Auteur principal			Co-auteurs(s)
Nom :	Dr. Lisa Townsley		Nom :
Courriel :	ltownsley@ben.edu		Courriel :
Institution ou compagnie:	Benedictine University		Nom :
Département:	Mathematics		Courriel :
Ville :	Lisle		Nom :
État/Province :	IL		Courriel :
Pays :	USA		Nom :
Type de présentation:	Conférence :  50 minutes.		Courriel :
Conférence et numéro :	ACDCA ,    Numéro : A54		Horaire :   Local :	samedi, 14h00   1302
Site Internet :
Titre de la communication :	Why DO We Teach Theorems in Calculus?
Résumé de la communication :
Why is it that we teach theorems to our students in Calculus? And how can technology, especially Derive and a web-based discussion tool, help this endeavor? The speaker aims to convince you that the study of key theorems is important to student development of reasoning, problem solving, logic and language skills. In this presentation, we will examine some theorems from College Algebra and Trigonometry and contrast them with the types and usage of theorems in Calculus. It is proposed that the student interaction with theorems in calculus undergoes significant development, from a first interface with the Intermediate Value Theorem, through the Fundamental Theorems, to more advanced notions such as applying the Mean Value Theorem to definite integrals or the interaction between orthogonality and dot product. The distinctions between “if p then q” and its converse or contrapositive, and the full implications of an “if and only if” theorem can be developed gradually in the context of a calculus sequence, with the student making significant progress in just one semester of study. Course software, especially graphing utilities and computer algebra systems, can aid in exploration of the theorems, or be utilized as experimental tools to gather data in the development of a conjecture prior to proof. And a web-based discussion tool can be helpful in fomenting further discussion of related topics, such as interpretations of a recent theorem in context.