tag:blogger.com,1999:blog-235276292454918436.post2716888587574259096..comments2020-05-31T14:46:59.357-04:00Comments on Math Hombre: Teacher's BlockJohn Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-235276292454918436.post-51879973318628465132016-02-22T20:33:25.722-05:002016-02-22T20:33:25.722-05:00I've used a number of new visions activities f...I've used a number of new visions activities for my college algebra. It seems as though we are trying to teach it in a similar way and are seeing similar frustrations. Solidarity, John. Megan Schmidthttp://mathybeagle.comnoreply@blogger.comtag:blogger.com,1999:blog-235276292454918436.post-7792883437819148282016-02-22T08:00:26.395-05:002016-02-22T08:00:26.395-05:00And sorry, related the image you chose above that ...And sorry, related the image you chose above that I created was for the second type of instructional activity we support called Connecting Representations.Davidhttps://www.blogger.com/profile/08098221991466148258noreply@blogger.comtag:blogger.com,1999:blog-235276292454918436.post-65230464087034062152016-02-22T07:59:45.210-05:002016-02-22T07:59:45.210-05:00John,
Our project supports a whole bunch of schoo...John,<br /><br />Our project supports a whole bunch of schools with students with an extremely wide variety of mathematical understandings. We've been asking our teachers to use a couple of different instructional activities with their students and many of them have, and found that repeated use of these instructional activities helps with a bunch of different things including student confidence in mathematics and students capacity to talk to each other about mathematics.<br /><br />Some sample tasks are here: http://math.newvisions.org/instructional-activities Each task has a link to the "how to guide" for running the instructional activity but for Contemplate then Calculate, this guide is the best I've seen: http://tedd.org/?tedd_activity=contemplate-calculate-submitted-bpes-boston-teacher-residency-program<br /><br />Contemplate then Calculate asks students to first identify what they notice when an image is flashed. By flashing the image for just a moment, no one can notice everything and so students have to rely on each other. More importantly, there are some critical things to be noticed in a mathematical problem and typically we find that many students have not been taught to stop and see what they notice before attempting a mathematical problem. Once noticings are recorded for everyone to use, we ask students to try and find a strategy for solving the problem, efficiently, in their head. Some of the strategies that students come up with are shared and annotated so that every student is likely to understand the strategy being suggested and why it works. At the end of the activity we ask students to reflect on their work and see what thing they think can use again to solve a different problem in the future.<br /><br />It's a thing to try if you have not yet.<br /><br />David <br /><br />Davidhttps://www.blogger.com/profile/08098221991466148258noreply@blogger.comtag:blogger.com,1999:blog-235276292454918436.post-43774903657542087852016-02-21T19:18:39.388-05:002016-02-21T19:18:39.388-05:00Thanks, Julie! I appreciate the general encouragem...Thanks, Julie! I appreciate the general encouragement. It's probably wishful thinking that I could be intimidating. I am big on encouragement; I never say this is easy. I do say that it is hard, BUT I know they can do it. Our semester long theme is 'what do you do when you're stuck?' and we explicitly work on forming questions. Or, I try to. We're slowly getting some people to come to the board to share work, rather than answers. <br /><br />I think that kind of linear generalizing is something they haven't done, which is why the block problems were so good for us. The regression is literal here. With a table of data, they don't think about getting the expression from the pattern, nor when they have an expression from regression, try to see it in the context. They treat equations like poorly understood magic, which require arcane handling. No sense making.<br /><br />John Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.comtag:blogger.com,1999:blog-235276292454918436.post-74033220097692113172016-02-21T18:45:12.704-05:002016-02-21T18:45:12.704-05:00"The strength of the temptation to give in, t..."The strength of the temptation to give in, to teach them how they think they'd like to be taught is way stronger than I would have guessed." Thanks for your honesty! It's very tough sometimes to know what's right, because you do have to work with what they want and expect: if they tune out completely or stop showing up, nothing you do after that will help. <br /><br />I've met you, so I imagine you are very encouraging and positive. I don't think things like using proximity to get someone to quit working on another class's assignment during your class are a problem: that's just reasonable. But with this crowd, you basically cannot oversell your confidence that they each, as individuals, can do math. (And if you don't have this confidence for your activities, then yes, you need to alter the activities.) Part of their passivity is probably having others tell them, implicitly or even explicitly, that they are not "math people" and SHOULD wait to be told the right way to do things.<br /><br />On a more specific issue, by "getting by on regression rather than representation," do you mean they see a pattern as "adding 3 every time, so it's y = x + 3" rather than "x sets of 3 plus another 4, so y = 3x + 4" ? If so, the best way I've found to break through this (and I have found it is SOOOO much easier to break through with 6th graders, even the least confident mathematically, than with 8th graders, so it may take a lot with your age group) is to get them to think about Figure/Step/whatever #100. "We definitely don't want to draw all the figures up to 100, or to keep adding 3 a bunch of times, right? That would be a pain. Can we find a shortcut?" A lot of times they are able to describe what the parts of that would be and how big each would be. Then helping them move from doing that to doing it for a general x is not such a big step. That intermediate step helps a lot with the jump from the concrete to the abstract.Julie R Wrighthttps://www.blogger.com/profile/07693711947104069224noreply@blogger.com