Introducing students and prospective teachers to the notion of proof in mathematics

Stylianides, Andreas J.; Stylianides, Gabriel J.

doi:10.1016/j.jmathb.2022.100957

The Journal of Mathematical Behavior

2022

DOI: 10.1016/j.jmathb.2022.100957

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Introducing students and prospective teachers to the notion of proof in mathematics

Andreas J. Stylianides

Gabriel J. Stylianides

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Cited by 5 publications

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Transitioning to proof via writing scripts on the rules of a new discourse

Kontorovich,

Liu,

Kang

2024

Educ Stud Math

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Coming from the commognitive standpoint, we consider proof-based mathematics as a distinct discourse, the transition to which requires special rules for endorsement and rejection of mathematical statements. In this study, we investigate newcomers’ learning of these rules when being taught them explicitly. Our data come from academically motivated high-school students who took a special course in undergraduate mathematics. The course teacher dedicated three academic hours to introducing and explaining selected rules of proof to support students’ shift to the new discourse. The homework assignment consisted of typical proof-requiring problems and a scriptwriting task, asking students to compose a dialogue between fictional characters about a proof-related mistake of their choice. We analyzed the differences and similarities between the rules discussed in the classroom and those that students addressed and implemented in their proofs. The analysis showed that while students’ solutions to proof-requiring problems required rule implementation, fictitious dialogues opened the space for rule formulation and substantiation. In many cases, the students discussed the rules presented in the classroom, extending, elaborating, and specifying the teacher’s formulations. Furthermore, while the students’ proofs were mainly consistent with the teacher’s expectations, some of their rule formulations were more radical and overgeneralized than expected. These findings suggest that newcomers’ communication about the rules of proof may lag behind their capability to implement those rules to prove mathematical statements.

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Transitioning to proof via writing scripts on the rules of a new discourse

Kontorovich,

Liu,

Kang

2024

Educ Stud Math

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Proof and proving in school and university mathematics education research: a systematic review

Stylianides,

Moutsios-Rentzos

2023

ZDM Mathematics Education

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This systematic review aims to provide a complementary to existing synopses of the state-of-the-art of mathematics education research on proof and proving in both school and university mathematics. As an organizing framework, we used Cohen et al.’s triadic conceptualization of instruction, which draws attention not only to the main actors of the didactical process (i.e., the Teacher and Students) and the Content around which the actors’ work is organized (herein, content related to proof and proving), but also to the relationships among the actors and the content. Out of the 103 papers we reviewed, almost half fell in the Student-Content category, which is consistent with the existence of a substantial number of frameworks, methods, and research findings related to students’ engagement with proof and proving. About a quarter of the papers fell in the Student–Teacher-Content category, which reflects an emphasis on viewing instructional practice in proof and proving in a holistic, systemic way. Only few papers fell in the categories that did not include Content in them, namely, the categories of Student, Teacher, and Student–Teacher; this suggests mathematics education research on proof and proving has a strong disciplinary identity, which potentially differentiates it from other mathematics education research strands. About a fifth of the papers were oriented towards ‘breaking ground’ through making an explicit theoretical and/or methodological contribution (Student–Teacher-Content and Content were the main categories where such contributions appeared), whilst the majority of the papers were focused on ‘building ground’ through elaborating or employing existing methodological and/or theoretical approaches.

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Introducing Students to the Role of Assumptions in Mathematical Activity

Komatsu,

Murata,

Stylianides

et al. 2023

Cognition and Instruction

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Introducing students and prospective teachers to the notion of proof in mathematics

Cited by 5 publications

References 41 publications

Transitioning to proof via writing scripts on the rules of a new discourse

Transitioning to proof via writing scripts on the rules of a new discourse

Proof and proving in school and university mathematics education research: a systematic review

Introducing Students to the Role of Assumptions in Mathematical Activity

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Introducing students and prospective teachers to the notion of proof in mathematics

Cited by 5 publications

References 41 publications

Transitioning to proof via writing scripts on the rules of a new discourse﻿

Transitioning to proof via writing scripts on the rules of a new discourse﻿

Proof and proving in school and university mathematics education research: a systematic review

Introducing Students to the Role of Assumptions in Mathematical Activity

Contact Info

Product

Resources

About

Transitioning to proof via writing scripts on the rules of a new discourse

Transitioning to proof via writing scripts on the rules of a new discourse