Literacy event

Last week, I gave my students a problem about circles and I had them read it, understand it, and solve it in groups. Then I had them all come up in groups and present their solution to the class as if they were the teachers.

It was really great to watch my students (8th grade) figure out the following problems:

"I need your help. I’m baking a pie for Ms. Barraco, but I’m having some difficulty figuring out what size to make it. I bought a nicely decorated circular container for the pie that has a circumference of 4. How wide across (at its widest) should my pie be so it will fit perfectly into the container?"

"A wheel has a radius of 5 feet. What is the minimum number of complete revolutions that the wheel must make to roll at least 1000 feet?"

The second one in particular was really interesting. The concept of revolutions to a 13 year old is baffling. They would raise their hands and ask me if I meant the kind of revolution in a country, when the people rise up against the government. Of course I would get frustrated and respond as if the students were being smartalecks, but really, it's fascinating in a literacy context. Should we analyze the relationship between the two different definitions? Does it really matter. But it was fun to watch my students try to contextualize the words.

Then, watching them come up to the board and explain the problem and then their answers was also really interesting. A lot of the students appreciate my efforts to put the math in terms of 'reality,' (i.e. the pie). They would explain what the problem was asking for, and then provide a solution that was (hopefully!) accessible to their peers.

When I first decided to become a math major, all I had taken was single-variable calc and linear algebra. I had NO idea it was going to be as hard as it was. I thought I was pretty good at math, my calculus professor encouraged me to declare a major in the field, and I wanted job security (I was also an English major). I also decided to do this all in my senior year. When I started my analysis and abstract algebra classes, I realized how little I actually knew about mathematics. I wasn't a superstar student anymore; we were all fighting bravely for what we hoped would be a grade higher than a C+. Some struggled more than others. I was somewhere in the middle. The classes were so hard, and required so much out of class work, I didn't think I was going to make it through the year. In one year I took Multivariable calc, two semesters of analysis, two semesters of algebra, numerical analysis, financial math, number theory and ordinary differential equations. It humbled me to the point of self doubt. I scraped some As, A-s, B+s, a B- and my FIRST ever C. In this one year (june to august), I realized that I will really be a student and a learner of mathematics forever. There's so much out there, I can't possibly ever learn it all, or even come close to understanding it all!

Are you smarter than a first grader?

As I read Gallas's book, I really just can't ignore the fact that these are first graders. Maybe I'm biased since I teach grades 7-12, but I really can't see the long-term merit of this "study." While I agree that verbalizing one's understanding of issues, particularly the math and sciences, can be very helpful for students of any age, I find that at this particular age, when the teacher can't structure the conversation, much of the dialogue is meaningless. I find it amazing that one of the students actually knew, somewhat, why leaves turned change color. Although, Eureka moments like that happen, I saw one last week in my 8th grade math class, I feel as though Gallas somewhat wants to depend on those kinds of occurrences, and they're just not that common, particularly with 1st graders!!!

I would, however, like to see this same activity done with older children. I think that many of the issues Gallas is trying to get at would be more prominent with older children. I think 7th and 8th graders have the same kinds of questions, and i think it is more productive for 12 and 13 year-olds to discuss science than 7 year-olds. When we talk about literacy in the science classroom, for example, I agree with Gallas that as a society, we should aim for all students to be proficient enough in the subject to hold their own in a basic scientific discussion. For example, if a student is in a physics course, I would expect them to be able to explain to me why some objects fall faster through the air than others, despite everything being affected by the same amount of gravity. I would expect to hear words like 'air resistance,' and for the child to understand what it means conceptually. I just think first grade is too young for this! And I'm really having trouble getting past that. I hope to talk about this issue further in class.