What value does this have for them? Each week, I collect and provide feedback on all assignments. I randomly grade some problems to see if they are doing them accurately, and I comment on: the difficulty of the problems chosen, whether they seem to have already mastered this topic and ought to move on to another, if they are not checking answers against the back of the book, or if they demonstrate repeated procedural issues and need more work on this topic. Over the course of 2 or 3 weeks, I saw kids go from completely not doing any problem correctly to getting close to 100% correctness. WOW! I even had one kid write me a grateful note at the bottom of the paper, for helping her understand the concept. The truth is, I have not changed anything I am doing -- I had always been there at lunch time to answer questions, but it is the kids who have changed their behavior significantly. They now realize when they are doing something wrong, versus when they are doing it correctly every time, so their questions have become a lot more purposeful.
Amazing, eh? And I am up to about 90% homework receipt rate in most of the classes. Even my one remedial class is doing this with enthusiasm. (In that class, I took a giant leap of faith and let them choose what amount of problems to bring me, and the class agreed on 20. I was shocked, because 20 problems a week is a LOT for kids who normally don't even do 5 problems a week on their own time! But, they didn't want to lose face considering that the younger kids are bringing me 15.... And so far, they've been good on their word.) Some kids are even bringing me extra problems and turning work in when I forget to remind them the week before. It has indeed changed the dynamic of my classes, simply by offering kids a voice in setting their own goals in homework and making homework a continuous dialogue of their learning. (And, grading different problems on homework from different kids keeps me from wanting to stab my own eye in boredom.)
This is not new, but I took my 9th-graders outside for 60 minutes of out-of-the-classroom trigonometry today, armed with their inclinometers, calculators, and measuring tape. It was so lovely, and they now have a really concrete idea of situations involving both the angle of elevation and the angle of depression. YEAH!
I worked with my students on a systems of equations word problem today involving a mystery 2-digit number. "A mystery 2-digit number has a sum of digits equal to 7. When you reverse its digits, the value of this number increases by 27. What is the original number?"
It was such a lovely problem because I got to work with kids one on one and discuss base-10 number system at length. We worked through 639 = 600 + 30 + 9 = 6(100) + 3(10) + 9 and I asked them what a two-digit number "ab" will have as its value. Kids were all able to come up with a(10) + b, and then come up with the equation a(10) + b + 27 = b(10) + a more or less all on their own!
It was awesome. I love it when I remember to facilitate students using the concrete -> abstract continuum and I can see the mind spark that it generates. I had a professor in grad school who used the same continuum whenever introducing new abstract ideas, and he is one of the clearest lecturers I've ever had. Note to self: Never start a discussion with algebra...
Lastly, I am really excited to get into the nitty-gritties of mathematical modeling with my 8th-graders. We are finishing up the second round of lab writeups this year, and this time they even incorporated graphing calculator regression results and discussed the R^2 values. I think that during the rest of the year, I will guide them through a series of optional MYP pattern-investigation tasks as enrichment to our regular curriculum, and they will need to choose one task at some point to complete a full writeup for. This way, before they even go into the high school, they would have already had some experience with the two types of portfolio tasks in the IB program and understand mathematical processes at a high level.
(For example, right now I am looking at a task that ties nicely into our systems unit. They need to generate multiple systems with consecutive odd coefficients and constants, such as 5x + 7y = 9 and 23x + 25y = 27, to recognize the pattern in their solutions, to test their generalization, and then to prove their generalization using algebra. How brilliant and challenging.)
For this and other reasons, work is INSANELY busy. The weather is starting to be beautiful in Berlin, but I have yet had any time to enjoy it!