2010
DOI: 10.1007/bf03219777
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Abstract: 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 … Show more

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Cited by 15 publications
(10 citation statements)
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“…Based on Table 6, the achievement of the lowest interpretation dimension compared to other dimensions, which is 74%, implies that students are still less than optimal in understanding and interpreting the meaning of the problem in the given question. Previous research stated that students have not been able to understand the questions well because they are not familiar with the problems given (Piatek-Jimenez, 2010). Students are accustomed to working on questions with a fairly low level of difficulty so that when faced with questions that require high thinking skills, they have difficulty understanding the meaning of the questions given.…”
Section: Discussionmentioning
confidence: 99%
“…Based on Table 6, the achievement of the lowest interpretation dimension compared to other dimensions, which is 74%, implies that students are still less than optimal in understanding and interpreting the meaning of the problem in the given question. Previous research stated that students have not been able to understand the questions well because they are not familiar with the problems given (Piatek-Jimenez, 2010). Students are accustomed to working on questions with a fairly low level of difficulty so that when faced with questions that require high thinking skills, they have difficulty understanding the meaning of the questions given.…”
Section: Discussionmentioning
confidence: 99%
“… Öğretmenin sınıf içerisinde önermeleri ifade ederken benimsediği üslup öğrencilerin önermenin manasını kavramada etkili midir? Literatürde yer alan çalışmalar "∃∀" niceleyici sıralamasını içeren önermelerin anlaşılmasının "∀∃" niceleyici sıralamasını içeren önermelere kıyasla daha zor olduğunu söylemektedir (Dubinsky & Yiparaki 2000;Piatek-Jimenez, 2010). Lakin bu çalışmada öğrencilerin cevapları bu durumu destekleyecek bir desen oluşturmamıştır.…”
Section: Tartişma Sonuç Ve öNeri̇lerunclassified
“…Lakin, öğrenciler için niceleyicileri içeren matematiksel önermelerin anlamını yorumlamanın ve bu önermeleri ispatlamanın kolay olmadığı rapor edilmiştir (Epp, 1999). Literatürde yer alan araştırmalar, öğrenciler için "∃∀" sıralamasını içeren matematiksel önermeleri yorumlamanın "∀∃" sıralamasını içeren önermelere nazaran daha zor olduğunu ortaya koymuştur (Dubinsky & Yiparaki, 2000;Piatek-Jimenez, 2010). Dubinsky ve Yiparaki (2000) bu durumun sebebi olarak "∀∃" yapısına sahip olan ifadelerin günlük konuşma dilinde diğerine nazaran daha fazla bulunmasını göstermektedir.…”
Section: Introductionunclassified
“…One common example of disambiguation pertinent to real analysis arises in multiply quantified statements, which includes most limit definitions. A common definition for sequence convergence is, Ba sequence {a n } of real numbers converges to a real number L if ∀ε > 0, ∃N ∈ N such that ∀ n > N, |a n − L| < ε.^Previous mathematics education studies show that students often interpret such statements in ways unintended by their instructors (Burn 2005;Cory and Garofalo 2011;Cottrill et al 1996;Dubinsky and Yiparaki 2000;Durand-Guerrier and Arsac 2005;Epp 2003;Piatek-Jimenez 2010;Roh 2009Roh , 2010Swinyard 2011). While this sequence convergence definition is often called a Bfor-every, there-exists^statement (∀∃), other multiply quantified statements introduce the quantifiers in the order Bthere-exists, for every^(∀∃).…”
Section: Disambiguation and Systematization Of Languagementioning
confidence: 99%