Engaging students in roles of proof

Bleiler-Baxter, Sarah K.; Pair, Jeffrey

doi:10.1016/j.jmathb.2017.05.005

Cited by 16 publications

(9 citation statements)

References 31 publications

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“…This corroborates the idea that because of the nature of proof writing, experience in working with it is the key to performance and facilitation the learning, enabling students to think fundamentally and broadly [18]. Students demonstrate proving not only to mirror their understandings and values but also to fulfill the desired expectation by which their work will be judged [19]. However, we should be aware completely grasp the idea of classroom proof-writing activities, much the same that we cannot see the end of a rhizome.…”

Section: Resultssupporting

confidence: 78%

Embedding Proof-Writing in Phenomenon-based Learning to Promote Students’ Mathematical Creativity

Asahid¹,

Lomibao²

2020

EDUCATION

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The study aimed to identify the significant impact of phenomenon-based learning and embedding proof writing to this new teaching strategy on students' mathematical creativity in tertiary education. The study used a quasi-experimental pretest-posttest non-equivalent control group design. There were 2 experimental groups, one exposed to phenomenon-based learning alone and the other was exposed to phenomenon-based learning with classroom proof-writing activities, and one control group exposed to the conventional method. Multiple solution tasks were used to measure students' level of creativity. The data were analyzed using mean, standard deviation, and ANCOVA. The analysis revealed that students exposed to phenomenon-based learning with proof writing had the highest posttest creativity score. Students in this group had a significantly higher level of creativity among the three groups. Further, students exposed to phenomenon-based learning alone may not outperform students exposed to phenomenon-based learning with proof writing, but they still had significantly higher posttest mean scores compared to students exposed to the conventional type of teaching. The researchers recommend to teachers in tertiary education to use phenomenon-based learning with proof writing in teaching mathematics and its related courses since this instructional approach engages students in learning that is more focused to real-life issues, apply skills and knowledge from different subjects, and enhance important skills like creativity, problem-solving, communication, and teamwork.

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Section: Resultssupporting

confidence: 78%

Embedding Proof-Writing in Phenomenon-based Learning to Promote Students’ Mathematical Creativity

Asahid¹,

Lomibao²

2020

EDUCATION

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“…And the reality is that usually the students do not even understand the purpose of proof at all. This situation led Bleiber-Baxter & Pair [22] to look for opportunities to engage students in the different roles of proof, using their reflections to identify activities that enhanced their participation in mathematical proof (examples of tasks to promote experience with the different roles of proof can be found in [31]).…”

Section: Functions Of Proof: From Mathematics To School Mathematicsmentioning

confidence: 99%

“…But another is to 'explain why a statement is true, to communicate mathematical knowledge, to discover or create new mathematics, or to systematize statements into an axiomatic system' [13, p. 63]. According to Bleiler-Baxter & Pair [22], for a mathematician, a proof serves to convince or justify that a certain statement is true. But it also helps to increase the understanding of the result and the related concepts.…”

Section: Perspective Of One Teacher [1 P 78]mentioning

confidence: 99%

“…Getting conviction about the truth of a result (meaning verification) is the basic role of proof, nevertheless, students are usually asked to prove intuitive results or theorems presented by the teacher, where the verification is not really a question. As a consequence, the role of verification is only experienced superficially by the students [22]. Besides that, the students (as well as the mathematicians) often become convinced about the truth of a result based on some experiences with examples.…”

Section: Perspective Of One Teacher [1 P 78]mentioning

confidence: 99%

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Mathematical proof: from mathematics to school mathematics

Rocha

2019

Phil. Trans. R. Soc. A.

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Proof plays a central role in developing, establishing and communicating mathematical knowledge. Nevertheless, it is not such a central element in school mathematics. This article discusses some issues involving mathematical proof in school, intending to characterize the understanding of mathematical proof in school, its function and the meaning and relevance attributed to the notion of simple proof. The main conclusions suggest that the idea of addressing mathematical proof at all levels of school is a recent idea that is not yet fully implemented in schools. It requires an adaptation of the understanding of proof to the age of the students, reducing the level of formality and allowing the students to experience the different functions of proof and not only the function of verification. Among the different functions of proof, the function of explanation deserves special attention due to the illumination and empowerment that it can bring to the students and their learning. The way this function of proof relates to the notion of simple proof (and the related aesthetic issues) seems relevant enough to make it, in the future, a focus of attention for the teachers who address mathematical proof in the classroom. This article is part of the theme issue ‘The notion of ‘simple proof’ - Hilbert's 24th problem’.

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“…This technique is very helpful for researchers, writers and lecturers of algebraic structure in writing formal proof (Hungerford, 2014;Gallian, 2017;Misri, 2017). The more diverse techniques used in each proposition that will be proven, of course, really helps undergraduate students skilled in proofwriting and applying it in algebraic structure courses (Lee, 2016;Bleiler-Baxter & Pair, 2017;Brown, 2017;Yan, 2019), likewise with lecturers/ mathematicians in capturing the contents of undergraduate students' proofs (Miller, Infante, & Weber, 2017). This paper aims to investigate the diversity of proofing techniques and their effects on students' skills in applying them.…”

Section: Introductionmentioning

confidence: 99%

Propositional Proofing Techniques application in Algebraic Structure Research

Misri¹

2020

Eduma : Mathematics Education Learning and Teaching

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This paper investigates proofing techniques which are used in algebraic structure research and how to apply those techniques. This paper also investigates the reasoning behind the application of the techniques and their effects. The data was collected by reviewing some algebraic structure textbooks used recently. Books reviewed were domestic and foreign books. The results of the review process were noted and documented, and then finally transcribed and coded. The review process of each book was carried out twice. The data obtained were then triangulated, to get the valid data, and eventually used for further analytical purposes. The results obtained show that not all the proofing techniques were used in the proofing process in the algebraic structure research. They tended to use the same technique in every proofing activity. This might be due to mastery of proofing techniques, preferences for certain proofing techniques, lack of information about the development of various proofing techniques. The resulting impact can be identified from the steps of proofing, meanwhile, if it is conducted using another technique, it can reduce the steps, is more acceptable also comprehensible.

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Engaging students in roles of proof

Cited by 16 publications

References 31 publications

Embedding Proof-Writing in Phenomenon-based Learning to Promote Students’ Mathematical Creativity

Embedding Proof-Writing in Phenomenon-based Learning to Promote Students’ Mathematical Creativity

Mathematical proof: from mathematics to school mathematics

Propositional Proofing Techniques application in Algebraic Structure Research

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