Session Information
SES F 03, Paper Session
Paper Session
Contribution
Over the last decade there have been several initiatives to reform mathematics education in Belarus. One of them is a shift from a top-down model of teaching to learners’ active engagement in construction of knowledge. Development of learners’ cognitive culture has become one of the top priorities in teaching mathematics while mathematical intuition as one of its major components –– a focus of research and development. Another factor that has impacted mathematics education in Belarus is cultural change that have recently emerged due to influx of refugees coming from former Soviet republics. Finally, after about some 10 years of experimenting with students’ streaming, Belarus is returning back to inclusive schooling and heterogeneous classes.
The theme of our research is: "The formation of students' cognitive culture through solution of problems developing mathematical intuition in heterogeneous classes". Through our research we: a) identify the main components of "learner’s cognitive culture” concept in studying mathematics; b) develop a theoretical model of learner’s cognitive culture formation by means of mathematical education; c) identify the essential features of "mathematical intuition" concept in the structure of learner’s cognitive culture; d) theoretically justify and develop a typology of tasks aimed at developing learner’s mathematical intuition in heterogeneous classes; e) elaborate a methodology for application of tasks aimed at developing learner’s mathematical intuition, and experimentally verify its effectiveness.
The research is based on the following assumptions:
Cognitive culture is a complex dynamic quality of a learner, which is a set of interrelated core components such as knowledge about the ways and tools of cognition, cognitive skills, experience of creative activity, cognitive norms and values.
Mathematical intuition is an essential component of learners‘ creative activity experience in studying mathematics and it is required for the formation of their cognitive culture. Thus it can be regarded as a mathematical ability.
Each learner has to some extent, mathematical ability and the task of teachers is to assess and develop these abilities.
For the development of learners abilities it is important to diagnose and then develop natural strengths of a learner through her/his inclusion in the systematic work under the direction of a specialist.
"The main goal of teaching mathematics - is to develop abilities of the mind, and among these abilities intuition is by no means the least valuable" [1, pp. 359].
«Mathematical intuition is the ability of students to see the final solution of the problem, in which the conclusion is based largely on conjecture, feeling, almost sudden illumination" [2, pp. 28]
Mathematical intuition as a quality of an individual is demonstrated in the following components of abilities: to advance hypotheses; to quickly assess the results; to grasp a graphic image or model; to notice clearly erroneous conclusions.
The set of tools aimed at developing students' mathematical intuition should include specially designed sets of tasks that contribute to the development of each of the above components of ability.
Cultural diversity in heterogynous school environment needs to be taken into account to support each learner’s development based on her/his interests and needs.
Method
Expected Outcomes
References
1. Пуанкаре, А. О науке. / А. Пуанкаре, (под ред. Л.С. Понтрягина). – М.: Наука, 1983. – "Ценность науки. Математические науки" (пер. с фр. С.Г. Суворова) – 560с. 2. Гуцанович, С.А. Дидактические основы математического развития учащихся: Монография / С.А. Гуцанович. – Минск: БГПУ им. М. Танка, 1999. – 301 с. 3. Крутецкий В.А. Психология математических способностей школьников/ В.А. Крутецкий. – М.: Просвещение, 1968. – 432 с. 4. Ананченко, К.О. Теоретические основы обучения алгебре в школах с углубленным изучением математики: Моногр. для науч. работников по спец. 13.00.02 – теория и методика обучения / К.О. Ананченко – Минск: БГПУ им. М. Танка – 2000. – 307 с. 5. Мышкис, А.Д. О развитии математической интуиции учащихся / А.Д. Мышкис, П.Г. Сатьянов // Математика в школе.– 1987.– № 5.– С. 18–22. 6. Poincaré, Henri The foundations of science, Washington, D.C.: University Press of America, 1982, 553 pp 7. Polya, George. Mathematics and Plausible Reasoning. Princeton, NJ, Princeton University Press, 1954, 496 pp 8. Hadamard, Jacques The Mathematician's Mind: The Psychology of Invention in the Mathematical Field, Princeton University Press, 1996, 166 pp. 9. Myers D. G. Intuition: Its Powers and Perils, Yale University Press, 2004, 336 pp 10. Bastick T. Intuition: How we think and act. New York: John Wiley & Sons Inc. 1982 11. Bowers K.S., Regher G., Baltazard C. & Parker K. Intuition in context of discovery. Cognitive Psychology. 1990
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