I had the opportunity last week to teach a lesson three times, for three different teachers that I work with as a group. They also taught the lesson either before or after my model. It was a great experience and reminded me of the importance of both the reflective process and risk taking.
This is the part of blogging that I miss :)
The lesson was introducing (or reminding) students to one-variable inequalities, what they mean, and what they look like on a number line.
In all three classes, I started off by giving each partner a whiteboard and marker, and displaying two numbers on the screen. I started off with 3 and 7, and asked, "How do these numbers relate to each other?". In each of the three classes, I got a lot of "they are both odd", "they are both numbers", "they are both prime", and I even got some students to talk about "they are factors of 21" and other math vocabulary.
Then, I changed the numbers to be 3 and 8, asking the same question. I got answers like "They add to 11" or "They are factors of 24". One or two students in every class got to what I was looking for, which is "8 is bigger than 3" or something to that affect.
I'm still trying to think through how I could have phrased the question better in order to help more of them understand what I was looking for, but during the lesson I resorted to singing a line from one of my son's number videos that says, "1,2,3,4,5,6,7 ... 4 is greater than 2, 3 is less than 5" or something like that. Then, I got all the students to write at least two sentences: "8 is greater than 3" and "3 is less than 8". Some students put the < or > notation on their boards right away. However, after I wrote the two sentences on the board, I wrote a "math symbol sentence" like 3+5=8 and asked students how to write it in words. Then, I asked them to look at their whiteboards and write what they had in words in symbols. A lot of them remembered, although they still get the < and > mixed up.
At this point what I did in each of the 3 classes differed.
In the first class, I jumped right into the next activity, which was a Desmos Activity Builder about identifying numbers that are true for an inequality statement and writing the "math symbol sentence" to represent it.
I honestly can't remember what I did in the second class to transition anymore :)
In the third class, I spent some more time on the statement "3 is less than 8" and asked students what other number(s) besides 3 could fit in that statement and still make it true. We went around the room and I had almost every student contribute a number. I probably should have had them all write a number on a whiteboard and hold it up, but I didn't want any repeats so I went around the classroom whip-around style. What we came to realize is that there are a TON of number that could be in the place of 3 in that statement, so we can write a generalized "math symbol sentence" of "x is less than 8" or "x<8".
That was a definite improvement for the third class because it gave the students some context for what type of answers we were looking for later.
In the Desmos Activity Builder, which was these teacher's first ever experience with it and put together in about 15 minutes as a "let's try it", students were asked to simply drag a dot to any point that would make the statement true, and then try to come up with the "math symbol sentence" that would work for any answer.
In the first class, I had the students do slides 1-5 and then I pulled everyone back together to go over it. I used the overlay feature to show all the responses. I hadn't done the context building that I described above from the third class, so it was a little tough getting the students to see how I wanted them to write the statements. I kept the class very "together" and structured, but I wasn't very happy with it because I felt like there were a lot of students who were bored that were being held back and they weren't necessarily getting my point. That's what happens the first time you teach something.
In the second class, I modified it a bit but still left with a feeling of dissatisfaction for reaching all learners at an appropriate pace for their needs. I don't remember why I can't remember the details for that class!! I'll have to ask the teacher.
The structure in the first two classes did allow me to model some strategies for classroom management with laptops. I use the "half mast" strategy for when I want students attention - they have to put their screens halfway down so I know I have their attention. I do feel like that was a success.
In the third class, I did something completely different. Besides opening the class differently (as mentioned above), I divided the slides into three parts: 1-5, 6-9, 10-15. I told the students that once they thought they were done with 1-5, they had to check in with me before moving on to 6-9. Once most students were done with 1-5, I paused the class and pulled everyone back together to go over it. One thing I didn't do that I regret is ever show the overlay to reinforce the idea of a generalized statement.
I really liked the third class. It reminded me of my "organized / controlled chaos" class where students are working on all different things at their own pace. It was a little harder in this case, because I didn't know the students or their names, so I wasn't able to intentionally check in with the students who needed checking in with. I was able to monitor results and tell certain students to "go back and look at slide 7", but I didn't actually walk over to them and check in with them in person. I wish I had.
We did not "get through" nearly as much as they had wanted, as the students were also supposed to solve two step inequalities and graph them. I spent the last 3 minutes of class trying to rush through an example when I should have just stopped everyone and summarized the day, doing some form of "exit ticket".
I'm not in the classes today so I can't do any follow-up, but I am debriefing with the teachers in just a little bit so we will see how it went from their perspectives and when they taught the lesson.
So in summary, if I had to re-do the day:
1. Start off with the same activity, but think of a better guiding question?
2. Use the transition I used in the third class to help students generalize what is true for an inequality with a "math symbol statement".
3. Allow students to move at their own pace through the sections like I did in the third class, but instead of just calling out students, go and walk over to them and have a conversation
4. Call the students back together at certain points in order to show the overlay and make some connections.
5. Call everyone back together with 5 minutes to go to wrap up, review, and do some form of "exit ticket" formative assessment to see what they got from the day.
6. Keep equations for day 2 and don't try to rush into it!
Thoughts or feedback? Leave it in the comments!
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