Month: March 2014

Creating a Safe Classroom. How?

I had my second and final observation by my content area professor recently. We followed the same setup as before by identifying what we are looking to work on and then complete a coaching session about the experience. As I am nearing the end of my teaching during this semester I feel confident about the planning and instruction part of teaching for where I’m at in my growth. As I thought more about my instruction I began to wonder about what students I call on and how often I call on them during a lesson. With this I decided to have my professor record which students I called on and when during the lesson in hopes of seeing areas where I can approve.

After the lesson I felt pretty good about how it went getting more people involved, especially considering the topic that we covered was rather confusing. After looking at the chart that my professor filled out I noticed some interesting aspects about it. First off the same group of students that usually answers question had answered the most questions. There were some students who answered a question or two when they are normally quiet. One of the biggest successes for the day when our newest student, who still seems reluctant to participate in class, answered a question voluntarily. The most surprising item I saw was that one group of students only answered one question between the four of them and the more I thought about this it seemed clearer to me that this has happened on more that one occasion. The only answer that I have for this is that this group is in my peripheral vision and they are consistency one of the best behaved groups in the class so I don’t feel the need to keep an eye on them, which I have found lets them off the hook for answering questions during class.  This is not my intention with the group but was an interesting observation opening my eyes to where my attention is during a lesson. Another goal of mine that came to light was that for me it’s not so much having the variety of people answering questions that is important to me but rather having the type of  classroom environment that allows students to feel comfortable answering questions, without having to worry about people thinking they’re dumb, without having to worry about whether they have the answer completely correct. I think if I can set up my classroom like this I will not have any problems in getting the variety of students answering questions because a majority of them will be raising their hands to answer.

So where do I go from here? First and foremost I need to be aware or where I am at in the classroom and what groups I can see. I want to be able to get input from the group that right now I just don’t see and I think I can do that with much more ease if I am changing my position in the class frequently during a lesson. My next step is going to be looking more into what strategies can help in creating the type of classroom environment that I want. I feel like this is something that we always stress is important during the teacher preparation process but it’s something that I don’t recall ever talking about really what steps should be taking to ensure this. My goal is to learn more about this over the summer when I’m not so crazy busy and try some of what I find in my student teaching so I have an idea of what I should be doing when I get my own classroom.

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What’s the Area of a Circle?

It has been a while since I have had time to post. This semester is getting crazier and crazier as it nears the end.

But anyway, we have been working on a measurement unit the past couple of weeks with our 7th graders. We started with finding the area of the different types of polygons; rectangles, parallelograms, triangles, and trapezoids. We spent the first part of each class deriving the area of the polygons by transforming them into shapes that we already knew. Students started out by cutting out the shapes on graph paper and then manipulating them to turn them in shapes they already know the area formula for. These activities came from my CT, check our her blog post on it here.

I also got a great idea for deriving the area of a circle from a fellow math TA in the program. We started with a circle that that was divided into 12 equal sections. The last section was also divided into two equal parts. When I did this I had labeled those sections as 12 and 13, but after thinking about how the lesson went and talking with my CT I think it is easier to label the two smaller sections as 12a and 12b.

Circle Uncut labeled 

Here’s a copy of the circle that we used. Circle Document 

I then cut the circle into these sections and lined them up so that they formed a shape that closely resembled a rectangle, although it wasn’t perfect because it was only cut up into 12 pieces.

Circle Proof 

We then talked about what the height would be for this rectangular shaped we created. I was impressed at how quickly they identified it as the radius of the circle. We then talked about what the base of the shape would be. This wasn’t as smooth as the height but they still got it. We talked about how many of the arcs made up each base, which they found was 6 and when we compared it back to the uncut circle and found that the base would be about half the circumference of the circle. We used what we knew about the area of a rectangle and found that the area would be:

A = r*.5C.

A= r*.5(2πr)

A= πr^2.

I was really pleased with how this activity worked out. This was something that I had never seen before and I wasn’t sure how it would go since the rectangle made wasn’t as clear cut as the previous shapes we had used. It is something that I most definitely plan on using in the future.