tag:blogger.com,1999:blog-5964889903484807623.post4031943829864377821..comments2023-12-18T04:44:25.358-08:00Comments on Questions?: What to do...David Coxhttp://www.blogger.com/profile/06277427735527075341noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-5964889903484807623.post-40712224969515739152009-08-22T12:11:02.000-07:002009-08-22T12:11:02.000-07:00David,The teacher in question did create the "...David,<br><br>The teacher in question did create the "choose your own adventure" curriculum at the different levels. She used many of the textbook resources that we have, but she did the majority of the work (and it took a lot of time). Our school is such that we often get kids that are not developmentally ready for the classes, but end up sitting in a state standards level course, and sometimes two courses happen in the same room at the same time. I'm looking for suggestions on how to remediate Algebra with a student that isn't very independent (1:1 class) while at the same time teach AP Calc to a very independent student, but one that deserves some quality instruction, too. Any suggestions for two different classes at the same time are wonderful and welcome. :-)Jessicanoreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-88860173159629256352009-08-22T09:08:18.000-07:002009-08-22T09:08:18.000-07:00I found this. I very much like some of the problem...I found <a href="http://www.exeter.edu/academics/84_9408.aspx" rel="nofollow">this</a>. I very much like some of the problems in the problem sets. Thanks for the tip Alison!Darren Kuropatwahttp://adifference.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-84887198085157473862009-08-21T23:09:47.000-07:002009-08-21T23:09:47.000-07:00Oof - I was with you until you said you decided to...Oof - I was with you until you said you decided to accelerate them. I'd love to hear/read about a public school who decided to DE-celerate, as in give kids/teachers the freedom to play with fun problems and discover math as they need it. Oh well. I'm in the same position you were at a high school, so I can't talk. <br><br>I'm a little confused about your question, though. I think you are saying you have 8th graders who are expected to take HS-level geometry, but you feel some of them aren't ready. Is that accurate?Kate Nowakhttp://function-of-time.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-70682785981926752982009-08-21T23:17:47.000-07:002009-08-21T23:17:47.000-07:00Most everything I do is a situation like the one y...Most everything I do is a situation like the one you describe. I am in a very small school, so my classes are whoever needs the class or has nowhere else to go that block. Sometimes the ability levels are in the basement and the roof. Something that my colleague did with her Geometry class last year was to allow students to "Choose their own Adventure" of sorts. Any time there was going to be independent or paired practice, she started students with a low or medium challenge paper. If it was completed with minimal errors, they continued onto more challenging problems. I know, not always the best to be doing worksheets, but sometimes you need it.<br><br>Plan remedial mini-lessons for the kids who need it at the beginning of a topic while the other students are working on a related project or problem?<br><br>I'm only just starting my 2nd year, so I'm new at this. Thanks for starting the conversation.Jessicanoreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-70777417830844204502009-08-22T05:39:26.000-07:002009-08-22T05:39:26.000-07:00@KateMy question is two fold, I suppose. By accel...@Kate<br>My question is two fold, I suppose. By acceleration, I mean kids have an opportunity to complete three levels of math in two years (ie. pre alg, algebra 1 and geometry). Of the 60 kids who come to us as GATE students, I would say 25 or so are really solid math students and the rest have just learned to play school very well. The primary question is should the program be geared towards moving students through the math that quickly...if they are ready for it? Or should we just try to have kids go deeper into the grade level curriculum? <br><br>Moving kids through geometry isn't very difficult to do when you get a class of kids who have all succeeded in algebra. For example, my 8th graders last year crushed the state test (4 proficient, 21 advanced) and about 12 of them successfully completed geometry. My standards are that they must score advanced on the state test and earn at least a B in my geometry class before I will recommend them to take algebra 2. Otherwise, they can just take geometry again as a freshman. <br>But what happens when the classes get mixed and some of them are going to need real instruction in algebra? Do I allow the kids who are geometry ready prove their proficiency in algebra then let them move through the geometry at their own pace? What do those lesson plans look like? <br><br>The problem is that this isn't simply a matter of differentiating instruction. I'm having to figure out how do differentiate the curriculum. <br><br>@Jessica<br>I like the idea of "choose your own adventure" lessons. Did this teacher create the curriculum for this? I don't mind trying to reach kids on their level when we are all covering the same topic. But I am struggling with how to have kids in two different curricula and at different levels within the curricula.David Coxhttp://coxmath.pbwiki.comnoreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-37086382646688623532009-08-22T05:43:23.000-07:002009-08-22T05:43:23.000-07:00I agree with Kate although I would describe her ap...I agree with Kate although I would describe her approach as acceleration; by which I mean acceleration of learning as opposed to acceleration of "covering content."<br><br>I would look for ways to have the students create content that educates. i.e. design their own problems, based on what they've learned, then have them solve, annotate and share what they've learned.<br><br>The challenge is coming up with problems that are rich enough to be explored at multiple levels. That's where I would spend my prep time. <br><br>An example:<br><br><b>Phase One</b><br>How many square are there on a chess board?<br>Hint: the answer isn't 64.<br><br>This is an excellent problem to teach strategies such as:<br>solve a simpler related problem (a 2x2 chess board)<br>draw a diagram (pictures almost always help)<br>look for a pattern<br>... I'm sure others will arise in conversation with the students; I've often been blown away by their ingenuity.<br><br><b>Phase Two</b><br>What about a 7x7 chess board? 6x6? 5x5? Can we generalize a solution? Predict the solution for a 9x9, 10x10, or 20x20 board.<br><br><b>Phase Three</b><br>How many rectangles are there on a chess board?<br>Interesting aside: What's a rectangle? Does limiting the "kind" (dimensions) of the rectangles under consideration lead to different solution spaces? (What the heck is a solution space?!?)<br><br>Can you generalize each of these solutions?<br><br><b>Phase Four</b><br>Based on what you've learned, can you suggest/create a new problem? Maybe one in three dimensions? (Rubik's cubes come to mind.) Can we play with other geometric shapes in 2D? 3d? Do you know what a tesseract is? (Let them research that last one.)<br><br>The nice thing about all this is you'll be able to show how the algebra and geometry are connected and each helps us to understand the other.<br><br>Introduce them to Pascal's Triangle and, without going into the binomial theorem, have them do a few binomial expansions (a + b)^2, (a + b)^3, and so on, then remind them to explore the limiting cases (a + b)^1, (a + b)^0 ... can they find any related patterns?<br><br>Explore Pascal's Triangle for: powers of 2, powers of 11, counting numbers, triangular numbers, hexagonal numbers, other figurate numbers (what's a figurate number?), Fibonacci numbers.<br><br>Fibonacci opens a door into exploring math in nature, leaves on plants, they way trees branch and grow, the way bees and rabbits reproduce, ... FIELD TRIP! Send them out with digital cameras to find math in nature, publish the pics to <a href="http://flickr.com" rel="nofollow">flickr</a> and annotate them (<a href="http://adifference.blogspot.com/2007/01/flickr-assignment-roundup.html" rel="nofollow">here's how I did that</a>).<br><br>You might also explore some sort of long term projects with them, I called this <a href="http://adifference.blogspot.com/search/label/expertvoices" rel="nofollow">Developing Expert Voices</a> in my classes; you can see some student work <a href="http://expertvoices.blogspot.com/" rel="nofollow">here</a> or <a href="http://expertvoices08.blogspot.com/" rel="nofollow">there</a>, and <a href="http://expertvoices09.blogspot.com/" rel="nofollow">these</a> are from this year.<br><br>I hope this long answer doesn't come across as "too much." I couldn't help, it's seems to me you're walking into such a golden opportunity to do some real teaching with your kids. <br><br>I tend to think about it like this: the more teaching they do the more they'll learn.Darren Kuropatwahttp://adifference.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-13215199476578539172009-08-22T05:58:02.001-07:002009-08-22T05:58:02.001-07:00Hi DarrenThanks. The long answer is exactly what ...Hi Darren<br>Thanks. The long answer is exactly what I needed. The real beauty of my situations is that as far as the geometry is concerned, I am not confined by pacing guides, standards and/or state tests. My kids will all take the algebra test. This fact isn't lost on me. I don't want acceleration to simply mean "cover content" either. However, that seems to be the way things are structured. So the real question may be: What does the geometry curriculum need to look like? But is there a better course to allow kids to explore than geometry?David Coxhttp://coxmath.pbwiki.comnoreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-27295916315516550332009-08-22T05:58:02.000-07:002009-08-22T05:58:02.000-07:00OK so then I vote for "go deeper into the cur...OK so then I vote for "go deeper into the curriculum." Rushing any of them through algebra is not going to serve them well. Why not let the group discover/invent algebraic reasoning together collaboratively by working on interesting and fun problems. The quicker students will learn the material way better if they assume some responsibility for bringing the rest of the class along on the journey.<br><br>Darren lays out a nice progression. I might back up one step with the initial question. Imagine a triangle where you drop a bunch of segments from one vertex to the opposite side. How many total triangles?Kate Nowakhttp://function-of-time.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-5713320429527954502009-08-22T06:05:28.000-07:002009-08-22T06:05:28.000-07:00KateI agree that rushing them isn't going to h...Kate<br>I agree that rushing them isn't going to help. That was a big concern. The thing is this: my 7th graders get nearly a full year of algebra and then we do things like the Farming with Google project when they are in 8th grade. So my first priority is definitely making sure they have a solid algebra foundation. Thanks for the input. I knew I could count on you. :)David Coxhttp://coxmath.pbwiki.comnoreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-5887741070345935092009-08-22T07:40:41.000-07:002009-08-22T07:40:41.000-07:00Hi David,I recently acquired a list of meaty geome...Hi David,<br>I recently acquired a list of meaty geometry questions that might be appropriate in terms of going deeper into the curriculum. They've been culled from the Phillips Exeter Academy collection. If you'd like to check them out, you can email me at alison.blank at gmail.comAlison Blankhttp://axiomstoteachby.blogspot.comnoreply@blogger.com