Contextualizing Calculus with Everyday Examples to Enhance Conceptual Learning

Abstract

lecturer and a pedagogical developer at the Staff Development Centre at the Royal Institute of Technology in Stockholm, Sweden (KTH). He has worked for fifteen years with pedagogical courses for different types of teachers and is also responsible for the Research Supervision course that more than five hundred supervisors have taken. He has published in the areas of teaching and learning and supervision. His current field of interest is postgraduate supervision and the learning and teaching of mathematics in engineering education. Contextualizing Calculus with Everyday Examples to Enhance Conceptual Learning AbstractMany engineering students in Sweden have difficulty passing the initial mathematics courses. Teachers complain that students are ill-prepared in pre-calculus and even the best students can only solve standard problems using standard procedures. The aim of teaching in mathematics at university is to develop deep understanding of the subject and to produce conceptually trained students who can then creatively solve unforeseen problems. But how should we educate such students' We hypothesize that the root of the problem lies in decontextualized abstract teaching. The approach adopted in this study is to introduce contextualized teaching of mathematics through concrete examples and to focus students' attention on the role of definitions in mathematics in order to scaffold their development of conceptual understanding. The general idea is to start from the most concrete, everyday examples and work towards more abstract mathematics. By everyday examples, we mean those that can instantly be understood by the students with reference solely to their life experience. Each new concept in the course is introduced verbally, numerically, graphically, and algebraically when applicable. Everyday examples are introduced in the verbal phase of the sequence. Application examples are also used to boost the students' motivation. Quantitative data were gathered from both a diagnostic test and the exam, and qualitative data come from a student questionnaire. The exam results show that the students in the intervention group succeeded better than the control groups. They also became more motivated and had a better grasp of abstract thinking in mathematics.

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