Corpus ID: 60700728

Students' language in computer-assisted tutoring of mathematical proofs

@inproceedings{Wolska2015StudentsLI,
  title={Students' language in computer-assisted tutoring of mathematical proofs},
  author={Magdalena Wolska},
  year={2015}
}
Truth and proof are central to mathematics. Proving (or disproving) seemingly simple statements often turns out to be one of the hardest mathematical tasks. Yet, doing proofs is rarely taught in the classroom. Studies on cognitive difficulties in learning to do proofs have shown that pupils and students not only often do not understand or cannot apply basic formal reasoning techniques and do not know how to use formal mathematical language, but, at a far more fundamental level, they also do not… Expand
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References

SHOWING 1-10 OF 362 REFERENCES
Towards an Intelligent Tutor for Mathematical Proofs
TLDR
It is shown how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. Expand
Supporting the formal verification of mathematical texts
TLDR
This paper first performs an analysis of three textbook proofs by hand, then describes a computational framework that aims at mechanising such an analysis and constitutes promising steps towards a natural mathematician–machine interface for proof development and verification. Expand
Student Proof Exercises Using MathsTiles and Isabelle/HOL in an Intelligent Book
TLDR
This paper investigates using an automated proof assistant, particularly Isabelle/HOL, as the model supporting first year undergraduate exercises in which students write proofs in number theory, using MathsTiles: composable tiles that resemble written mathematics. Expand
MENON: automating a Socratic teaching model for mathematical proofs
TLDR
This thesis presents techniques to automatically integrate different aspects of teaching in a unified natural-language output, and proposes a method for automating adaptive feedback and implements the tutorial manager Menon as a proof-of-concept for the domain of set theory proofs. Expand
The Language of Quantification in Mathematics Instruction
TLDR
C cultivating students’ sensitivity to logic and language in the pre-college years could check the formation of these habits before they become deeply ingrained, and the success of programs such as TexPREP provides objective support for such a conclusion. Expand
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
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
A Computer Environment for Writing Ordinary Mathematical Proofs
TLDR
The main goal of the project is to create a system that imitates standard mathematical practice in the sense that it allows for natural modes of reasoning to generate proofs that look much like ordinary textbook proofs. Expand
A generalized system for university mathematics instruction
EXCHECK is a system for developing mathematically-based CAI courses. It is currently being used at Stanford University to teach a college-credit course in axiomatic set theory The design of thisExpand
An Intelligent Tutoring System Incorporating a Model of an Experienced Human Tutor
TLDR
It is found that symbolization is difficult because it is the articulation in the "foreign" language of "algebra" and the discovery of a "hidden" skill in symbolization. Expand
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