tag:blogger.com,1999:blog-5358710624534833105.post7681065481096925945..comments2015-10-07T01:04:47.245-07:00Comments on reflections: Unreflectingly Applying Known StepsAbhijit Mahabalhttps://plus.google.com/106534726360390550650noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-5358710624534833105.post-35533278678083236142013-01-13T19:40:48.320-08:002013-01-13T19:40:48.320-08:00To be honest, I am not sure when or how those will...To be honest, I am not sure when or how those will emerge. Suhana already knows the word "add" and can add small numbers using fingers (including, for problems whose answer exceeds 10, "Baba, can I borrow your fingers?")My guess is that as she does more word problems, she'd realize that certain situations result in things that look like the operation of addition that she already does. We'll see.<br /><br />Of course, the very notion of addition as you understand it today is very abstract and complex --- if you include additions of fractions, complex numbers, polynomials, elements of fields, adding 3 hours to "11:53 PM", the overriden addition operator of a C++ class, additions with infinitely many terms (such as the "addition" that defines pi), not to mention seeing integration as a limiting case of addition. Addition is not a monolithic concept; the conceptual apparatus for this rich concept must co-develop with the many other concepts it depends on. Multiple leaps of abstraction are needed and the notion of addition as understood by different people is perhaps quite different --- most people and neither mathematicians nor programmer, and a notion of addition restricted to real numbers is sufficient. Is there a qualitative difference in understanding this "simple" concept? I don't know. I am quite curious to see how it develops :)amahabalhttp://www.blogger.com/profile/14822036398618537534noreply@blogger.comtag:blogger.com,1999:blog-5358710624534833105.post-4400511762415219972013-01-13T00:43:13.601-08:002013-01-13T00:43:13.601-08:00It will be interesting to see when the abstract co...It will be interesting to see when the abstract concepts of addition and subtraction emerge from the word problems. Are there links related to that (from studies)?ashish mahabalhttp://www.blogger.com/profile/16301823501547206274noreply@blogger.com