Welcome Back & Get To Work!

Holy Moly - it's been TWO MONTHS since I last posted?!?  Yowza.  I'm sorry.  But we're back from the hectic realm of December and my math students are already rocking the kazba.

We are finishing up our study of transformational geometry, which was the perfect, most natural route to go after wrapping up graphing, because the students were so accustomed to using a grid.  I built on their understanding of coordinates and we went from there.  I had originally planned to work on measuring angles, but this just seemed to flow better.

The kids came back ready to work.  Thank goodness, because I want to squeeze in another study of numbers before finalizing their report card marks.

What I love about transformational geometry is how endless the possibilities are for answering the questions.  Today, I gave the students a triangle in its first position, and in its prime position (where it ended up, or as we labelled it today, "point B").  I asked them to copy the shapes onto their own grid properly, and the describe all of the possible ways to get there.  Okay - they'll never finish ALL of the possible ways, because they are seemingly endless - but the point is, they could work and work and still have more work to do, but feel accomplished after each successful transformation.  The trick with today's work was that they needed to also reflect the shape, in addition to translating the shape across and up the grid.

Students have really built some skill in using computers to work on math problems.

This is what I was looking for:
- Can they use the grid properly, by finding the coordinates on the board and plotting them appropriately on their own graph?
- Can they move the shape from Point A to Point B successfully? Can they translate? Can they reflect?

Some students only found one transformation.  One student found TWELVE.

One student said to me, "Uh, Mr. Patrick, I don't want to be rude or say you're not a good teacher, buuuut ... this is really easy.  You're supposed to be challenging us, remember?"

I replied with, "Well, doesn't it make me a good teacher if you understand it SO WELL that it is easy?"

She said, "No, it's too easy!"

So I said, "Did you remember the part about finding ALL possible transformations?"

Silence.  Then, "Uh ... yeah ... okay ...."  She trailed off back to her seat where her friends were giggling at the conversation they'd overheard, as she whispered to them, "Okay, Mr. Patrick IS a good teacher!"

The kids were using loads of math vocabulary, unprompted.  My biggest explicit lessons lately have been about organizing their work so that I can understand it.  I showed them some examples of how to organize and label their work, but told them to find the way that works for them.  This class is blowing my mind in how they just take the very small amount of information I actually give them outright, and use it the way a person living through the Depression would have used a dollar.  They are accessing the word walls, dictionaries, and each other; asking me meaningful, necessary and important questions; listening to the help I do choose to provide (only when it is necessary, which of course varies per child and learning need).

We have a couch, and students have found their own purposes for it.  This student has settled right in and is using multiple geoboards to solve her problem, since one geoboard didn't have enough coordinates to work on the question.

Through their problem solving (both math and learning skill related), their focus and attention to details, whether they finished or not, whether they were correct or not,

Students at all levels achieved success today.