What is DesCartesian Division?
"If they were alive, how might René Descartes and Isaac Newton explain division to mathematics education professors?"
Addition and subtraction are inverse operations. So, it is no surprise elementary mathematics teachers often explain multiplication via repeated addition and division via repeated subtraction. Yet such pedagogies are problematic as they cannot be extended to the set of Real numbers. By contrast, the original ideas and writings of René Descartes and Isaac Newton on multiplication and division easily extend to the Reals. So, if they were alive today, I reveal how they might depict division more deeply and simply than modern mathematics educations professors, in ways currently absent from western K–8 curriculums.
Have fun with the division applet below. Then scroll down on my blog post to read more about what has gone astray in the development of elementary mathematics pedagogies!
CLICK THE LINK BELOW FOR THE APPLET! https://www.jonathancrabtree.com/mathematics/what-is-descartesian-division/
CLICK THE LINK BELOW FOR THE APPLET! https://www.jonathancrabtree.com/mathematics/what-is-descartesian-division/
leading research at cern
7 年An excellent context to Descartes. .emlo-portal.bodleian.ox.ac.uk/collections/?catalogue=rene-descartes
Attorney & NYS Licensed Real Estate Broker
7 年I was also taught - or given the impression - that multiplication is simply repeated addition. I've never seen it shown on a graph. Is it possible to move points a,b, & c on this? I wasn't able to on my PC