By Sergei Abramovich
This e-book promotes the experimental arithmetic strategy within the context of secondary arithmetic curriculum by way of exploring mathematical types looking on parameters that have been commonly thought of complex within the pre-digital schooling period. This method, by means of drawing at the energy of pcs to accomplish numerical computations and graphical buildings, stimulates formal studying of arithmetic via making feel of a computational scan. It permits one (in the spirit of Freudenthal) to bridge severe mathematical content material and modern instructing perform. In different phrases, the idea of training test should be prolonged to incorporate a real mathematical scan. while used thoroughly, the process creates stipulations for collateral studying (in the spirit of Dewey) to take place together with the advance of talents very important for engineering functions of arithmetic. within the context of a arithmetic instructor schooling application, the ebook addresses a decision for the guidance of academics in a position to using glossy know-how instruments for the modeling-based instructing of arithmetic with a spotlight on equipment conducive to the advance of the entire STEM schooling on the secondary point. via a similar token, utilizing the book’s pedagogy and its mathematical content material in a pre-college school room can help lecturers in introducing scholars to the guidelines that increase the root of engineering profession.
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Extra resources for Computational Experiment Approach to Advanced Secondary Mathematics Curriculum
Which, 2 3 n as is well known, tends to infinity along with n, a fact originally proved by the fourteenth century French scholar Nicholas d’Oresme. , Lienbach 1974) because, due to a slow growth of the sequence, the results might lead one to conclude that the harmonic series converges. 28333... 8001301; that is, whereas n has increased by than 30 million, sn has increased by 15 only. The use of a spreadsheet in modeling Bolzano-Cauchy principle of convergence gives more accurate results in the case of the harmonic series (Abramovich 1995).
9). 4). Following are eight examples of using the classic Archimedes’ approach and modern educational ideas in the context of solving algebraic equations. Most of the problems discussed, however, are not technology-immune as far as equation solving is understood as the root finding alone. Yet, they were chosen to introduce basic skills and strategies needed to deal with problems discussed in other chapters of the book. Furthermore, considering the end result of solving an equation to be more than just root finding, TEMP encourages learners to understand the meaning of mathematical techniques and problem-solving strategies.
2). This makes it possible not only to diagnose possible errors but better still, to provide explanatory feedback in conceptualizing the very sources of these errors. A naïve view of similarity between equations and inequalities—two relations that on the surface level differ in one symbol only—gives birth to an extrapolation technique responsible for the occurrence of that type of errors. For example, Tsamir and Bassini’s (2004) research showed that many pre-college students believe “that solving inequalities and equations are the same process” (p 809, italics in the original).