A Study of Students' Reasoning About “There exists no ...”

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A Study of Students' Reasoning About “There exists no ...”

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[SHS.EDU]Humanities and Social Sciences/Education [MATH.MATH-HO]Mathematics [math]/History and Overview [math.HO][SHS.EDU] Humanities and Social Sciences/Education [MATH.MATH-HO] Mathematics [math]/History and Overview [math.HO]metatheoretical reasoning proof by contradiction

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International audience; In this paper, we report findings from two studies of students' engagement in metatheoretical tasks drawn from a model of the reasoning requirements of a proof by contradiction. The studies explored students' engagement in and success with the tasks, as well as the similarities and differences in students' and mathematicians' approaches. Findings indicate students tended towards syntactic, logical theory approaches while mathematicians gravitate towards semantic, mathematical theory approaches. Drawing on interview data, it is shown that students may use symbols to avoid employing fragile content knowledge, yet encounter further difficulties by viewing quantifiers as appended symbols.

year	journal	country	edition	language
2018-04-05

https://hal.archives-ouvertes.fr/hal-01849955

PEPhysical Sciences and Engineering
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  - PE2_2 Phenomenology of fundamental interactions
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  - PE2_6Nuclear, hadron and heavy ion physics
  - PE2_8Gas and plasma physics
  - PE2_5Classical and quantum physics of gravitational interactions
  - PE2_7Nuclear and particle astrophysics
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  - PE2_10Atomic, molecular physics
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  - PE2_17Metrology and measurement
  - PE2_16Non-linear physics
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- PE1Mathematics
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  - PE11_14Computational methods for materials engineering
LSLife Sciences
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  - LS4_11Haematopoiesis and blood diseases
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  - LS4_13Other non-communicable diseases (except disorders of the nervous system and immunity-related diseases)
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  - LS5_4Neural stem cells
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SHSocial Sciences and Humanities
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  - SH1_16Quantitative economic history, economic systems, institutional economics
  - SH1_5Corporate finance; international finance
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  - SH4_2Personality and social cognition; emotion
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