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ERIC Number: EJ914119
Record Type: Journal
Publication Date: 2010
Pages: 16
Abstractor: As Provided
Reference Count: 19
ISSN: ISSN-1033-2170
Students' Interpretations of Mathematical Statements Involving Quantification
Piatek-Jimenez, Katrina
Mathematics Education Research Journal, v22 n3 p41-56 2010
Mathematical statements involving both universal and existential quantifiers occur frequently in advanced mathematics. Despite their prevalence, mathematics students often have difficulties interpreting and proving quantified statements. Through task-based interviews, this study took a qualitative look at undergraduate mathematics students' interpretations and proof-attempts for mathematical statements involving multiple quantifiers. The findings of this study suggest that statements of the form "There exists . . . for all . . ." (which can be referred to as EA statements) evoked a larger variety of interpretations than statements of the form "For all . . . there exists . . ." (AE statements). Furthermore, students' proof techniques for such statements, at times, unintentionally altered the students' interpretations of these statements. The results of this study suggest that being confronted with both the EA and AE versions of a statement may help some students determine the correct mathematical meanings of such statements. Moreover, knowledge of the structure of the mathematical language and the use of formal logic may be useful tools for students in proving such mathematical statements. (Contains 1 table and 3 footnotes.)
Mathematics Education Research Group of Australasia. GPO Box 2747, Adelaide SA 5001, Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A