4/19/07

I love having a really small math class! It has helped me so much as a teacher, and I can already see the benefits for the students. As in any classroom, I have one or two students who barely participate, or only participate if they are 100% sure of their answer. But for the most part, the students in this class are starting to get really comfortable with sharing their thoughts.

Yesterday we had an awesome discussion about problem 2.1. This is the problem with Henri and Emile. For the previous few problems, we began by throwing out ideas on how to solve each one. I decided that I would not give students any direction at the beginning of problem 2.1, especially since it's so open-ended. We read it together and then they began on their own.

Since there are only 10 students, I had them work in groups of two, allowing them to choose their own partner. This worked wonderfully, for the most part. There was one group that had trouble figuring out some place to begin, but after they had struggled for a while we discussed the problem, and then they were ready to take off with their own ideas. The other four groups did amazingly well. They used a mixture of strategies to solve the problem. Two groups decided right away to make a graph of the race, and started from there. The third group used a table, and the fourth group used a both a graph and a table.

I was happy to see that Louis and Adam felt confident with the problem and were rocking! They are both resource special education students. Adam is Hispanic and comes from a very supportive family. Louis's parents are also very involved in his education. They are both incredibly hardworking and do well in classes. But both of them have anxiety about presenting in school or answering questions, if they feel they have even the slightest chance of being wrong. Yesterday they did great.

As we did our summary, students began to draw connections between the ways that they solved their problems, but they also noticed that every group had a different answer. This led us into an awesome conversation about how every group gets a different answer for this problem. The part of the conversation I was most impressed with was when we looked at Adam and Louis's work. They began their exploration by using a table. They created one that looked something like this:

Their table continued until they reached:
T 26 sec
Hen 71 m
Em 65

They explained that they chose to stop there because the question asked how long the race should be in order for Henri to win. The question said it's a close race, and it's close at 26 seconds because Henri only wins by 6 meters. They went on to explain that they decided to check their work with a graph, and when they graphed it, they realized that it could be even closer if they made the time longer. So in the end, they settled on a 28-second race, in which Henri will win by 2 meters. I wish I could show you the graph they created; the picture I took didn't really capture how it looked.

Our discussion led us to conclude that their first answer would have been acceptable, because they answered the question for problem 2.1 and 6 meters is pretty close. However, when they graphed it, they found it was possible to make the race results even closer, so they changed their answer. We then discussed how we can tell when an answer makes sense.

I hope that my students will begin to think about this a little more as we go through the book. At times this group tends to come up with completely random numbers or words that have nothing to do with the problem. I hope our conversation will at least make them think about how they are answering a problem.

Later this week, before we begin problem 2.3, we are going to do some poster reviewing. What I mean by that is that we are going to create posters that highlight important topics that we have already covered. We will then put these posters up in the classroom and leave them there for the rest of the year. This makes a great math word/concept wall. This project also allows me to walk around and do an informal assessment of how well my students understand the concepts.

This week, we'll make four posters:

1. What is an independent variable?
   What is a dependent variable?
   What is "steepness"? What does it tell you?




2. What is y-intercept?
   How do you find y-intercept in a(n):
   Graph Table Equation




3. What is linear?
   How can you tell if there is a linear relationship in
   a(n):
   Graph Table Equation




4. How to write an equation:
   Dependent variable = coefficient/rate of change *
   independent variable +/- y-intercept