Pre-Service Teachers’ Benefits from an Inquiry-Based Transition-to-Proof Course with a Focus on Generic Proofs

Kempen, Leander; Biehler, Rolf

doi:10.1007/s40753-018-0082-9

Cited by 6 publications

(3 citation statements)

References 20 publications

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“…We will rely on the following research questions taken from the study of Kempen and Biehler (2019b) (i) How do pre-service teachers rate the different kinds of proofs concerning the perceived explanatory-quality and conviction at the beginning of their university studies? (ii) How can students' proof acceptance of the four kinds of proofs be described?…”

Section: Proof-acceptance Explanatory Power and Convictionmentioning

confidence: 99%

“…While Kempen and Biehler (2019b) investigated the changes in students' proof perception and acceptance while attaining the course "Introduction into the culture of mathematics, " we will have a close look at the corresponding results from the pre-test at the beginning of the course.…”

Section: Proof-acceptance Explanatory Power and Convictionmentioning

confidence: 99%

“…This study was originally conducted with a bigger sample size. The students dealt with inKempen and Biehler (2019b) are those, that could be tracked from the pre-to the post-test. The whole sample contains 145 pre-service teachers.…”

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confidence: 99%

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Using Figurate Numbers in Elementary Number Theory – Discussing a ‘Useful’ Heuristic From the Perspectives of Semiotics and Cognitive Psychology

Kempen

Biehler

2020

Front. Psychol.

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The use of figurate numbers (e.g., in the context of elementary number theory) can be considered a heuristic in the field of problem solving or proving. In this paper, we want to discuss this heuristic from the perspectives of the semiotic theory of Peirce ("diagrammatic reasoning" and "collateral knowledge") and cognitive psychology ("schema theory" and "Gestalt psychology"). We will make use of several results taken from our research to illustrate first-year students' problems when dealing with figurate numbers in the context of proving. The considerations taken from both theoretical perspectives will help to partly explain such phenomena. It will be shown that the use of figurate numbers must not be considered to be any kind of help for learners or some way of 'easy' mathematics. Working in this representational system has to be learned and practiced as another kind of knowledge is necessary for working with figurate numbers. The named findings also touch upon the concept of 'proofs that explain.' Finally, we will highlight some implications for teaching and point to a number of demands for future research.

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Section: Proof-acceptance Explanatory Power and Convictionmentioning

confidence: 99%

Section: Proof-acceptance Explanatory Power and Convictionmentioning

confidence: 99%

See 1 more Smart Citation

Using Figurate Numbers in Elementary Number Theory – Discussing a ‘Useful’ Heuristic From the Perspectives of Semiotics and Cognitive Psychology

Kempen

Biehler

2020

Front. Psychol.

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Investigating High School Graduates’ Basis for Argumentation: Considering Local Organisation, Epistemic Value, and Modal Qualifier When Analysing Proof Constructions

Kempen

2022

Practice-Oriented Research in Tertiary Mathematics Education

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Changes in Students’ Mathematical Competencies at the Beginning of Higher Education Within the Last Decade at a German University

Büchele

Feudel

2023

Int J of Sci and Math Educ

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Mathematics plays a significant role in many study programs. However, several studies show deficiencies and a decline in beginning undergraduates’ skills in mathematics in many content domains. However, it remains unclear whether they have improved in so-called process competencies like modeling, mathematical reasoning, or using different representations instead, because there has been a shift towards the acquisition of such in many recent curricula. We investigated this issue at a university in Germany based on data from a (non-standardized) mathematics entry test taken by 3076 economics students divided into different cohorts from 2012 to 2019. Using regression analyses, we found that, on the one hand, students’ ability to carry out symbolic calculations decreased. On the other hand, their performance increased in some test questions focusing on other process competencies like reasoning, mathematizing, or using different representations, which have become common tasks at school due to a stronger emphasis on these process competencies after a curriculum reform. Our data indicate that this reform might have had the desired effect.

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Pre-Service Teachers’ Benefits from an Inquiry-Based Transition-to-Proof Course with a Focus on Generic Proofs

Cited by 6 publications

References 20 publications

Using Figurate Numbers in Elementary Number Theory – Discussing a ‘Useful’ Heuristic From the Perspectives of Semiotics and Cognitive Psychology

Using Figurate Numbers in Elementary Number Theory – Discussing a ‘Useful’ Heuristic From the Perspectives of Semiotics and Cognitive Psychology

Investigating High School Graduates’ Basis for Argumentation: Considering Local Organisation, Epistemic Value, and Modal Qualifier When Analysing Proof Constructions

Changes in Students’ Mathematical Competencies at the Beginning of Higher Education Within the Last Decade at a German University

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