Reflections on a Math Day: November 17, 2009

I don't know why I don't take the time to reflect more often. I may think some of the things in my head, but once that thought has passed, what else can I do with it? I could come up with excuse after excuse as to why I don't do this more, but that's not productive.

In my Integrated Math 2 classes, we have been working on distance, midpoints, and slope. As a math teacher, I feel that these are relatively easy concepts to work with, and many of my students have expressed that they know what slope is, blurting out "y = mx+b!" Of course, slope is only a part of the slope-intercept form (which we will cover later this chapter), but it gives me some insight into what my students know, and what they think they know.

Now, with my Math for Standards class, I have them blog about what they think they know before we begin a unit, and then have them reflect upon what we covered at the end of the unit. It helps me to better adjust the unit to their needs, and it allows for them to see their growth through the unit. (Visit my class blog here, student blogs are linked on the right). I also plan on using the blogs more with my Integrated Math 2 students as we move through the year.

Hearing the students yell out the slope-intercept form when we are only looking at slope gave me the idea that my students had indeed learned about slope before and knew a way to apply it. Yet, when I asked them what slope actually was, they stumbled. So we did some math calisthenics. We discussed how slope represented the ratio of change in vertical distance to change in horizontal distance. Of course, many of us teach it as "rise over run." So, from their seats, I asked them to run across the room. Of course, they all started by rising first, so I stopped them. Right there, they realized that before they can run (horizontal), the have to rise (vertical) when dealing with slope. The light bulbs came on.

Today, the Integrated students were working on a graded worksheet on distance, midpoint, and slope. One of the students (who, coincidentally had not completed the practice problems assigned for the concepts) looked at the midpoint formula and noticed something. He raised his hand, saying, "Mr. Lamb, there's a comma in this formula!"

"Why do you think that is?" I asked him.

He paused, thinking about what we were covering, what he was trying to find, and what was given to him in the problem. He was not coming up with an impulsive answer. I could tell he really wanted to understand this. "Well," he replied, "since we're looking for the midpoint, that means we need a point, and a point is given as an ordered pair. And, the midpoint is in the exact middle of the other two points, so if we know the distance between the points, we just cut it in two, so that's why each part gets divided by two!"

He had a smile on his face. Can you imagine it? A student enjoying understanding math! We continued our conversation (which also happened to be loud enough for the rest of the class to hear) about being able to understand the formula. I asked if he'd be able to choose the correct formula from a series of formulas, and he was confident he could, as he now understood why the formula worked.

I wish I had more time to have these types of discussions with my students. This is where the real learning occurs for some of them, and the boost in confidence on one skill can go a long way in the classroom, especially for students who feel they cannot do math.

One other change I have implemented is with the comments I place on report cards. I was sitting and typing the comments last week as I always have: "Timmy should..." or "Mary needs to..." when I stopped. Something hit me, and I had to ask myself, "Who am I writing these comments for?" I have always written them as if only the parent would see them and directed them to the parent (And yes, I am a firm believer that a parent/guardian should be an active participant in a student's education). But I want my students to realize that, ultimately, they are responsible for their own education. So this year, I am writing comments for the students, not about them. I have already gotten input about this from a few students, as they seem to be thankful that I am talking to them.

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