tag:blogger.com,1999:blog-5957896812820341397.post7529372899355264307..comments2024-01-14T18:14:23.866-08:00Comments on Delta Scape: What is Fluency in Math?delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-5957896812820341397.post-23759717636864640942019-11-27T10:40:36.612-08:002019-11-27T10:40:36.612-08:00Maybe it means proficient. Tried to connect it to ...Maybe it means proficient. Tried to connect it to a <a href="http://duyorreviewandtutorialcenter.ph/" rel="nofollow">review and tutorial center</a> I'm working with where some of my colleagues just misused the words.oduyorhttps://www.blogger.com/profile/03129546996971255634noreply@blogger.comtag:blogger.com,1999:blog-5957896812820341397.post-4849465742310894982017-11-18T17:51:58.942-08:002017-11-18T17:51:58.942-08:00The thing about your German knowledge back in coll...The thing about your German knowledge back in college wasn't that you were only fast and accurate -- it's that you only knew that one sentence! Even if you could perfectly explain why that sentence meant what it does it wouldn't have helped -- you'd still only know one sentence of German.<br /><br />(And, more to the point, how well can you really explain why a sentence means what it does if you only know one sentence?)<br /><br />The math-version of your German story is a kid who literally only knows like 7 x 9 = 63 and no other multiplication.<br /><br />The Klingon analogy works better for me. Of course, though, nobody is trying to teach Klingon to the actors.Michael Pershanhttps://www.blogger.com/profile/17046644130957574890noreply@blogger.comtag:blogger.com,1999:blog-5957896812820341397.post-53208862215537526392017-11-17T14:14:42.082-08:002017-11-17T14:14:42.082-08:00I think the metaphor between language fluency and ...I think the metaphor between language fluency and mathematics fluency can sometimes get a bit strained. Fluency to me mostly means the ability to communicate back and forth (you don't have to be verbally sophisticated or use figurative phrases). But even under the setup you posit: knowing a single sentence in German didn't make you fluent. Knowing a single answer in math isn't going to make you fluent in this domain either. <br /><br />But there's a line: at a certain point knowing enough words/sentences in German and being able to understand them is basically fluency. <br /><br />Likewise, knowing all the basic facts and being able to communicate with them i.e. do problems represents something more than a single one.<br /><br />Thinking about this from another angle. In computer science there is the Turing test to determine if a computer program is an artificial intelligence. If it can answer all the questions from an interrogator and you can't tell the difference between it and a human then it passes. Looking at kids and judging fluency is somewhat similar. If they can answer all the basic questions it doesn't matter how or why they did so, they are indistinguishable and fluent.<br /><br />Note: being fluent doesn't mean you say intelligent things just that you can communicate back and forth. So I think when we ask for flexible mathematical thinking and problem solving its another level beyond fluency. Perhaps this is a good time to introduce numeracy into the conversation.<br /><br /><br />Benjamin Leishttps://www.blogger.com/profile/10974191081762367425noreply@blogger.com