Summer

After yet another grueling, yet deeply satisfying day in the embedded class room, I reflected on my day. I thought about Summer, a second grader, who really struggled with some of the tasks we gave her. For Summer, each problem had to be counted one by one. So for 3+3 she needed to put out three fingers on each hand. Then carefully touched each finger to her cheek to count them all. She proudly said 6!

When we got to 5 + 6, her finger counting became more difficult, as she realized she did not have enough fingers to use her finger counting strategies. She counted several times slowly and carefully but she did not know what to to with the 6th finger on one hand when she needed it for the 5th finger too. She just kept trying! Finally, she looked up and said 11! She seemed to see an extra finger in her imagination. The point is, even though adding 5 + 6 was easy for most of our second graders that day, it was hard for Summer. But her persistence was more than awesome.

According to researchers who look at how people think of themselves as learners (Carol Dweck is one), it is exactly this kind of persistence, a belief that a person isn't stuck in his or her knowledge state (e.g. "smart" or "dumb") but that we are malleable--our intelligence is malleable and can be improved by hard work. Summer is just that kind of kid! Hopefully, her teacher will see that and encourage her in this way.

Later, in whole group, I offered the entire class a problem that turned out to be pretty hard for most of them. I spied Summer at the back of the room counting her fingers so very carefully. The problem was: Abby has 6 candy bars, and she gets some more while she is trick o treating. Now she has 13. How many did she get when she was out trick o treating?  About half the class was convinced it was 19. After class she came quietly up to me to show me what she had been doing. She counted up from 6 to 13 using her fingers. She told me the answer was 6. Okay, so she made a counting error (not surprising since I knew was still working on counting). But, she was proud, and she had a valid strategy for that problem. Go Summer!

Small things are Big things!

I am in Arkansas this week working with elementary teachers. They are in the their second year of Cognitively Guided Instruction. During this year we do this workshop format that is very ambitious to say the least. We conduct embedded class lessons. This entails LOTS of planning by myself, the hosting teacher and the CGI participants. On the first day on this follow-up (we spent 4 days together this summer, this is Day 5 of the PD), we interview all of the kids in one 2nd grade class. Each teacher pair interviews two children (one at a time). Then we all gather back together to analyze what the kids did, how they were thinking and try to create a sort of class profile. Then we decide what what we want as our focus group of kids, and what our goals for the class and this focus group are in particular. Then we choose/design problems and or tasks to present to the kids and anticipate what they might do and how the teacher might respond. Next we go the classroom. I taught the lesson. What a hoot. All 24 teachers crowded into the room watching the lesson. 24 kids learning math. One teacher. After the lesson we return the training room to debrief and talk about what we learned and what we would plan for the next lesson. A lot to do in one day and so so so exhausting, but well worth it.

The next day(Day 6, or second day of the follow-up) we do the same thing all over again, only with kindergarten! Kindergarteners solve math story problems and explain their strategies to the class, while being observed by 24 teachers. WOW. Lots of mathematics and teaching talk happened during these two days, too much to say here. Along the way we also learn some interesting things about kids ways of thinking about numbers. We learned that one Kindergartner had invented a new number! All this time his teacher did not know why his counts were one off, but we discovered he counted 11 cubes like this" one, two, three, four, five, six, seven, eight, nine,teneleven, twelve. HA. Only in Kindergarten classes do you learn how new everything is for them and how small things are big things for new learners.

Why Math Nerd?

Lots of times I am confronted with negative comments about what I do for a living. My sister calls me a math nerd. People automatically believe I love Sudoku. If I make a calculation error, someone will say-and you are a mathematician? Ha!  The other night while at a dinner with professionals including two lawyers, an engineer and a realtor, I mentioned the word quadratic and I was immediately hit with a barrage of statements including, "oh come on! math who wants to talk math?".  Huh? I did not have that reaction when you said " latest house bill" or when you say "Selling trend"? What? I thought you guys were educated, and most of all my friends?

I am over it (sort of), but I realize that I AM a math nerd, just like someone is a Star Wars nerd, or a chess nerd or even a football nerd. I am interested in math. I like talking and hearing about things that involve interesting math ideas, like "I wonder if the number of people have died in the world is more or less than the number of people living right now?" No, I am not GREAT at math. I do not use calculus at all, for anything, but I am interested in how calculus works and how it was developed and how the graphs created using calculus change when something about the equation changes. Anyway, I like math in a way that some people enjoy lots of things but aren't experts at it. Talking about math stuff (and actually science too) is enjoyable social activity for me.

This blog will give me a chance to explain this point of view, and also describe what I do that makes me a math educator with a PhD. I get to do research on how people learn and think about math. How people feel about math and how that effects their ability to do math. I get to teach. In the past two months I've taught a bunch of second graders, some pre-service teachers, some in-service teachers and some teachers of teachers. I have also been researching the relationship between the quality of a professional development experience and teachers' content knowledge. It is fun and promises to be "funner" all the time. Yup I am a math nerd.

Other Cool Blogs

Stinky's Cool Math Blog

I really like this blog at first glance because it seems honest and also informed. Plus, the author highlights Diane Ravitch, who is fast becoming one of my most favorite school policy persons.

Learning Math, Teaching Math

This is an excellent blog (the link is actually to the archived version) about many issues in math education. Susan Empson, my friend, advisor (and overall guru or sensei), and author of  this blog is in the process of publishing much of the work you can see here that was done with struggling 2nd graders.

Enjoy!