older students-slice of life day 22

Whew! I made it. Not that I thought it would be bad at all, but it's been a few years since I last taught upper elementary students in a math class during intersession*. When you teach 3rd grade on a daily basis, ten and eleven year olds might as well be middle schoolers. I was going to have to adjust. Given that most of us didn't know one another, our first day of Exploring Design through Architecture went pretty well. We had an ice-breaker, talked about idioms, and discovered all kinds of non-mathematical things about one another. Students explored the classroom, checking out all the manipulatives and materials they might use for designs and the books they might use for research. The budding architects created drafting books for notes and drawings. We also worked out logistical stuff like how to set up the smartboard and projector, how to check out books from the classroom library and where to find office supplies. I remember a few students from their third grade days and I have a few siblings of my own students. I tried hard to not make any assumptions about how it would go this week. I thought it was a lot like the first day of school- that great honeymoon time. The day went so quickly. Fifth graders don't need as many directions. They reminded me about a few procedures. Good thing. They need a bit of reassuring, but who doesn't. We didn't have to establish a bunch of rules. We talked about treating one another respectfully and about the importance of communicating politely. I didn't have to add much to that. I have high hopes for the week. Not just for the students- had that; but, for me.

*our 1-2 week optional school sessions that fall between our quarters during our modified (year round) schedule

more math! slice of life day 11

Algebraic thinking came to me about 6th maybe 7th grade. I'm not sure if I was exposed to it earlier with anything other than an unknown variable a la 42 + ____= 63. It certainly didn't look like: 4x + 2= 3x + 9 in third grade. This is what our students get to work on with Ms. G who comes in once a week for Hands On Equations. I'm seeing and hearing mathematical thinking and organization that I hadn't seen in other units of study. Even if my students can't write a complete sentence because they are learning English, their creative thinking and expression comes out in this class. They are becoming the experts and sharing various ways to isolate x (they don't call it that). They are realizing instead of writing x + x + x + x (4x) they can chunk by using doubles (2x + 2x) or go all they way and multiply! They are building flexibilty in their thinking without even knowing it.

I hope they are building a love for math and mathematical thinking. Some things heard today: "When you take away the pawns from both sides it's like working with a mirror, you have to do the moves equally." "I can check to see if my 'x' is correct lots of ways. I can count each one; I can skip count them, I can multiply them." "I can try lots of numbers for the pawn but I make sure the sides are balanced and equal."

They work hard to line up and match the teacher version of the balance. I think this kind of matching may even help them when tracking on a standardized test. A lot went on in 30 minutes today!

teaching math- slice of life day 9

Our students are reviewing math strategies for adding multidigit numbers. There are guaranteed to be 18 strategies for finding a solution when there are 18 whiteboards and brains working. The hard work for them isn't getting the answer, but sharing their process; the HOW they did it. The photos show a couple of students working on partial sums to find the answer. Students weren't given anything but the problem in horizontal format. There were no strategies prescribed for solving. Students just went to it. We have worked this year on how mathematicians and scientists and other inventors have to know how to express/share their findings or the world will never get to use their great strategy, proof, invention, product. In our class, metacognition of their processes has been developed since the beginning of school. Hopefully this awareness will be something that will help them pull out a strategy as needed and eventually they will see how those strategies will help solve more complicated problems. More often than not, having been a kid who grew up memorizing algorithms to solve, watching students show their thinking gets me to open up a new avenue of thought about a problem. Love that!