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Structured Derivations Supporting High-School Mathematics

Ralph-Johan Back, Mia Peltomäki, Tapio Salakoski, Joakim von Wright, Structured Derivations Supporting High-School Mathematics. In: A. Lavonen J. & Meisalo V Laine (Ed.), Current research on mathematics and science education, Research Report 253, 104-122, University of Helsinki, 2004.

Abstract:

At high school and lower level education, using exact formalism in definitions and
proofs is usually avoided on mathematics courses. Many students consider mathematical
proofs as tricks and, indeed, as they develop fear of the whole subject, rigorous
mathematical reasoning remains an everlasting secret to most of them. In this study,
we examine if the use of a special paradigm and notation called structured derivation
can improve high-school students’ understanding of mathematical reasoning and
problem solving. The method is theoretically well founded and more rigorous and
exact than the traditional methods used in high-school mathematics, and it contributes
not only to the preciseness of expression but also to more systematic and
straightforward presentation of mathematical reasoning. Furthermore, this method
allows mathematical expressions and derivations to be considered on various abstraction
levels according to teacher’s desires and students’ skills. The use of structured
derivations in mathematics teaching has been examined and tested at a Finnish High
School in Turku on the compulsory courses in advanced mathematics since autumn
2001. The study is done with two groups at the same entry level using the new method
in teaching the test group and traditional methods with the control group. We are also
interested in comparing advantages and disadvantages of the method with groups at
different entry levels. The project is still in progress but the preliminary results are
very encouraging, suggesting that this method can improve the performance of high
school students and, moreover, deepen their learning on mathematical thinking.

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BibTeX entry:

@INPROCEEDINGS{inpBaPeSavo04a,
  title = {Structured Derivations Supporting High-School Mathematics},
  booktitle = {Current research on mathematics and science education},
  author = {Back, Ralph-Johan and Peltomäki, Mia and Salakoski, Tapio and Wright, Joakim von},
  series = {Research Report 253},
  editor = {Laine, A. Lavonen J. & Meisalo V},
  publisher = {University of Helsinki},
  pages = {104-122},
  year = {2004},
  keywords = {high-school mathematics, structured derivation},
}

Belongs to TUCS Research Unit(s): Learning and Reasoning Lab

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