Solving Mathematical Problems: A Personal Perspective

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Degrande, T., Verschaffel, L., and van Dooren, W. (2016). “Proportional word problem solving through a modeling lens: a half-empty or half-full glass?,” in Posing and Solving Mathematical Problems, Research in Mathematics Education. Editor P. Felmer. The word mathematics comes from Ancient Greek máthēma ( μάθημα), meaning "that which is learnt", [11] "what one gets to know", hence also "study" and "science". The word came to have the narrower and more technical meaning of "mathematical study" even in Classical times. [12] Its adjective is mathēmatikós ( μαθηματικός), meaning "related to learning" or "studious", which likewise further came to mean "mathematical". [13] In particular, mathēmatikḗ tékhnē ( μαθηματικὴ τέχνη; Latin: ars mathematica) meant "the mathematical art". [11] Jordan, M. E., and McDaniel, R. R. (2014). Managing uncertainty during collaborative problem solving in elementary school teams: The role of peer influence in robotics engineering activity. J. Learn. Sci. 23 (4), 490–536. doi:10.1080/10508406.2014.896254

Problem solving in mathematics - Royal Society Problem solving in mathematics - Royal Society

Something becomes objective (as opposed to "subjective") as soon as we are convinced that it exists in the minds of others in the same form as it does in ours and that we can think about it and discuss it together. [154] Because the language of mathematics is so precise, it is ideally suited to defining concepts for which such a consensus exists. In my opinion, that is sufficient to provide us with a feeling of an objective existence, of a reality of mathematics ... Kazak, S., Wegerif, R., and Fujita, T. (2015). Combining scaffolding for content and scaffolding for dialogue to support conceptual breakthroughs in understanding probability. ZDM Math. Edu. 47 (7), 1269–1283. doi:10.1007/s11858-015-0720-5 There is still a philosophical debate whether mathematics is a science. However, in practice, mathematicians are typically grouped with scientists, and mathematics shares much in common with the physical sciences. Like them, it is falsifiable, which means in mathematics that, if a result or a theory is wrong, this can be proved by providing a counterexample. Similarly as in science, theories and results (theorems) are often obtained from experimentation. [103] In mathematics, the experimentation may consist of computation on selected examples or of the study of figures or other representations of mathematical objects (often mind representations without physical support). For example, when asked how he came about his theorems, Gauss once replied "durch planmässiges Tattonieren" (through systematic experimentation). [104] However, some authors emphasize that mathematics differs from the modern notion of science by not relying on empirical evidence. [105] [106] [107] [108]

Clarke, B., Cheeseman, J., and Clarke, D. (2006). The mathematical knowledge and understanding young children bring to school. Math. Ed. Res. J. 18 (1), 78–102. doi:10.1007/bf03217430 Khan Academy is a nonprofit with a mission to provide a free, world-class education to anyone, anywhere.

Mathematics - Wikipedia Mathematics - Wikipedia

Zawojewski, J. (2010). Problem Solving versus Modeling. In R. Lesch, P. Galbraith, C. R. Haines, and A. Hurford (red.), Modelling student’s mathematical modelling competencies: ICTMA, p. 237–243. New York, NY: Springer.doi:10.1007/978-1-4419-0561-1_20Cillessen, A. H. N., and Marks, P. E. L. (2017). Methodological choices in peer nomination research. New Dir. Child Adolesc. Dev. 2017, 21–44. doi:10.1002/cad.20206

problems - BBC Bitesize Challenge: Maths problems - BBC Bitesize

Until the 19th century, the development of mathematics in the West was mainly motivated by the needs of technology and science, and there was no clear distinction between pure and applied mathematics. [109] For example, the natural numbers and arithmetic were introduced for the need of counting, and geometry was motivated by surveying, architecture and astronomy. Later, Isaac Newton introduced infinitesimal calculus for explaining the movement of the planets with his law of gravitation. Moreover, most mathematicians were also scientists, and many scientists were also mathematicians. [110] However, a notable exception occurred with the tradition of pure mathematics in Ancient Greece. [111] Frequently Asked Questions about Khan Academy and Math Worksheets Why is Khan Academy even better than traditional math worksheets? To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.Main articles: Mathematical notation, Language of mathematics, and Glossary of mathematics An explanation of the sigma (Σ) summation notation