“REINVENTING” TECHNIQUES FOR THE ESTIMATION OF THE AREA OF IRREGULAR PLANE FIGURES: FROM THE EIGHTEENTH CENTURY TO THE MODERN … (original) (raw)
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YOUNG PUPILS’ INTUITIVE UNDERSTANDING AND STRATEGIES OF AREA MEASUREMENT
The 28th International Scientific Conference “Educational Research and School Practice”, BOOK OF PROCEEDINGS "THE STATE PROBLEMS NEEDS MODERN EDUCATION COMMUNITY", Editors Jelena STEVANOVIĆ Dragana GUNDOGAN Branislav RANĐELOVIĆ, 2022
Learning area measurement in mathematics instruction implies certain phases that entail rhetorical and symbolical generalizations in terms of mathematical formulas (Smith III & Barrett, 2017; Zacharos, 2006; Zeljić & Ivančević, 2019). It is through mathematical formulas that geometry is represented in Serbian mathematics curricula and this fact is the starting point of our research. When pupils have to solve mathematical tasks, they use various strategies that differ in terms of the correctness of their solution, the time needed for completing the task, and task requirements and scope (Siegler, 1991). To measure the area of a rectangular and overcome the problems arising from pupils’ misunderstanding of the area formula, it is recommended to take a closer look at the structure of the rectangular array by covering the area of the rectangular with a mathematical manipulative in the form of a unit of measurement that pupils are intuitively familiar with from the onset (Đokić, 2014, 2017; Van de Walle, Karp & Bay-Williams, 2013). The concept of covering would enable pupils to conceptualize the relationship between the unit’s dimensions and the dimensions of the rectangular. After this phase, through length measurement and multiplication, pupils can solve the area measurement task using mathematical formulas with understanding. Apart from the covering strategy, the paper looks at the ways pupils conceptualize area (Outhred & Mitchelmore, 2000; Reynolds & Wheatley, 1996; Nunes, Light & Mason, 1993). Can an actual misunderstanding of the structure of a rectangular array be found in our mathematics curricula and, if so, can it be overcome by applying the idea of covering the area of a rectangular array? We conducted an empirical study on pupils’ strategic approaches to covering the area of a rectangular in order to understand how pupils calculate its area. We identified the strategies used by pupils and examined their stages of development.
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