250539730-Teaching-Calculus.pdf - Everyday calculus teaching Torbj\u00f6rn Lundh This is a collection of different citations and my own na\u00efve pedagogical

250539730-Teaching-Calculus.pdf - Everyday calculus...

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101Emanuelsson, J., Fainsilber, L., Häggström, J., Kullberg, A., Lindström, B. & Löwing, M. (Eds.) (2009), Voices on learning and instruction in mathematics (p. xx–yy). National Centre for Mathematics Education, University of Gothenburg.Everyday calculus teachingTorbjörn LundhThis is a collection of different citations and my own naïve pedagogical reasoning, as a mathematics teacher in higher education, concerning the teaching of mathemat-ics at an introductory university level. I will start with some comments about the present calculus-teaching situation, from both a teacher and a student viewpoint. Then I will present an interview with one of my favorite teachers. I will also comment on some books and texts that I found helpful to me, when trying to better understand the current calculus teaching challenges. Finally, I will briefly discuss two challenges didactics research are facing today: How to manifest itself as an accepted science, and how to convince active teachers about its usefulness in daily teaching.How is my own calculus-teaching situation? It is far from steady state. On some days, I can almost picture myself as a flexible and perceptive musician in a band. Improvising, answering and commenting the other musicians’ previous phrases and musical ideas. The whole mesh of ideas that creates the calculus we know today is slick, well formulated, and, above all useful. When I am able to help students see some of its beauty, which sometimes can even be viewed in poetic terms, I feel great. Then on other days, I feel that it is a bit of low quality time spent out there for my students. I can then almost picture myself as one of my old drill ser-geants in the army, shouting at the new recruits to get down and crawl in the boot camp mud. ”Expand this function into a Taylor series now!” Making them do some things that everybody that has done science at the university has gone through since the late days of Taylor himself. It is neither that pleasant, nor interesting for them, but it has to be done Torbjörn LundhReader, Department of Mathematical Sciences, University of Gothenburg and Chalmers University of Technology
Torbjörn LundhVoices on learning and instruction in mathematics.102nevertheless. Then, most of the other days, I have probably a more real-istic view of the world and my teaching in general. It is an important and challenging job.What is high quality teaching?Let me now try to exemplify some of the complexities, or paradoxes, one can meet in a learning environment. Does creating a warm cozy atmos-phere always give the best learning environment? We are all being raised to be polite and friendly and we naturally try to do the same in the class-room. We believe that it is vital that the classroom feels safe for the stu-dents in order for them to get the courage to ask any type of questions in order to travel on new paths. Having said that, let me here present two examples to indicate the complexity of the meaning of efficient teaching, where a not-to-recommend teaching styles made me, as a student, work

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