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**1 - 6**of**6**### © 2009 Science Publications Why College or University Students Hate Proofs in Mathematics?

"... Abstract: Problem Statement: A proof is a notoriously difficult mathematical concept for students. Empirical studies have shown that students emerge from proof-oriented courses such as high-school geometry, introduction to proof, complex and abstract algebra unable to construct anything beyond very ..."

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Abstract: Problem Statement: A proof is a notoriously difficult mathematical concept for students. Empirical studies have shown that students emerge from proof-oriented courses such as high-school geometry, introduction to proof, complex and abstract algebra unable to construct anything beyond very trivial proofs. Furthermore, most university students do not know what constitutes a proof and cannot determine whether a purported proof is valid. A proof is a convincing method that demonstrates with generally accepted theorem that some mathematical statement is true and each proofs step must follow from previous proof steps and definition that have already been proved. To motivate students hating proofs and to help mathematics teachers, how a proof can be taught, we investigated in this study the idea of mathematical proofs. Approach: To tackle this issue, the modified Moore method and the researcher method called Z.Mbaïtiga method are introduced follow by two cases studies on proof of triple integral. Next a survey is conducted on fourth year college students on which of the proposed two cases study they understand easily or they like. Results: The result of the survey showed that more than 95 % of the responded students pointed out the proof that is done using details explanation of every theorem used in the proof construction, the case study2. Conclusion: From the result of this survey, we had learned that mathematics teachers have to be very careful about the selection of proofs to include when introducing topics and filtering out some details which can obscure important ideas and discourage students.

### 107 Knowledge Acquisition in Students’ Argumentation and Proof Processes

"... Expert problem solving may be regarded as a process of understanding and modelling real world phenomena. Inductive thinking, empirical observations and deductive reasoning are crucial parts of this process. Experts and students differ in this respect, but they often show similarities in their proble ..."

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Expert problem solving may be regarded as a process of understanding and modelling real world phenomena. Inductive thinking, empirical observations and deductive reasoning are crucial parts of this process. Experts and students differ in this respect, but they often show similarities in their problem-solving behaviour. Our research aims at identifying similarities and differences between experts and students in their mathematical problem solving with respect to argumentation and proof at the upper secondary level. Moreover, we will argue that adequate, as well as inadequate scientific models guiding the students ' argumentation are influenced by the practices in the mathematics classroom. Proof and Scientific Reasoning In the last few years there has been an intense discussion in mathematics education research on students ’ concepts of argumentation and proof. Both aspects are regarded as important for the understanding and application of mathematics. This positive attitude towards argumentation and proof is the result of an important debate among mathematics educators. It was Freudenthal who argued against geometrical proofs, particularly those in the form of classical Euclidean proofs. Accordingly, for many years proofs were regarded as superfluous in the mathematics classroom. It was conjectured that Euclidean proofs were far from providing any kind of mathematical insight, but were a means of initiation into a highly standardised and schematised type of argumentation cultivated only in school mathematics.

### Knowledge

, 2011

"... Abstract In this paper, we present an analytic framework for investigating expert mathematical learning as the process of building a network of mathematical resources by establishing relationships between different components and properties of mathematical ideas. We then use this framework to analyz ..."

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Abstract In this paper, we present an analytic framework for investigating expert mathematical learning as the process of building a network of mathematical resources by establishing relationships between different components and properties of mathematical ideas. We then use this framework to analyze the reasoning of ten mathematicians and mathematics graduate students that were asked to read and make sense of an unfamiliar, but accessible, mathematical proof in the domain of geometric topology. We find that experts are more likely to refer to definitions when questioning or explaining some aspect of the focal mathematical idea and more likely to refer to specific examples or instantiations when making sense of an unknown aspect of that idea. However, in general, they employ a variety of types of mathematical resources simultaneously. Often, these combinations are used to deconstruct the mathematical idea in order to isolate, identify, and explore its subcomponents. Some common patterns in the ways experts combined these resources are presented, and we consider implications for education.

### Michael StarbirdEffects of Traditional and Problem-Based Instruction on Conceptions of Proof and Pedagogy in Undergraduates and Prospective Mathematics Teachers

"... This work is dedicated to my parents. Acknowledgements There are many people who have been helpful and supportive throughout my dissertation work. I have been fortunate to have people in my life who encouraged me to continue on this educational journey. First of all, I appreciate my supervisor, Dr. ..."

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This work is dedicated to my parents. Acknowledgements There are many people who have been helpful and supportive throughout my dissertation work. I have been fortunate to have people in my life who encouraged me to continue on this educational journey. First of all, I appreciate my supervisor, Dr. Jennifer Smith, for guiding me through the process of dissertation research. Jenn, thank you for willing to be open to my ideas and encouraging me with unfailing support and positive feedback. I would also like to thank my dissertation committee, Dr. James Barufaldi, Dr. Kathleen Edwards, Dr. Susan Empson, and Dr. Michael Starbird, for their advice and thoughtful comments on my work. I am very thankful to the professors who allowed me to conduct the study with the students in their courses. I also must thank the participants in this study, especially the 6 prospective secondary mathematics teachers who shared their experience and honest thought with me during the series of interviews. I deeply appreciate the support provided by the Educational Advancement Foundation for being interested in my research, demonstrating belief in my potential and supporting my dissertation work. I would like to thank Dr. Yon-Mi Kim, who believed in my ability and supported me when I decided to study abroad, pursuing a doctoral degree in mathematics education. Thanks to friends, without whom I would not have survived graduate school:

### Sherry FieldStudent-to-Student Discussions: The Role of the Instructor and Students in Discussions in an Inquiry-Oriented Transition to Proof Course

"... 2008 The Dissertation Committee for Stephanie Ryan Nichols certifies that this is the approved version of the following dissertation: ..."

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2008 The Dissertation Committee for Stephanie Ryan Nichols certifies that this is the approved version of the following dissertation: