Proofs as bearers of mathematical knowledge

Hanna, Gila; Barbeau, Edward J.

doi:10.1007/s11858-008-0080-5

Cited by 72 publications

(23 citation statements)

References 20 publications

(17 reference statements)

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“…Mathematical proof can be used to relate mathematical information, develop strategies and as a means which is necessary to solve the problems students encounter in mathematics (Hanna & Barbeau, 2008;Mariotti & Balacheff, 2008). It is seen that with regard to importance of mathematical proof, academicians emphasize its contribution to the development of higher order thinking skills, its being the basis of mathematics, its verification of results, and its contribution to communication and meaningful learning functions.…”

Section: Discussionmentioning

confidence: 99%

The Difficulties Experienced in Teaching Proof to Prospective Mathematics Teachers: Academician Views

Güler¹

2016

HES

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The aim of this study is to examine the difficulties prospective mathematics teachers experience in mathematical proving, the courses in which they have difficulties in proving, the importance of proof in mathematics education and its functions in their professional lives. The data of the study was collected via semi-structured interviews with fifteen academicians who volunteered to take part in the study. Content analysis method was used to analyze the data obtained. As a result of the study, based the views of the academicians, it was seen that prospective mathematics teachers experience four different difficulties in proving. Besides, in line with the views of the academicians the following categories were formed: the courses that prospective teachers experience difficulty, the importance of proof in mathematics education and its functions in prospective teachers' professional lives and these categories were presented with their subcategories.

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Section: Discussionmentioning

confidence: 99%

The Difficulties Experienced in Teaching Proof to Prospective Mathematics Teachers: Academician Views

Güler¹

2016

HES

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“…Additionally, introducing students to the nature of university mathematics with its characterizing activities, formal concepts and tools (e.g., Leviatan 2008) as well as facilitating students' confidence (e.g., Carmichael and Taylor 2005) have been reported to ease the transition to university mathematics in context of bridging courses. With respect to mathematical processes, research suggests the importance of problem solving skills (Carlson and Bloom 2005) and experiences with proofs (Balacheff 2008;Hanna and Barbeau 2008;Harel 2008) and (formal) definitions (Harel 2008) as requirements for mathematics courses at universities. Additionally, adequate expectations regarding university mathematics (Hoyles et al 2001;Nardi 1996;De Guzmán et al 1998;Thompson 1994) and the learning of mathematics at the universities (Kajander and Lovric 2005;Inglis et al 2012;Thompson 1994), as well as appropriate interest (e.g., Marsh et al 2005;Carlson 1999), motivation, beliefs and self-regulation (e.g., Carlson and Bloom 2005;Hailikari et al 2008) and persistence with regard to complex mathematical problem-solving (Carlson 1999) seem to be important for the transition to university mathematics.…”

Section: The Environment-side: Mathematical Requirements Of First Yeamentioning

confidence: 99%

“…In line with considerations of Carlson et al (2015), the university instructors expect that students have a concept image of mathematical functions that corresponds with the concept definition and thus enables covariational reasoning. Additionally, students are required to comprehend and verify given proofs and generate mathematical hypotheses and support arguments of plausibility as well as to comprehend mathematical definitions and formulate their own definitions of known concepts (see Harel 2008;Hanna and Barbeau 2008). Regarding problem solving, the university instructors in our study rated necessary conceptual knowledge, heuristics and affects (as described by Carlson and Bloom 2005).…”

Section: Implications For Research On the Transition Between School Amentioning

confidence: 99%

Mathematical Prerequisites for STEM Programs: What do University Instructors Expect from New STEM Undergraduates?

Deeken

Neumann

Heinze

2019

Int. J. Res. Undergrad. Math. Ed.

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In many countries STEM degree programs face high dropout rates, which are often attributed to insufficient mathematical preparation of incoming undergraduates. However, it is largely unclear which mathematical prerequisites universities expect from their new STEM undergraduates. There are hardly official documents and it is even an open question whether there is a consensus among university instructors. The main goal of this study is therefore to describe the expected mathematical prerequisites for new STEM undergraduates. We conducted a Delphi study with German university instructors for first semester mathematics courses in STEM programs. The participants identified 179 prerequisites addressing: (1) mathematical content, (2) mathematical processes, (3) views about the nature of mathematics, and (4) personal characteristics. For 140 of these prerequisites there was a consensus regarding their necessity among the university instructors. The expected mathematical prerequisites are mainly on a basic level and do not require formalistic or abstract mathematical knowledge or abilities.

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“…This paper suggests that technology be introduced at the heart of the mathematical curriculum. The four papers addressing proof were: Borwein (2005), Hanna and Barbeau (2008), de Villiers (2008), andHanna (2000).…”

Section: The Role Of Proofmentioning

confidence: 99%

Enhancing Assessment in Teacher Education Courses

Roscoe

2013

cjsotl-rcacea

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Several faculty members including the author were involved in exploring the implementation and effectiveness of research-based assessment strategies in their undergraduate teacher education courses at a Canadian university. The paper describes the process and the results of their ongoing improvement efforts and implications for teacher education and higher education in general. After attending several assessment workshops lead by the author, 12 faculty members implemented new assessment strategies in their own courses to enhance student learning. As the 12 faculty members reflected on their efforts to enhance assessment, a number of themes emerged. These included assessment as authentic performance, establishing clear learning targets, collaboration and community, and integrated assessment and instruction. Our results support the claim that current ideas about K-12 assessment are applicable to post-secondary education and can improve student learning outcomes. Developing balanced and integrated assessment systems is perhaps the most significant innovation we engaged in and we conclude that it has the potential to fundamentally change what occurs in university classrooms. Plusieurs professeurs, y compris l’auteur, ont exploré la mise en oeuvre et l’efficacité de stratégies d’évaluation basées sur la recherche dans le cadre de leurs cours de formation pour les enseignants. L’article décrit le processus et les résultats de leurs efforts pour améliorer la formation des enseignants et plus généralement l’enseignement, ainsi que les implications de cette approche. Après avoir participé à plusieurs ateliers sur l’évaluation dirigés par l’auteur, 12 professeurs ont mis en oeuvre de nouvelles stratégies d’évaluation dans leurs propres cours pour améliorer l’apprentissage des étudiants. Quand les 12 professeurs ont réfléchi sur leurs efforts pour améliorer l’évaluation, un certain nombre de thèmes sont apparus, entre autres : l’évaluation en tant que performance authentique, l’établissement d’objectifs d’apprentissage clairs, la collaboration et la communauté, l’intégration de l’évaluation et de l’instruction. Nos résultats étayent l’affirmation selon laquelle les théories actuelles sur l’évaluation dans les écoles (K-12) sont applicables en enseignement post-secondaire et peuvent améliorer l’apprentissage des étudiants. Le développement de systèmes d’évaluation équilibrés et intégrés est peut-être l’innovation la plus importante dans laquelle nous nous engageons et nous en concluons que cette pratique a le potentiel de changer radicalement ce qui se passe dans les salles de classe des universités.

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Proofs as bearers of mathematical knowledge

Abstract: Yehuda

Cited by 72 publications

References 20 publications

The Difficulties Experienced in Teaching Proof to Prospective Mathematics Teachers: Academician Views

The Difficulties Experienced in Teaching Proof to Prospective Mathematics Teachers: Academician Views

Mathematical Prerequisites for STEM Programs: What do University Instructors Expect from New STEM Undergraduates?

Enhancing Assessment in Teacher Education Courses

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