# 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

#### 133 Citations

Investigating and improving undergraduate proof comprehension

- 2015

Undergraduate
mathematics
students
see
a
lot
of
written
proofs.
But
how
much
do
they
learn
from
them?
Perhaps
not
as
much
as
we
would
like
–
every
professor
knows
that
students
struggle
to
make
sense… Expand

COMPUTATIONAL AND INFERENTIAL ORIENTATIONS: LESSONS FROM OBSERVING UNDERGRADUATES READ MATHEMATICAL PROOFS

- 2020

This paper presents selected findings from an assessment of university students’ moment-bymoment reading of mathematical proof. This method, adapted from an assessment of narrative reading validated… Expand

How mathematicians assign points to student proofs

- Mathematics
- 2017

Abstract In this paper, we present an exploratory study on the important but under-researched area in undergraduate mathematics education: How do mathematics professors assign points to the proofs… Expand

Mathematics Professors’ Evaluation of Students’ Proofs: A Complex Teaching Practice

- Mathematics
- 2016

This article reports on an exploratory study of mathematics professors’ proof evaluation practices and the characteristics they value in good proof writing. Four mathematicians were interviewed… Expand

Proof Construction and Evaluation Practices of Prospective Mathematics Educators.

- 2015

This study was conducted with 93 freshmen and 82 senior prospective mathematicians and mathematics teachers in order to investigate how they construct and evaluate proofs and whether there are any… Expand

Mathematics majors’ beliefs about proof reading

- 2014

We argue that mathematics majors learn little from the proofs they read in their advanced mathematics courses because these students and their teachers have different perceptions about students’… Expand

Reading Proofs for Validation and Comprehension: an Expert-Novice Eye-Movement Study

- Psychology
- 2018

Does reading a mathematical proof for validation engender different behaviors from reading it for comprehension? Experts and novices each read two mathematical proofs under different sets of… Expand

University Undergraduate Science Students’ Validation and Comprehension of Written Proof in the Context of Infinite Series

- 2017

The reported study explored undergraduate science students’ validation and comprehension of written proofs, reasons given either to accept or reject mathematical procedures employed in the proofs,… Expand

Providing written feedback on students’ mathematical arguments: proof validations of prospective secondary mathematics teachers

- 2014

Mathematics teachers play a unique role as experts who provide opportunities for students to engage in the practices of the mathematics community. Proof is a tool essential to the practice of… Expand

Teaching reader engagement as an aspect of proof

- 2019

For the past decade, philosophers of mathematical practice have examined the nature and function of proofs in mathematical practice, most often in mathematical research practice. More recently they… Expand

#### References

SHOWING 1-10 OF 91 REFERENCES

Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem?

- Psychology
- 2003

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 proofs… Expand

Mathematics Majors' Perceptions of Conviction, Validity, and Proof

- Psychology
- 2010

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 the… Expand

Making the transition to formal proof

- Mathematics
- 1994

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 in… Expand

Facilitating the Transition from Empirical Arguments to Proof.

- Mathematics
- 2009

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 this… Expand

PROOF FRAMES OF PRESERVICE ELEMENTARY TEACHERS

- Psychology
- 1989

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 a… Expand

On Mathematicians' Different Standards When Evaluating Elementary Proofs

- Mathematics, Computer Science
- Top. Cogn. Sci.
- 2013

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

- Psychology
- 2000

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 considered… Expand

Proof constructions and evaluations

- Mathematics
- 2009

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 own… Expand

Why and how mathematicians read proofs: an exploratory study

- Psychology
- 2011

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 reach… Expand

A study of pupils' proof-explanations in mathematical situations

- Sociology
- 1976

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 from… Expand