On skepticism and its role in the development of proof in the classroom

Brown, Stacy

doi:10.1007/s10649-014-9544-4

Cited by 21 publications

(9 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another reason for classifying the students' arguments as invalid was that they used numbers to verify the statements instead of proving them. In fact, students at various levels, even undergraduate students, think that numerical values and examples are more convincing than mathematical proofs (Brown, 2014;Jahnke, 2007;Martin & Harel, 1989;Segal, 2000;Stylianides & Stylianides, 2009). However, Weber (2010) stated that most of the mathematics majors who completed a transition to proof course did not accept empirical arguments as proof.…”

Section: Discussion Implications and Recommendationsmentioning

confidence: 99%

An Investigation of Pre-service Middle School Mathematics Teachers’ Ability to Conduct Valid Proofs, Methods Used, and Reasons for Invalid Arguments

Demiray

Işıksal-Bostan

2015

Int J of Sci and Math Educ

View full text Add to dashboard Cite

The purposes of this study are to investigate Turkish pre-service middle school mathematics teachers' ability in conducting valid proofs for statements regarding numbers and algebra in terms of their year of enrollment in a teacher education program, to determine the proof methods used in their valid proofs, and to examine the reasons for their invalid arguments. A proof questionnaire containing three proof statements was administered to 115 pre-service middle school mathematics teachers in a large state university in Ankara, Turkey. The results showed that more than half of the pre-service teachers were able to conduct valid proofs for the given statements. In terms of year levels, it was seen that the seniors were the least successful group in conducting valid proofs for each statement. When pre-service teachers' valid proofs were analyzed, it was concluded that mathematical induction and direct proof were the mostly used methods for the given statements. When pre-service teachers' invalid arguments were analyzed, it was seen that "inserting numbers to verify the given statement" and "rewriting the givens in the statement" were the common reasons for stating invalid arguments.

show abstract

Section: Discussion Implications and Recommendationsmentioning

confidence: 99%

An Investigation of Pre-service Middle School Mathematics Teachers’ Ability to Conduct Valid Proofs, Methods Used, and Reasons for Invalid Arguments

Demiray

Işıksal-Bostan

2015

Int J of Sci and Math Educ

View full text Add to dashboard Cite

show abstract

“…Moreover, dilemma form proofs are of interest since they can be viewed as a natural extension of students' early reasoning with proofs by cases -extensions which call on the student to reason with inherent uncertainties and, therefore, employ a form of reasoning necessary for engaging in advanced mathematics. Indeed, since uncertainty and doubt have been shown to be a driving force for the production of proofs (Zaslavsky 2005;Brown 2014) and prior research (Leron 1985;Harel and Sowder 1998) had indicated that students' sense of conviction is tied to issues of constructiveness when presented with proofs by contradiction (i.e., when learners are called to reason from false premises), it seemed likely that similar reactions might be found when students are called on to obtain conviction from an inherent uncertainty (i.e., when students are called to reason from multiple premises, one or more of which might be false); that is, dilemma proofs. 6…”

Section: Argument Bmentioning

confidence: 99%

Who’s There? A Study of Students’ Reasoning about a Proof of Existence

Brown

2017

Int. J. Res. Undergrad. Math. Ed.

Self Cite

View full text Add to dashboard Cite

Drawing on prior research on indirect proof, this paper reports on a series of exploratory studies that examine the extent to which findings on students' ways of reasoning about contradiction and contraposition characterize students' views of indirect existence proofs. Specifically, Study 1 documents students' comparative selections and selection rationales when asked to choose the Bmost convincing^proof, given a constructive and nonconstructive existence proof. Study 2 further examines findings from Study 1 by documenting novices' levels of conviction and interpretations of a nonconstructive existence proof. Findings show that when presented with a nonconstructive proof, students tended to not only find the proof convincing but also interpreted the proof constructively. Moreover, the data indicate students who exhibit an awareness of the nonconstructive structure were divided in terms of their views of which form -constructive or non-constructive -was the most convincing. The discussion considers students' reactions to the disjunctive structure of nonconstructive existence proofs and use of pragmatic and theoretical modes of thought.

show abstract

“…While students' methods of obtaining personal conviction and persuading others are related, they are not identical (Segal 2000). In particular, students might recognize that an empirical argument is not an acceptable proof, but still find it personally convincing (Brown 2014;Healy and Hoyles 2000;Segal 2000) and they may believe that proofs must include symbols or be written in a two-column format, even if they find arguments lacking symbols or written as a narrative paragraph to be convincing (e.g., Healy and Hoyles 2000;Martin and Harel 1989). In this paper, we are concerned with the persuasive aspect of mathematics majors' proof schemes-what types of inferences do students think are acceptable in a mathematical proof?…”

Section: Students' Proof Schemesmentioning

confidence: 99%

“…When given proving tasks, such students rarely submit empirical arguments (Iannone and Inglis 2010) and if asked to evaluate such an argument, they will reject it as not meeting the standards of proof (e.g., Bleiler et al 2014;Pfeiffer 2011;Segal 2000;Weber 2010). There is debate as to whether advanced mathematics majors do this because they recognize the limitations of empirical reasoning (Weber 2010) or are merely following the social conventions of their classes or the directives of their instructors (Brown 2014;Segal 2000).…”

Section: Students' Proof Schemesmentioning

confidence: 99%

Mathematics Majors’ Perceptions of the Admissibility of Graphical Inferences in Proofs

Zhen

Weber

Mejía-Ramos

2015

Int. J. Res. Undergrad. Math. Ed.

View full text Add to dashboard Cite

In this paper, we investigate mathematics majors' perceptions of the admissibility of inferences based on graphical reasoning for calculus proofs. The main findings from our study is that the majority of mathematics majors did not think that graphical perceptual inferences (i.e., inferences based on the appearance of the graph) were permissible in a proof, but the majority of mathematics majors did believe that graphical deductive inferences (i.e., inferences based on what must necessarily be entailed by a graph having a certain property) were permissible.

show abstract

On skepticism and its role in the development of proof in the classroom

Cited by 21 publications

References 29 publications

An Investigation of Pre-service Middle School Mathematics Teachers’ Ability to Conduct Valid Proofs, Methods Used, and Reasons for Invalid Arguments

An Investigation of Pre-service Middle School Mathematics Teachers’ Ability to Conduct Valid Proofs, Methods Used, and Reasons for Invalid Arguments

Who’s There? A Study of Students’ Reasoning about a Proof of Existence

Mathematics Majors’ Perceptions of the Admissibility of Graphical Inferences in Proofs

Contact Info

Product

Resources

About