What I’m going to do with this
Apr 13th, 2009 by Nick
So I’ve been breaking my back for the last few days writing up a unit on factoring. All the problems get solved either by me in writing in LaTeX (for the answer key) or by Maxima (a godsend) which factors, simplifies, and prepares smoothies (if you upgrade to the Pro version). Maxima is free and awesome. A winning combination.
Anyway, so, in order to teach factoring with algebraic precision and a minimum of boring lecturing, and a maximum of inductive skill-building is have my students go through my factoring unit (posted below). This post isn’t so much about that, as how I’m going to try to pull it off in class. I’ve put in a lot of elbow grease this year trying to get students to pay attention to process, but at the same time, the resources they are often given pay NO attention to process. At least, in a problem-by-problem sense. In the book, if you didn’t get the right answer, and you can’t connect the dots to figure out where you went wrong, you’re out of luck.
I tried to do a few things with these activities. First, to provide students with clear reasoning, examples, and practice in tidy little punches. And second, I included correct answers and process for nearly every problem to try to make these activities run smoothly for kids at varying skill levels. Third, I ended the assignments explicitly with questions that don’t hand hold – questions that force students to know when and where to apply a strategy. This type of you’re-on-your-own pracatice is an area that I want more of in these resources. Questions that could be from topic x or m2 (from anywhere), and are there without context so that students have to select their technique from the tool box and apply it are good indicators of how well students understand the skills they’ve been taught and the context surrounding them.
Implementing this I intend to give kids a copy of the problems and solutions to work through. They will have to decide how long they are willing to struggle on a problem before turning to the answer. I kind of feel like I’m cutting a path between the belief that kids need to struggle to learn, and the idea that constant success is the best medicine for the novice. 1
Resources like the pdf’s below and others as I make them go in the box. Activities with answers like the motivator, grouping, x2+bx+c, and split the middle activities. Big shout out to Jonathan for his factoring posts and materials, as well as Dan Greene. And if you want to see how they’re made, check out the .tex files in the box.
I’d be interested in any comments or criticism out there.2
- A debate on this happened over at D-ed Reckoning between Ken DeRosa and Chris Lehmann. I don’t particularly like DeRosa’s choice to respond paragraph-by-paragraph. In refusing to respond to the argument as a whole the debate gets bogged down in little nit-picking details – it’s a failure to prioritize and identify key issues. That’s the downside, the upside is that there is depth to the arguments, it’s worth the read. ↩
- Incidentally, when I published this, my blog registered the post as a comment on itself. Not exactly the kind of criticism I’m fishing for here. ↩
Thanks for the shout out. I’m going to skip the DeRosa – Lehmann stuff – I find neither informs my teaching. But which documents in which order should I open if I want to get a sense of what you are planning?
Open the unit-factoring.pdf – the sequence is in there. In fact, if you download the folder in its’ entirety, and open the unit-factoring.pdf file, you can click the links from within the file to see the worksheet/activities.
Nick, my main argument was presented in my initial post and in this follow-up post.
Also, I’m not sure what you mean by my not responding to Chris’ “argument as a whole. ” Chris’ main argument consisted of his disagreeing with my initial criticism and then providing reasons which were either not supported or contradicted by SLA’s pwn Family Handbook. I responded by pointing out the deficiencies in Chris’ response rather than restating my main argument because Chris’ response offered no new arguments that were supported and needed to be rebutted.
Let me also say that I’m not generally opposed to the problem based learning as practiced at SLA, I am only opposed to those methods in the instruction of novices, especially novices without much general background information. The use of such methods with novices is often problematic as exemplified by the model student sample offered by SLA.
Maybe that was poorly phrased. My comment was meant as a statement of my preference for your response to be given as a single coherent argument perhaps in a separate post or below his completed argument. Splicing into the middle feels like you are interrupting. As I read your argument, I found myself re-reading each line of Chris’s to decide whether or not you had responded to the best position put forth not the easiest to knock down. The general debate on the merits of student generated and teacher supplied knowledge in this instance and generally as you frame it is one that I’m certainly interested in.
Oh, I see what you were getting at now. Let me know if I failed to address any serious argument that was raised.
I’m addressing the issue again, hopefully in a more complete way, in a new series of post starting today.