Teaching Mathematical Problem-Solving with the Brain in Mind: How Can Opening a Closed Problem Help?

By Ambrus, András | CEPS Journal : Center for Educational Policy Studies Journal, April 1, 2014 | Go to article overview

Teaching Mathematical Problem-Solving with the Brain in Mind: How Can Opening a Closed Problem Help?


Ambrus, András, CEPS Journal : Center for Educational Policy Studies Journal


* In the international literature, increasing numbers of articles and books are published about teaching and learning, with the brain in mind. For a long time, I have been sceptical about this question. However, seeing many unresolved issues in the teaching and learning of mathematics, I slowly started to study the relevant literature and have attempted to implement some ideas in my teaching. In this article, I will report on my experience with a selected mathematical problem in mathematics lessons and group study sessions; I will demonstrate how I modified the problem, based on my experience with the students, and I will reflect on my studies of brain-based mathematics teaching and learning.

Keywords: problem solving, brain based learning, working memory, open problems, representations, students' activity

U?enje resevanja matemati?nih problemov z upostevanjem mozganov: kako lahko pomaga odpiranje zaprtega problema?

András Ambrus

* V mednarodni literaturi naras?a stevilo objavljenih ?lankov in knjig o pou?evanju in u?enju, ki upostevata delovanje mozganov. Dolgo ?asa sem bil skepti?en do tega vprasanja. Vendar pa sem ob opazanju ve- liko neresenih tezav pri pou?evanju in u?enju matematike po?asi za?el analizirati relevantno literaturo in skusal vpeljati nekaj idej v svoje pou?evanje. V prispevku bom predstavil svoje izkusnje z izbranim matemati?nim problemom pri urah matematike in skupinskih studijskih sre?anjih. Pokazal bom, kako sem na podlagi svojih izkusenj s studenti problem modificiral, reflektiral pa bom tudi svoj studij pou?evanja in u?enja matematike ob upostevanju delovanja mozganov.

Klju?ne besede: resevanje problemov, u?enje na podlagi mozganov, delovni spomin, odprti problemi, prikazi, aktivnost u?encev

Introduction

For a long time in the Hungarian teaching practices of mathematics, the scientific aspect of mathematics dominated, while the psychological, ped- agogical, social, biological aspects were mostly neglected. It is not surprising that in Hungarian mathematics curricula and in the mathematics textbooks (including in lower grades) there is a chapter with the title 'Sets. Logic', which cannot be found in other European and American curricula and mathematics textbooks. In short, in Hungarian mathematics teaching, the symbolic, abstract and verbal aspects are dominant.

Regarding mathematical problems and tasks, the so-called closed prob- lems are predominantly used. I can characterise our mathematics teaching by quoting the opinion of Laurinda Brown, who, after numerous visits to Hungar- ian secondary schools, summarised her experiences in the following way: 'You in Hungary are teaching mathematics; we in England children'.

Another main characteristic of Hungarian mathematics teaching is the fostering of talented pupils, which is in the centre of mathematics teaching. Hungary is a small country from which many world famous mathematicians come. The idea is that such a small country must honour its talent, because they can contribute in a great manner to the development of our country. A direct consequence of focusing mainly on fostering talented students is that 90% of the students suffer from this situation. Teaching not only the rather talented but also average students, I slowly started to seek some possibilities to help the aver- age pupils. Many books and articles have been published recently on the topic of learning with a specific focus on how the brain works, which can be also ap- plied for mathematics education. Based on my studies, I started to change my mathematics teaching style.

In this article, I will report about my experience with a selected problem, which was formulated and used in Hungarian mathematics teaching in a closed form. However, seeing the immense difficulties my students had, I opened the problem. I have fifty years mathematics teaching experience; nevertheless, I think sometimes it may be appealing to watch and listen to other experts. …

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