tag:blogger.com,1999:blog-7718462793516968883.post5597970873129209052..comments2020-07-28T08:29:43.413-04:00Comments on MadMath: First Exercises with VariablesDeltahttp://www.blogger.com/profile/00705402326320853684noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-7718462793516968883.post-39404115075380194152012-10-03T20:37:22.094-04:002012-10-03T20:37:22.094-04:00^ To complete the thought: It's the marriage o...^ To complete the thought: It's the marriage of the two approaches, both estimation and precise writing, that gives true strength: i.e., a <a href="http://www.angrymath.com/2012/07/backup-parachutes.html" rel="nofollow">backup parachute</a>. Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-89421992936007408522012-10-03T20:35:42.341-04:002012-10-03T20:35:42.341-04:00In some sense I agree. Like my philosophy on prett...In some sense I agree. Like my philosophy on pretty much everything, I think you need both (a) broad conceptual intuition (like basic properties of numbers), and (b) detailed fact knowledge (like memorizing add & multiply tables). I teach a basic math class where I've just added direct training in rounding and estimating, since those oft-assumed skills are totally missing for that population of student.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-19579329967686320262012-10-03T13:38:30.695-04:002012-10-03T13:38:30.695-04:00I have used a similar approach when teaching my so...I have used a similar approach when teaching my son to add and subtract: focusing on patterns of numbers rather than just memorizing. <br /><br />For example, 8+8 is a particular case of adding a number to itself, or doubling. It will always give an even number. These cases seem to be easier for a child to remember.<br /><br />So a problem like 17-8 might be analyzed like this:<br /><br />What is 17-8? <br />I don't know.<br />Whell do you know 8+8?<br />Yes its 16!<br />Then what is 16 - 8?<br />Oh, its 8.<br />Then what's 17-8?<br />Its 9!<br /><br />Likewise, multiplying a number by 5 can be seen as counting by 5. <br />Or, multiplying 11* 11 = 11* 10 (easy!) + 11.<br /><br />This approach seems a little tedious at first, but a young child can learn to do this rapidly. Also it gives a better intuition, they are less likely to come up with an answer that is dramatically wrong.Gregory Matoushttps://www.blogger.com/profile/02695669454780832427noreply@blogger.com