A Teaching Victory

So as some of you may know I have been struggling with teaching so far. Your first year teaching is difficult because it is often the first time you are teaching the topics. It is tough managing the course load, grading load, and finding your presence in the classroom. It also takes you longer to plan such a good lesson. After more years of experience you know what activities work and you have lots of good teaching strategies.

So for me it is really tough because I am teaching Calculus. I never thought of teaching it. I am much more rusty with Calculus. I don't have good Calculus role models to mimic. I had horrible professors in college. I drew a lot of what I think a good teacher is from my Algebra and geometry teachers. So I have been struggling to keep up with planning, grading, and actually knowing the subject. The students expect me to be super on top of my game and all my bosses do too. The students I have ask some of the most challenging questions. They also will remember if you didn't answer one of their questions and will keep reminding you.

So I have been trying to bring in group work more and more. I have been working on incorporating that. It was going ok. I kept trying to rethink how to do group work and what questions to use. I kept trying to think of ways to get everyone talking. I was doing decent, but I had to be doing better.

I went to a workshop on highly effective teaching practices. We spent one morning preparing a lesson plan. I used this lesson plan today and the person who led the workshop came to see how I implement this lesson plan. So this what I did today and what went well.

So today I introduced how to do the chain rule.
I started with students looking at a graph of the function sin(x^2 - 4). I had this graph projected under the document camera. I gave the students 4 minutes to write down any observations about the graph. I timed them and kept them to 4 minutes. I then had them lift up their white boards and asked a few students to talk more about what they wrote. I talked over with the head of the math department about this. I should have had students come up and put their white boards under the document camera to extend the discussion. However what I was looking for was talking about the period, oscillation, and if it was symmetric. The graph gets as one student more and more dense because it oscillates more. This later translates to the graph of the derivative having a bigger and bigger slope.  I then handed out a hard copy version of the graph for students to attempt to graph the derivative function. This was to get them to think about the derivative. I gave them five minutes to do this which was appropriate and I stuck to this time limit. I also gave them time warnings. Some saw that the graph of the derivative got a more and more positive slope. I got students who finished early to explain the graphing process to other students. I then projected the derivative graph to show them what they should have gotten. They are some crazy graphs. You should take a look. If you then look at the derivative function it turns out the original function is not symmetric (although looks very much like it). So this was the intro into the chain rule. So this lead amazingly into the objective for today which was to find this derivative algebraically.

So this led into talking about looking at the two equations and seeing that the derivative function is made up of two derivatives of which we already know. This lead into the objective beautifully because the objective was that students would be able to find the derivative using the chain rule. I wrote this up on the board.

So know that students have sort discovered or observed what the chain rule is. I introduced the theory and went over the theorem. I connected it back to the example in the beginning of class. Now I should have gone slower and provided one more example.

After this theory and explanation of the example. I had students work on three different problems. I chose increasingly harder problems. The first one was similar to the first example. The next was (3x^2 + 1)^2. This one was a little different and they could solve it using the old way. The last one required the use of the chain rule a couple of times. I gave the first one to the group of mostly weaker students. Then I gave the second one to some of my better students. Then I gave the last one to some of my better students. If a student solved the problem within the five minutes I told them to explain it to the other students around them. I then gave them another five minutes to solve the other problems. If one student solved the problem I encouraged them to explain it to the other students. Then near the end of the three minutes I asked students if they would present their answer. The first student was good. The second student made a mistake and I handled directing him to the right answer fantastically. He stayed to try and figure out the problem through the break. I then had the third student present the last problem. I was really proud of her because she struggled at getting this last problem. A few students were talking at the beginning of class and I quieted them. They still were talking so I went into the class and stood next to them. That sent the right message. So I was on my teaching game today. Now I just got to keep it up.

Then I had students fill out an exit slip. I asked them to write about one thing they learned today. However the more fun question was having students come up with the example that uses the chain rule and to solve it. I told them to get real creative and think of one that might use the chain rule more than once. There were some amazing answers. Some students were just laughing at how difficult they made the problem. I was so excited and the students enjoyed the chance to be creative. I think I will show some of these examples at the beginning of class. I could not do it during class because I had to move on.

I brought in four different Free response questions over the material we had covered so far. I gave students three minutes to solve the problem. This was not enough time to solve the problem. Then when they had to rotate they had to read the work from the person before them and add to it. We did this a few times so that each student saw each problem. Then they will have to present a problem they have not seen before in class next time.

This was good on paper, but I didn't think the groups or the problems enough. The rotation did not work out and not all of the students saw each problem. So I realized how my math was off and I am changing the structure some for tomorrow.

There was also this funny movement where I was going to make all of the students move about the room to each problem. The students did not like this idea and one girl raised her hand to ask why the papers couldn't switch from group to group. I laughed it off and said well I thought we could get some exercise in Calculus and thought you would like that exercise in Calculus. They laughed at the joke and I said sure we can make the questions move if you don't want your exercise. I was debating over these two structures and though moving would be more fun.

Tomorrow I  will be getting the students in groups of four. Each student in the group will get a different question. Then they will rotate questions after three minutes. I will do four rotations so each student sees each problem. Each student will have to add on to the previous students work. Then at the end the group will work together to present one of the four problems. Then now that they have seen each one they can help work on the presentation.

The students were engaged through out the lessons. They had fun and I had fun. They laughed at my jokes. I made the lesson personal by throwing in a few comments.

I had also planned for students to work on a challenge question, but I cut it because it was more important for the students to present answers and work on the exit slips and free response questions. It was a great choice.

So I handled the classroom management very well. I made good teaching decisions. I handled the teaching moments very well. I kept students moving by keeping them to strict time limits. I had a problem with this earlier. I used an online clock timer. It is a portable app that you can install on your USB stick (portable timer app). It is a great visual for you as a teacher and for the students. I have it counting down on the computer and have the projector displaying the computer screen. At the end if you have the volume on then it will give a buzz sound. If the students are really engaged then this jumps them right out of it and tells them it is time to move on. I still have areas to improve on. However today was a great lesson.

I had students missing today because they are on a habitat for humanity trip and I hope the classroom dynamics do not change when they come back. Today was great and dynamics were great, so hopefully it stays the same. The students who were missing I think are instigators of immaturity. It will be interesting indeed.

Overall the lesson went well. It will be absolutely excellent tomorrow. I left feeling great. I felt even great when the head of the math department reinforced this thought. She caught moments that I made good choices and decisions that I sort of just did instinctively. I want to parlay this great lesson into more great lessons. I will use this structure and activities to set up other lessons. It was lessons and days like that remind me why I want to teach. This is what I always dreamed my classroom to look like. Now did I imagine it in Calculus or in China, No I didn't. However I did picture stimulating students and making them think. I did imagine letting students be creative. I did imagine having students discussing how to solve problems together.

Earlier in the year I wanted to cry because I was just so overwhelmed with everything. I left today wanting to cry tears of joy. I felt like I had finally done in the classroom what I always dreamed of and I enjoyed it. I had lots of fun. I love this feeling too much not to have it happen again.