COMPATIBILITY OF ALGEBRAIC AND VISUAL APPROACHES IN SOLVING 3RD AND 4TH ORDER EQUATIONS
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The article analyzes a methodology for teaching third- and fourth-degree algebraic equations in which algebraic methods are employed as the primary instructional approach, while visual tools are used as auxiliary instruments. Students often encounter difficulties when searching for rational roots and applying Horner’s scheme in solving higher-degree equations. In the study, algebraic methods are considered the main teaching mechanism, whereas GeoGebra is treated as a tool for verifying and reinforcing algebraic solutions. The proposed step-by-step model emphasizes thorough instruction in algebraic methods at the initial stage, followed by visual verification to consolidate the results. Such an approach serves as an effective means of developing students’ functional thinking, enhancing their ability to independently identify errors, and fostering mathematical intuition.
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1.Vilenkin N.Ya., Schwartzburd S.I. Algebra and mathematical analysis: Uchebnoe posobie dlya uchashchikhsya school and classes with uglublennym izucheniem mathematiki. Moscow: Prosveshchenie, 2014. 288 p.
2.Drijvers P., Doorman M., Boon P., Reed H., Gravemeijer K. The teacher and the tool: instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 2010, Vol. 75, No. 2, pp. 213-234.
3.Hohenwarter M., Fuchs K. Combination of dynamic geometry, algebra and calculus in the software system GeoGebra. Computer Algebra Systems and Dynamic Geometry Systems in Mathematics Teaching Conference, 2004, Pecs, Hungary.
4.Mordkovich A.G. Algebra and nachala mathematical analysis. 10-11 klassy: methodicheskoe posobie dlya uchitelya. Moscow: Mnemozina, 2015. 202 p.
5.Preiner J. Introducing Dynamic Mathematics Software to Mathematics Teachers: the Case of GeoGebra. Dissertation, University of Salzburg, 2008. -289 p.