I am thrilled about how Precalculus is going! It's almost too good to be true -- the kids can build their own patterns from colored blocks; they can write recursive equations to represent those patterns; they can explain the limitations of knowing only the recursive formulas; they can write explicit equations that turn out to be linear; they can sum arithmetic elements and explain why that sum must be quadratic, both from a graphical standpoint and an algebraic standpoint. And they're ready to break down quadratic patterns into linear elements, in order to find the formula for the n-th quadratic element! ...Rock ON, 11th-graders!! They will start their first project very soon, either tomorrow (if they understand all preceding concepts) or next week. It is a project that I adopted from the IB, watered down quite a bit simply because I don't want the kids to be scared off right away.
My vision of tying linearity and quadratics neatly together for the kids with the concept of sequences is working out well so far; we'll see how they fare on the first quiz! :)
In Calculus, I discovered on Day 1 that the kids were strangers to the powers of the graphing calculator. I spent the next day walking them through basic features, and since then they've been flying through the conceptual material which I've presented through explorations. Unfortunately, this class has had the most amount of absences, since the Seniors and various special leadership folks had to miss class starting on Tuesday of this week. That has caused the pacing to be a bit chaotic. The kids who have been here everyday now have a solid grasp of the derivative: what it is, how to read it from the calculator, and how it relates to average rate. They can visualize derivative graphs when looking at an abstract original graph of f, and in general I think their calculator skills are slowly maturing. Yay!
My Algebra 2 classes are two diverse groups. One is full of international students, some of who had just stepped off the plane to arrive in America with very little English comprehension. This has made for a very interesting challenge, trying to teach those kids in the same class as the native speakers. I think it is great -- it helps to teach all kids the virtues of patience and kindness, because some of the non-native speakers are much stronger in math than some of their native-speaking peers, so in my mind at least, it's a bit of give-and-take for everyone. The other Algebra 2 class is full of bubbly tenth-graders, and most of them are my advisees. I simply love that class! They don't work as fast as the other group through the material, but they're very responsible, eager to learn, and nice. Kids from my Grade 10 class keep saying that that seems like the fastest-passing period, and they seem to genuinely enjoy their time in class even though we're still on the nitty gritties of basic algebra. We're working our way through some knowledge about how to use the graphing calculator flexibly to check our work alongside reviewing skills from Algebra 1 and wrapping our mind around visual linear patterns. The first big project will be coming up soon though (next week!), and it's the rubber chicken bungee jumping project (I think at most schools, they use barbies), which will involve a significant amount of writing and really show kids what I expect this year from their analyses. Whee! I'm excited!
How are your school years going??
I like that project. I've been using visualpatterns.org with my college pre-calc students, focusing on the linear patterns (which maybe was a cop-out), and now I want to expand to whatever is there when we do those. I want my students to do two problem-solving projects outside of class, and the IB project you linked to looks great.
ReplyDeleteI'd love to see the explorations you used for calculus. Most of mine come from the Boelkins open source textbook.
The only issue with doing it outside of class is you will probably need to clarify that they shouldn't need to rely on regression results to model the quadratic pattern. In my class, students will do BOTH regression and manual derivation of formula, in order to cross-check their answers and to show equivalence of results.
ReplyDeleteI've been uploading all of the Calculus material to my math folder link, http://bitly.com/mimisMath2013-2014 . We're still only 4 lessons into Unit 1. Some of the explorations were handouts that I created when I was teaching in Germany, and others are things that I've pulled off the web or from the textbook. Feel free to look around! I won't know until a week or two from now, how well the explorations worked in terms of laying the foundation that I was hoping for.
Oops. I knew about those folders, didn't I? I like the car and squirrel one, and am still perusing the rest.
ReplyDeleteI'm in the middle of grading the first test. I'll know soon how well they understand what I've tried to help them learn.
How did your retirement project go? I'm excited to give it a try myself at the end of the term with my kiddos!
ReplyDeleteSorry Miss Rudolph, but we won't get to the retirement project until end of our term! We're currently doing a quadratic sequences problem and reviewing general skills (functions, linearity). Next unit we'll be reviewing quadratic skills and transformations, and then exponential skills, followed by the retirement project! That project is quite challenging, so it made sense to build up various basic skills before it.
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