the effectiveness of deductive learning management with online exercises on grade 10 students learning achievement of mathematical relations; and 2) to investigate students’ satisfaction with the learning management. The study was conducted in a one-group pretest-posttest design. The participants were 41 Thai grade 10 students learning mathematics. The cluster random sampling method was employed in the participant selection process. The instruments were a learning management plan designed in a deductive learning management, a learning achievement test, and a satisfaction questionnaire. The effectiveness of the deductive learning management on students’ learning achievement of mathematical relation was assessed by considering the participant’s performance while learning in the class and at the end of the class. The statistics used in the data analysis were percentages, mean scores, standard deviation, a paired t-test, and an effectiveness test (E1/E2) with the determining criteria of 75/75. The results of the study indicate that the deductive learning management plan with online exercises was capable of improving grade 10 students’ learning achievement of mathematical relations. Moreover, it also brought about a satisfying experience learning the concept. The study contributed to the area of mathematics education as it provided an example to support the use of the deductive learning management on learners with limited mathematic skills.

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Section: Discussionsupporting

confidence: 89%

Section: ) Application Stagementioning

confidence: 96%

Developing Grade 10 Student Learning Achievement of Relation Using Deductive Learning Management with Online Exercises

Reangnok

Poonputta

2022

JEI

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“…For this reason, we agree with Ubuz and Yayan (2010) when stating that "an important step to improving subject matter knowledge should be better subject matter preparation for primary teachers" (p. 799). We also believe that addressing difficulties in the content knowledge of primary-school teachers (see, for instance, Oflaz, Polat, Altaylı Özgül, Alcaide, & Carrillo, 2019) would shed light on where to focus so that teachers to acquire essential content knowledge to teach in the various mathematical domains (regarding proving as mathematical content, see, for instance, Siswono, Hartono, & Kohar, 2020;van Dormolen, 1977). In this way, studying teachers' activities when they strive either to prove mathematical assertions or to formulate conjectures constitutes the first step and exploring the reasons behind the difficulties found when conjecturing and proving would be an interesting topic for further research.…”

Section: Some Reflections On the Resultsmentioning

confidence: 99%

A Case Study on How Primary-School in-Service Teachers Conjecture and Prove: An Approach From the Mathematical Community

2021

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This paper studies how four primary-school in-service teachers develop the mathematical practices of conjecturing and proving. From the consideration of professional development as the legitimate peripheral participation in communities of practice, these teachers’ mathematical practices have been characterised by using a theoretical framework (consisting of categories of activities) that describes and explains how a research mathematician develops these two mathematical practices. This research has adopted a qualitative methodology and, in particular, a case study methodological approach. Data was collected in a working session on professional development while the four participants discussed two questions that invoked the development of the mathematical practices of conjecturing and proving. The results of this study show the significant presence of informal activities when the four participants conjecture, while few informal activities have been observed when they strive to prove a result. In addition, the use of examples (an informal activity) differs in the two practices, since examples support the conjecturing process but constitute obstacles for the proving process. Finally, the findings are contrasted with other related studies and several suggestions are presented that may be derived from this work to enhance professional development.

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“…Action proof is one way to develop the basic skills needed in mathematics in the last 20 years (Wittmann, 2021). Besides, it takes time to understand and broad skills and knowledge to prove a fact (Siswono et al, 2020). This happens in every step process carried out by students to arrive at the correct statements and conjectures.…”

Section: Discussionmentioning

confidence: 99%

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

Amir

2021

International j.of Elementary Education

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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.

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Deductive or Inductive? Prospective Teachers’ Preference of Proof Method on an Intermediate Proof Task

Cited by 12 publications

References 29 publications

Developing Grade 10 Student Learning Achievement of Relation Using Deductive Learning Management with Online Exercises

Developing Grade 10 Student Learning Achievement of Relation Using Deductive Learning Management with Online Exercises

A Case Study on How Primary-School in-Service Teachers Conjecture and Prove: An Approach From the Mathematical Community

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

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