Glimpses into the Future: My First Classroom Observation

This past Thursday, I had the great pleasure to observe a classroom in my community. (I won't specifically name the school or the teacher I was observing for confidentiality reasons, but let's call the teacher Mr. T. For Mr. Teacher.) I volunteer at this high school twice a week, and I happened to see Mr. T in his classroom on my way out one day. I saw that he had several statistical models of data pasted to his door, so I took a chance, walked in, and asked if he was a math teacher. This led to a conversation about me pursuing my math education degree at Grand Valley, and we set up a time for me to observe in his classroom for two hours one morning. 

Flash forward to Thursday. 

I arrived at the school a little before 8 and got my visitor's pass in the office. I wasn't sure how I was going to feel, because while I had volunteered at this school before, I was unfamiliar with how it would feel sitting in a classroom wondering, "How would it feel to teach this class?" 

Class had already started when I arrived, and he motioned for me to sit in the desk at the back of the room. I was surprised, and a little excited. Silly, I know, but this is where I would be sitting in two years! I was really excited. 

The kids, of course, were sneaking glimpses at me, as kids do when strangers are in the class. Mr. T finally acknowledged the random person in the back of the room, introducing me briefly and saying, "She's studying to be a math teacher, and she's going to be around for the next few weeks, either in my classroom or in others, seeing how things are. It's really interesting to observe a classroom, and not sit in it trying to learn something new, but to think, 'How would I teach this class?'"  This is the moment the whole "Wow, I'm going to be a teacher!" thing really set in, and it was hard for me to pay attention as the teacher moved into his lecture about arithmetic sequences. But, the moment soon passed, and I found myself quickly jotting down notes, not only about what was being taught, but also what Mr. T did in his classroom. For your benefit on what the lecture was about, I've pasted my class notes below. But what I really want to talk about is all that I noticed in the first hour of my classroom observation. 

Mr. T made sure to help kids understand why they made the mistakes they made, and helped them learn from it. For example, when he asked a girl what the 15th term was of the sequence (above in my notes), she said 61, and when he asked a boy what the 150th term of the sequence was, he said 601. The girl said she added too many numbers together, since she just added 4 to the previous term until she got to what (she thought was) the 15th term. The boy, however, figured out that the explicit formula was t_0+d(n), where d was the constant difference (4, in this case). However, he didn't know that t_0 was actually not 1, and that t_1 was 1 while t_0 was -3. So, he asked, "Oh, so my mistake was that I treated 1 as the intercept instead of -3?" Mr. T, instead of simply saying "yes," loved this example, and used it to build on to the concept of intercepts and functions in relation to arithmetic sequences. This helped the boy, and probably other students, to understand what t_0 means, and helped them to relate it to something they already knew, which increased their understanding of what an arithmetic sequence was. 

Another thing I really liked was the lack of basic structure. Mr. T didn't have a lesson plan all laid out, with guided notes or anything. He gave the kids a worksheet to do, so they knew what example he was putting on the board and could follow along with where he was. But there was no pressure of time or structure: Mr. T just got through what he thought he should get through. I remember that, when I was in high school, my teachers would sit in front of the classroom and write under a document camera, and they would obviously have plans for what they wanted to cover that day. This type of approach doesn't take student understanding into consideration, and leaves students more confused if teachers don't take the time to properly ensure that students really get the concepts. The lack of structure really showed that Mr. T prioritized student understanding above all else, and I think that was my favorite thing about the class. 

Before I knew it, we were in hour two of the class. The students in his previous class left, and older students shuffled in, giving me weird looks, to learn about AP Stats. Mr. T had taken a little bit of time to explain what stratified sampling is to me, since I have never taken a stats class. This was a whole different experience, since a lot of Mr. T was doing was simply explaining the difference between SRS and stratified samplings. For those of you who, like me, are a bit unfamiliar with stats, SRS is a random sampling where you put the number of things in your calculator and pick a specific number (say 5 out of the total 24), see what random 5 numbers your calculator spits back out, and take the mean of this. Stratified sampling is essentially the same thing, except you separate different variables. So, you may have 2 sets of 5 where you take the mean of each. This makes more for less variation in the sample. 

My favorite thing Mr. T did with this hour was have the class take their own sampling of the data set (given on a worksheet), one stratified and one SRS. Then, he had each student put their respective means in the list 1 and list 2 of the graphing calculator and did a box plot in the calculator. This gave students a visual representation of the data, and showed them why stratified samplings offered a bit more accuracy than SRS. 

My biggest takeaway from this observation was this: It is ok to be disorganized. In every single case, students will thrive more from good examples and care given to their understanding. Mr. T was a great example of a teacher who cared a lot about his students' understanding and their overall success in his class. To give another example, in his AP stats class, he told students he talked to a girl who got a 98% on the last test, and said that she had told him that she had read the chapter the night before, which helped her to retain the information. This was an encouraging story, since he was, in his own way, giving students insight on how to succeed in their studying strategies. 

All in all, I consider myself very lucky to have observed in this classroom. Next week, I will be observing a different teacher in the same school, and I look forward to learning even more and gaining inspiration in what I will implement in my own classroom.