Before we could teach the lesson, we had to plan for it. I worked alongside our math coach and another intern in UTRPP to plan the lesson. Planning a lesson was an enlightening experience, there is a lot that goes into making a good lesson. We had to identify the standard and the objectives for the lesson. We had to think about the important vocabulary that was going to be in the lesson and think about how we were going to introduce the vocabulary to the students. We decided that we would tell the students the vocabulary word after showing them what it was. For example, we taught them how to write the number in expanded form and introduced the word "expanded form" after they had an example of what it was. We did this so they could focus on the new concept instead of trying to focus on the new word. Another area of focus for the lesson plan was how the students were going to be assessed. We decided that we would formatively assess them while they were working independently and on how they answered the questions during group discussions. We also decided on assessing them by using an exit ticket, as a wrap up of the lesson, to see if they had mastered the content. There would be two exit ticket groups, one group that "got it" and was ready for enrichment and another group who may have needed a little more help to fully understand the concept. While lesson planning, we also discussed any misconceptions that they might have and thought about how to teach so that any misconceptions were touched on.
After this, we planned on how we would teach the lesson (below is a copy of the lesson plan that we made). We went through many ideas on how to open the lesson and how we wanted the flow of the lesson to go. We finally decided on something that would work for all of us, but from what I experienced, lessons do not always go as planned.
From here, we went into the actual lesson, which was learning how to represent numbers in different ways. My math coach brought in this wonderful graphic organizer with the different ways on how to represent a number. When teaching this concept, we went from the least abstract representation to the most abstract representation (see lesson plan). We though that this was a good way for the students to understand how and why we represent the numbers the way we do. After we taught this concept, the students were able to practice on their own.
Honestly, I was a little dissatisfied with the lesson, mainly because I thought that the students did not get enough practice time on their own. We spent the majority of our time going deep into the opening questions and the initial teaching of the core content. We spent an hour and 15 minutes doing and discussing four problems. Don't get me wrong, I think that students need to dive deep into the content and really understand why they are doing what they are doing. Discussions like this are really valuable because they help the students form a conceptual understanding of the problem and discussion helps the teacher discover the students misconceptions and correct them. I just wish that the students did more than one problem of independent practice. We did not get to the other two practice problems, or the two problem solving problems, or the exit tickets for assessment. For a formative assessment, we walked around and looked at the student independent problem to see if they understood the content. Personally, I do not think that one problem is a valid assessment of how well they understood the problem. They need more practice before we can say whether they understood the material or not.
However, there were some good points in the lesson. I learned a new "attention getter" that is related to math. The teacher hold up some fingers, let's say three, and asks the students to "give me 5". The students then have to figure out three plus what number makes up 5, eventually holding up two fingers. Or, the student could hold up eight fingers, subtracting three to get 5. The teacher then asks the students why they are holding up that many fingers to check for understanding of the concept. I really like this "attention getter". It helps the students to stop what they are working on, think about math, and explain their reasoning. One positive from being able to go deeper into the content was that some student misconceptions were discovered. We were able to address these misconceptions and help the students gain a better understanding of the subject.
I also learned that it is important to display the lesson objectives and the essential questions for the students to see. We had them in two places, on the board and on their math worksheet that we created. Displaying the essential questions and objectives lets the students know what is expected of them, what the purpose of the lesson is, and what they will be able to do after the lesson. It also allows for discussion of what is going to be going on in math that day.
By far, the most important thing that I learned from teaching this lesson was how to take the important information from our math worksheets, and modify it for my class. To plan this lesson, we looked in the student's math packet and saw what the lesson was about. We then took the important information and made it our own. We thought about how we wanted to present the material to the class, what would work for our students, what questions we wanted to ask and how the students were going to display their learning. I really liked doing this, and I think the students did too. They were not confined to a math packet and neither were we. This is a much more valuable learning experience, especially since the lesson is tailored to our students.
Overall, I am glad I got the opportunity to teach with my math coach and learn some valuable lessons about teaching math.