<html><head><style type="text/css"><!-- DIV {margin:0px;} --></style></head><body><div style="font-family:courier,monaco,monospace,sans-serif;font-size:12pt"><div style="font-family: courier,monaco,monospace,sans-serif; font-size: 12pt;">Jay,<br><br>1. I agree the core issues in teaching programming and teaching formal math are the same core issues.<br><br>2. I'm glad you admit, as I do, that you're not really sure how kids learn algebra. Certainly we could teach the same way teachers have for the last 50 years and we would get the same results: some get it and most don't. Teaching in public education in the US now, though, we are pushed constantly to ensure that <a href="http://http://www.theonion.com/content/node/29730">all students get it</a>. I'm a pretty successful teacher at a challenging school. Why am I successful? I'm not sure. I have pretty good report with students and I'm by nature always wanting to learn more in
life. I think that gets me as far as any specific techniques I've tried through the years.<br><br>3. I had to laugh when I read what you wrote about educational consulting firms. They drive me nuts! The latest one my district paid beaucoup money for had to do with "tactile organization", so now teachers all over here are making sure they have their students folding bright colored paper into "<a href="http://http://www.robinfogarty.com/makingthelittlebooks76.html">magic books</a>" to try to bring those test scores up!<br><br>4. Finally, I think your point about kids taking a year of "brain growth "and trying again is a good one. We call that a "circular curriculum" in IMP math. Often if you just move on, even though you feel some of your students are not getting it, when you next come back to that topic you find that more of them have mysteriously become more capable at that skill. This happens a lot in math and I think the
same happens in learning programming. Kind of like how Ron Stephens, on the <a href="http://http://www.awaretek.com/python/index.html">Python 411 Podcasts</a> described his learning of Python by jumping from one tutorial to the next and seeing the same topic in several different ways and finally "getting it".<br><br>Richard<br><br><div style="font-family: times new roman,new york,times,serif; font-size: 12pt;">----- Original Message ----<br>From: Jay Bloodworth <jbloodworth@sc.rr.com><br>To: edu-sig@python.org<br>Sent: Sunday, July 8, 2007 1:37:24 PM<br>Subject: Re: [Edu-sig] a non-rhetorical question<br><br><div>I'm joining the discussion late; I'm going to respond on a couple of<br>points that resonated with me, but forgive me for neglecting a few<br>attributions. Also, I'm going to ramble a bit through some of the<br>things I think about as a math educator. Hopefully I can make it work<br>the trip for you to follow along.<br><br>I don't
teach programming. I teach math in a public school - algebra<br>and geometry to 7th and 8th graders. While certainly there are<br>differences, I think the core issues in teaching the style of analytical<br>thinking are the same for programming and formal math.<br><br>I've been teaching math for 8 years. I'm department head, National<br>Board certified, my test scores are pretty good, the high school<br>teachers generally say my students know their stuff. That being said, I<br>honestly have no idea how to teach algebra. I'm not positive anyone<br>does.<br><br>I present the algorithms correctly. I give mnemonics, organizers, and<br>shortcuts wherever I can. I show numerous examples, give the students<br>plenty of practice, accurately diagnose (at least the proximate cause)<br>and correct mistakes when students make them. Plenty of students are<br>very successful. But some
aren't, despite their and my (apparent) best<br>efforts.<br><br>In the more extreme of these cases, I tell the student and parents that<br>he or she is simply not ready for algebra, that they can repeat the<br>course next year and with a year of brain growth under their caps they<br>will probably be very successful. And they almost always are.<br><br>So at one level "not ready for algebra" is an entirely correct<br>diagnosis. But then the question becomes: What's going on in the brain<br>of the "ready" student that is different from the "not ready" student?<br>Call that question A. Once we've answered questioned A, question B is<br>obviously: Is there a different way to teach the "not ready" student so<br>he/she can be successful earlier? Important question, but I don't think<br>we have much chance of answering it until we make some progress on A,<br>and from where I am in the trenches, I don't even see any work being<br>done on
it.<br><br>Bit of an aside: The hip thing in education now is "brain research".<br>Some consulting firm sells the school 200 copies of their book and<br>charges us beaucoups of money for a three day inservice to tell us<br>things like the average human brain can hold 3-10 "chunks" of data at a<br>time; the amygdila is the part of the brain that controls attention and<br>that we need to engage the amydilas of students if we wish to teach<br>them; that students learn better when they're happy than when they are<br>sad or mad. I'm quoting selectively only because my brain (amygdila and<br>all) shuts down when I have to sit through this garbage. It's<br>frustrating not because the notion of brain research in the service of<br>is a bad idea, but because the brain research we need is the kind that<br>answers question A, not the kind that tells us that students learn<br>better if the walls are blue.<br><br>Now, getting back to Andy's question. My
first response to this was<br>that as a teacher he should have had a pretty good idea of how students<br>would do on this assignment because they should have been assessed<br>informally on assignments like this one before. But as I thought about<br>it before, I realized that there is a lot of room to debate what is<br>meant by "assignments like this one". Does that mean an assignment with<br>precisely the same logical structure but just different strings?<br>Another "loop until" with slightly different conditions? Loops, input,<br>and conditions separately? Or pairwise, but never all three? I<br>constantly see example of students who are fluent with two skills<br>individually but flail wildly when asked to compose them (e.g. they can<br>do 2x+3x and 2/5+3/4 but not 2/5x+3/4x). Why some students fail at<br>these composed tasks even when the interface between the modules is very<br>clean is a big part of the
answer to my "question A", and as I've said I<br>don't think we're very far along in terms of answering it. As a<br>practical matter, Andy, I think my answer to your question is that you<br>need to give your students a lot more practice that is a lot more<br>similar to what you plan to assess them on than your gut tells you you<br>need.<br><br>Whew. Sorry for the brain dump. My thought were a lot more focused in<br>my head. The upshot is I don't think there is an easy answer.<br>Programming computers is easy. Programming brains to program (or to<br>combine like terms, or to solve systems, or whatever) is hard,<br>particularly since a good portion of the brains at large seem to<br>implement the algorithms according to different semantics than than the<br>ones we intend. Hopefully one day we can reverse engineer these brains<br>enough that we can program them effectively as
well.<br><br>Jay<br><br>_______________________________________________<br>Edu-sig mailing list<br>Edu-sig@python.org<br><a target="_blank" href="http://mail.python.org/mailman/listinfo/edu-sig">http://mail.python.org/mailman/listinfo/edu-sig</a><br></div></div><br></div></div><br>
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