My weekly tutoring gig with "Artemis" is going well. When we started, he didn't know much algebra, didn't really understand distributing. He's learned distributing mostly through experimenting, and has learned an amazing amount of algebra through playing with his TI-84. (I wrote about the first time we played with the calculator here.)He loves coming in with graphs on his TI and getting me to guess the function. Here's the one he started with last week. (I got it. Can you?) I showed him some similar graphs to see how well he could do. He got them all. (I told his mom I figured we were into what would normally be the third year of algebra, after about two months of untutoring.)
I never have a lesson prepared for him, and we often go into college algebra sorts of topics (it's called math analysis in high school), riffing off those graphs. Some weeks I worry that we won't have a path in to good topics just by our inspirations. But it always seems to work out that we do something solid.
I know all kids wouldn't move this fast, but to me this demonstrates the power of play. That's all we're doing, playing with ideas...
My Other Student
R comes for tutoring about once a month. (I think it's a special treat for him.) He and I have been playing with Kenken and logic puzzles. He decided last week that he wanted to make his own Kenken puzzle. Yeay! That sounded like something Maria Droujkova would have suggested, but that I don't think of so readily myself. So we did it. We started with one box, and figured out what had to be true. Our puzzle isn't standard because we didn't give a total for many of the boxes. If you think about what has to be, you'll figure them out.
Here's the puzzle R
and I made...[I used Excel to make it pretty like this, and used print to save as a pdf. I learned that my blog doesn't want pdf's - it wants jpegs. So I saved the pdf as a jpeg. I don't see a jpeg option in Excel, so that might be the best way to do it...]
Anyone else want to try their hand at making their own kenkens?
Posts
In the Bronx/Manhattan/Jersey, we can see a series of hills, really parallel ridges. The Jersey ones are the biggest. By the time we get past the Bronx River, the last Bronx one we can see (before Williamsbridge) is barely noticeable by a skateboarder.
ReplyDeleteSo we can posit (and geologists know) that it was all once accordian-folded, and then tilted (Jersey up, Bronx down), and then the softer upper layers (frosting) worn away.
Same thing.
Parabola, vanilla looking. Lowered, folded, then lifted. Geology on the TI.
I have been playing "jd sketches a strange graph on the board, students try to create it on the calculator" with some success.
This week's best:
y = |(sqr(5-x))-1|
(I know there's extra parens - want to make sure you can see the reverse check mark)
Jonathan
>Parabola, vanilla looking. Lowered, folded, then lifted. Geology on the TI.
ReplyDeleteNice! Artemis doesn't care whether it has anything to do with real-world examples, but most students do.
Geology as related to graphs always makes me smile. I may have gotten my first time cc position by an example like yours.
During my teaching demo the geology prof, pretending to be a student, asked, "What's this good for?" I asked him what he was interested in. He said, "Rocks."
I asked if as a geologist he might sometimes know the shape of a layer of rock and want to know the volume. "Sure." Then I drew two curves that crossed, said we could imagine rotating that area, and that calculus could find the volume. They liked it...
Through a not entirely logical set of circumstances, my Bachelors is actually in Geology.
ReplyDeleteThere's really neat stuff in applied hard science, and lots of it comes back to math.
I think when a rock is ore-bearing, those volume calculations of yours are worth quite a bit...
Rocks demand math.
Lucky for me. :^)
ReplyDelete