tag:blogger.com,1999:blog-7718462793516968883.post5693278169330580468..comments2023-03-02T12:12:05.847-05:00Comments on MadMath: Automatic DrillsDeltahttp://www.blogger.com/profile/00705402326320853684noreply@blogger.comBlogger13125tag:blogger.com,1999:blog-7718462793516968883.post-66423395451836275622013-12-08T15:16:45.293-05:002013-12-08T15:16:45.293-05:00Nice, I think that's mostly my software engine...Nice, I think that's mostly my software engineering/numerical analysis bleeding through. :-)Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-6533306019370104482013-12-07T14:23:34.571-05:002013-12-07T14:23:34.571-05:00This is so cool! I sometimes feel like I don't...This is so cool! I sometimes feel like I don't have enough imagination. This is definitely the way to play with it. If students could build their own, and discuss advantages and disadvantages, I think they'd have a deeper understanding, even if they ended up thinking the convention wasn't the best chioce.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-42070758880232835832013-12-07T12:05:05.290-05:002013-12-07T12:05:05.290-05:00Yeah, here I'm thinking of the fast way to con...Yeah, here I'm thinking of the fast way to convert a string to an integer. Like: [oop] 3x^2+5x+2 = (3x+5)x+2, which in [oop*] would be 3x+5x+2. Which also has the advantage of being more computationally efficient (4 multiplies for [oop] vs. 2 multiplies for [oop*]). You could then define degree as the number of times "x" appears in the expression, etc.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-70824299791540860852013-12-07T10:16:48.181-05:002013-12-07T10:16:48.181-05:00Maybe I've been convinced too easily? Maybe po...Maybe I've been convinced too easily? Maybe polynomials just feel like natural sorts of things to want to describe. When translating from the particulars of a situation (three times as much as eight more than x is a fine example), there is probably no one oop (I'd call it ooo) that is better. But once we're hanging out in the world of mathematical stuff, I want to talk about how many of each power of x (polynomials) easily, and that requires the current oop.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-3867460327807477532013-12-07T04:14:34.930-05:002013-12-07T04:14:34.930-05:00Agreed, of course, that the existing order of oper...Agreed, of course, that the existing order of operations boils down to "strongest first". But it seems like the brevity in one direction is offset in another. Say we ignore juxtaposition, and denote [oop] for normal ordering, [oop*] for hypothetical reverse ordering. While [oop] 2*x+5 is shorter than [oop*] (2*x)+5, the translation of a common statement like "three times the sum of a number and eight" is [oop] 3*(x+8), longer than [oop*] 3*x+8. <br /><br />Just a thought -- to date I haven't seen a claim that [oop] is inevitable that convinced me. If I found one I'd be excited. :-)<br />Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-44031121777648685702013-12-06T14:12:45.808-05:002013-12-06T14:12:45.808-05:00Order of operations isn't as arbitrary as some...Order of operations isn't as arbitrary as some people think it is. Strongest operation comes first. And I'm guessing it was developed so that 2x^2-3x+7 (and things like it) would have the right meaning without parentheses. Hmm, I wonder if we could get students to figure out what order of operations they'd choose, if they were the queens and kings of math.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-73793238321197294842013-12-06T11:08:51.564-05:002013-12-06T11:08:51.564-05:00Definitely a prioritization issue, as there's ...Definitely a prioritization issue, as there's about 100 "would be nice" things on the first day. For algebra, among the top things for me are a correct order of operations (the only arbitrary thing; almost everything later can be explained by it), and seeing variables in translated identities (thinking abstractly, not about specific numbers, and incidentally reviewing some basic properties). Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-91470382799377167832013-12-06T10:57:10.155-05:002013-12-06T10:57:10.155-05:00I don't have any quickie tests to check pre-re...I don't have any quickie tests to check pre-requisites in any of the classes I'm teaching now. It's worth thinking about.<br /><br />On the other hand, I like a different emphasis on the first day. I want them to see that math is about thinking, not about memorizing procedures. Hmm... How to address both issues?Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-3166541451780225562013-12-06T10:55:22.702-05:002013-12-06T10:55:22.702-05:00gswp, I'd like to see what you come up with.gswp, I'd like to see what you come up with.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-79826642251574304092013-12-05T14:17:07.325-05:002013-12-05T14:17:07.325-05:00My students at the end of the algebra course seeme...My students at the end of the algebra course seemed thankful for the speed-graphing drills. I'll also now try doing stuff like that for prerequisites on the 1st-day, maybe it will motivate some people to get to the math workshop early to fix gaps. I'd be interested in hearing how this works for anyone else.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-13715205445521317842013-12-05T12:17:42.525-05:002013-12-05T12:17:42.525-05:00I've been assuming automaticity with simple al...I've been assuming automaticity with simple algebra in my engineering classes, but I suspect that it is not there. Perhaps I should do some timed drills in the Applied Circuits class on some very simple examples.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-35285210100288897172013-12-03T11:19:52.714-05:002013-12-03T11:19:52.714-05:00Sue, that's really good feedback, I'm glad...Sue, that's really good feedback, I'm glad to know about that. For first-day algebra, I was leaning towards a timed sheet on integer operations, which would include a lot of multiplications and divides along the way.<br /><br />Actually yesterday at the end of my algebra classes I did a timed worksheet on matching linear equations to graphs -- it went over pretty well, and the students who were present said it was helpful.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-16978882331461031432013-12-02T14:35:39.377-05:002013-12-02T14:35:39.377-05:00In beginning algebra (community college), I give a...In beginning algebra (community college), I give a timed multiplications test on day one. I have it on a spreadsheet, so I can randomize. It has one instance of every one-digit problem (7x8 or 8x7, not both). They can retake until they get it all. I don't have timed tests in any other classes, perhaps I should. Calc II students should be able to do derivatives quickly.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.com