Why College or University Students Hate Proofs in Mathematics?

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.