Some methods of problem solving in historical mathematical textbooks

Authors

  • Ján Gunčaga The Faculty of Education of the Comenius University in Bratislava
  • Matthias Brandl University of Passau

DOI:

https://doi.org/10.21344/iartem.v10i1-2.716

Keywords:

historical mathematical textbooks, history of education, Jakub Kresa, Franz Močnik, mathematics, method of generating problems, problem solving

Abstract

This paper makes an excursion into the history of mathematics as presented in mathematics textbooks. We describe some components of mathematical notions in textbooks by Jakub Kresa (1648-1715) as well as some approaches to the problem solving in textbooks by Franz Mo?nik (1814-1892). These historical approaches are connected to modern mathematics education because many international studies, such as The Programme for International Student Assessment (PISA) support the use of problem solving and real-life problems in mathematics education. Word tasks have an important place in school mathematics. There are three important stages for solving these tasks: mathematization, calculation and interpretation of the tasks’ results. We also highlight divergent thinking in problem solving during the educational process.

Author Biographies

  • Ján Gunčaga, The Faculty of Education of the Comenius University in Bratislava

    Ján Gunčaga is Associate Professor of Mathematics Education at the Faculty of Education of the Comenius University in Bratislava. His masters program focused on the teaching of mathematics and physics at the secondary level and was completed at the Faculty of Mathematics and Physics, Comenius University in Bratislava (1997). He completed his doctorate in Didactics of Mathematics in the Faculty of Science at Constantine the Philosopher University in Nitra (2004). His habilitation was at the University of Debrecen in the field of Mathematics Education, which belongs to the field Mathematics and Computer Science in 2010. His current research interests orient towards mathematics education at the primary and lower secondary level, the history of education and using ICT (Information and Communication Technologies) in educational processes.

  • Matthias Brandl, University of Passau

    Matthias Brandl is Professor of Mathematics Education at the Faculty of Computer Science and Mathematics of the University Passau. His masters program focused on the teaching of mathematics and physics at secondary level and was completed at the University Bayreuth (2004-2007). He completed his doctorate in Mathematics at Constantine the Philosopher University Bayreuth (2008). His current research IARTEM e-Journal Volume 10 No 1/2 Some Methods of Problem Solving in Historical Mathematical Textbooks. Ján Gunčaga & Matthias Brandl 78-90 IARTEM e-Journal Volume 10 No 1/2 Some Methods of Problem Solving in Historical Mathematical Textbooks. Ján Gunčaga & Matthias Brandl 78-90 90 interests orient towards mathematical giftedness, mathematical creativity, making connections/joint-up thinking in mathematics education, special needs/inclusion/ twice exceptional children and narrative didactics.

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Published

2019-08-04

Issue

Vol. 10 No. 1-2 (2018)

Section

Articles

License

Copyright (c) 2018 CC-BY-NC-ND

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How to Cite

Some methods of problem solving in historical mathematical textbooks. (2019). IARTEM E-Journal, 10(1-2), 78-90. https://doi.org/10.21344/iartem.v10i1-2.716