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Håkan Lennerstad
Blekinge Institute of Technology, Karlskrona, Sweden
This presentation describes a format of a calculus course (taking place 2015) with the main intention of interchanging two different elements during the course. The first is examination in small format, and the second is an examination-free opposite: maximal openness towards student’s mathematical problems in the spirit of ”It’s better to do the errors now than at examinations”. Also, students got used to verbal presentations during lectures since they did this every week. The gothenburgian method of pre- and postlectures was applied. In this method, new concepts are merely illustrated in the prelecture. Proofs are given mainly in the postlecture, which occurs after the students have some calculation experience of the new concepts.
Each week had a one page plan including main themes, goals,” 6 teacher’s problems” and ”6 student’s problems”. In the end of the Tuesday’s prelecture the 6 teacher’s problems were calculated. The first thing in the Friday lecture, students were expected to solve the 6 student’s problems, which was followed by a postlecture. All 42 student’s problems were actually solved by students during the course. Being explicitly non-examination encourages a more genuine mathematical dialogue. Teacher’s learning of students’ mathematical difficulties allows fine-tuning of lecture’s level. The Fridays were complemented by true-false-quizzes every week that pre-covers theory,
i.e. basic intentions and properties of new mathematical concepts. Students must complete each quiz online before each student lecture.
The curriculum of the course was Taylor series, integration, and linear and separable differential equations. Central to the course result is the way in which the teacher comments the students activities and makes it useful for listening students. There are many requirements for this teacher-to-student feedback:
1. To put mathematical problems and issues at the center of attention.
2. To encourage student activity the following weeks.
3. To make obvious common students mistakes in order to avoid them.
4. To encourage reflection about calculations, and thus a deeper understanding of mathematics.
5. To make the connection theory-calculation obvious.
The experience was that feedback almost always can be done both mathematically accurately, relevantly, encouraging, and so it is useful time for listening students.
Results
The students supported the organization of the course strongly. 98% of students participated in the final written exam, and 52% of them passed, which is a higher share than usual for this course. The exam was probably slightly more difficult than usual.
http://www.bth.se/people/hln.nsf/sidor/hakan-lennerstad-research