Expert and Novice Approaches to Reading Mathematical Proofs

@article{Inglis2012ExpertAN,
  title={Expert and Novice Approaches to Reading Mathematical Proofs},
  author={Matthew Inglis and Lara Alcock},
  journal={Journal for Research in Mathematics Education},
  year={2012},
  volume={43},
  pages={358-390}
}
This article presents a comparison of the proof validation behavior of beginning undergraduate students and research-active mathematicians. Participants’ eye movements were recorded as they validated purported proofs. The main findings are that (a) contrary to previous suggestions, mathematicians sometimes appear to disagree about the validity of even short purported proofs; (b) compared with mathematicians, undergraduate students spend proportionately more time focusing on “surface features… Expand

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References

SHOWING 1-10 OF 91 REFERENCES
Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem?
This article reports on an exploratory study of the way that eight mathematics and secondary education mathematics majors read and reflected on four student-generated arguments purported to be proofsExpand
Mathematics Majors' Perceptions of Conviction, Validity, and Proof
In this paper, 28 mathematics majors who completed a transition-to-proof course were given 10 mathematical arguments. For each argument, they were asked to judge how convincing they found theExpand
Making the transition to formal proof
This study examined the cognitive difficulties that university students experience in learning to do formal mathematical proofs. Two preliminary studies and the main study were conducted inExpand
Facilitating the Transition from Empirical Arguments to Proof.
Although students of all levels of education face serious difficulties with proof, there is limited research knowledge about how instruction can help students overcome these difficulties. In thisExpand
PROOF FRAMES OF PRESERVICE ELEMENTARY TEACHERS
This study asked 101 preservice elementary teachers enrolled in a sophomore-level mathematics course to judge the mathematical correctness of inductive and deductive verifications of either aExpand
On Mathematicians' Different Standards When Evaluating Elementary Proofs
TLDR
There was substantial disagreement among mathematicians regarding whether the argument was a valid proof, and applied mathematicians were more likely than pure mathematicians to judge the argument valid. Expand
A Study of Proof Conceptions in Algebra
After surveying high-attaining 14and 15-year-old students about proof in algebra, we found that students simultaneously held 2 different conceptions of proof: those about arguments they consideredExpand
Proof constructions and evaluations
In this article, we focus on a group of 39 prospective elementary (grades K-6) teachers who had rich experiences with proof, and we examine their ability to construct proofs and evaluate their ownExpand
Why and how mathematicians read proofs: an exploratory study
In this paper, we report a study in which nine research mathematicians were interviewed with regard to the goals guiding their reading of published proofs and the type of reasoning they use to reachExpand
A study of pupils' proof-explanations in mathematical situations
Viewed internationally, the proof aspect of mathematics is probably the one which shows the widest variation in approaches. The present French syllabus adopts an axiomatic treatment of geometry fromExpand
...
1
2
3
4
5
...