June 18, 2006
June 18, 2006
June 21, 2006
11.779.1 - 11.779.10
Integrating Applications in the Technion Calculus Course: A Supplementary Instruction Experiment
Science and Engineering students in the course of their academic studies and further carriers continue applying calculus as their professional tool. In higher education, the ability to apply mathematics has been recognized as one of the main learning outcomes required from graduates of the engineering programs1. The mission of mathematics education is more than to impart the knowledge of mathematical rules, theorems and procedures, but to develop the ability to put mathematical knowledge and skills to functional use in a multitude of contexts2. Applications and modeling are a central theme in mathematics education and mathematics education research. "Very many questions and problems, concerning human learning and the teaching of mathematics affect, and are affected by relations between mathematics and the real world" 3.
There is an intensive debate on applications and modeling in mathematics curricula for engineering students. Many educators believe that applied mathematics skills can be developed in undergraduate mathematics courses, particularly in calculus4-6. Kumar and Jalkio7 proposed a conceptual framework for teaching mathematics from the application point of view. It concerns the mathematical skills required by the engineering disciplines, mathematics courses for developing these skills, and relevant applied problems. A number of mathematics with applications textbooks has been recently published8-10, which implemented the following principles: - Topics are presented geometrically, numerically, analytically, and verbally. - Formal definitions and methods evolve from the investigation of practical problems. - The real world problems are open-ended and may have more than one solution.
This paper reports a study of applications-integrated Multivariable Calculus course at the Technion. In the study we developed and tested different methods of integrating applications in the calculus course without affecting its mathematical level and scope. The study examined the effect of learning applications on students' understanding calculus concepts and attitudes towards the course.
Cognitive psychologists noted that instruction should refer to individual characteristics of learners. The educational approach which coordinates student's abilities and teaching methods is Attitude Treatment Interaction11-13. ATI points that students can be convergent or divergent thinkers, short-term or long-term memorizers, extraverts or introverts, more or less confident, etc. ATI offers a variety of instructional methods and gives students opportunities to choose those which fit their learning styles. The educational approach emphasizes team- based inquires and project assignments in which the students can select their preferred learning strategies. The ATI indicated that integrating different instructional methods provided more students with opportunities of successful and motivated learning. It gave rise to substantial examination of different learning styles and approaches to address them in curriculum and instruction.
Aroshas, S., & Verner, I., & Berman, A. (2006, June), Integrating Applications In The Technion Calculus Course: A Supplementary Instruction Experiment Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--700
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