For our pre-brief, we planned the lesson together. We decided what part of the concept to cover, what the students would already know coming in, and what the end goal would be. Our focus for the lesson was on using InfuseLearning as a tool to monitor their progress continually throughout the lesson. Thankfully, I also decided after our pre-brief to use Google forms as an opener and an exit ticket, because Infuse Learning completely failed - none of the questions would load on the student computers!!
Funny thing is (and I think one of the awesome things about teaching - you are always seeing new things and making new connections) I actually taught the concept in a completely different way than I had before. Our focus was on making perfect square trinomials and why they are so useful to use in solving quadratic equations vs. expressions that aren't perfect square trinomials.
This was the first time students in this class have used their laptops, so I went and visited this class period the day before to introduce myself. I think that helped, because when they came to class that day, they already knew who I was and were excited they were going to get to use their devices that day.
I had this on the screen when they entered, so we could get started with class right away. I think having some sort of "opener" or "warm-up", even if it's as simple as this, is so important in making the best use of the class time you have with your students.
Below is my "rough" planning notes that I had made before the lesson. My reflections and comments are in green.
Overall lesson reflections and comments:
- It was fun to be up teaching again! The hard part was that I didn't know the students' names, or what levels most of them were at, so I had to learn a lot on the fly and try to reach all students in the class period. There was also a brand new student that day that transferred from another teacher's class that had already learned this concept, so I wanted to help him feel welcome and appreciated but didn't want him continually sharing the "right answer" since he already knew how to do it.
- Even I did not 100% monitor student laptop use. I made a big deal about the "half mast" with the laptops when we weren't using them. There was one kid in the back corner who was playing around with it during the first part of the lesson. Funny thing is, because of where the iPad was recording the lesson, you could see what he was doing the whole time! Ha! It was only for about 5 minutes but I'm disappointed I wasn't more aware of it, since that is something I really want to model for my fellows (classroom management w/ laptops)
- Seating arrangement in class really affects collaboration. The students were seated in rows and although they did a decent job of "talking to a partner" at different points throughout the lesson, it would have been great to have a better setup and expectations for what this would look like. Obviously, that is something that has to be built and can't just happen with a strange teacher on a random day.
- Tech Back-up plans! I feel I did a decent job adjust when Infuse Learning didn't work at all, but if I would have thought through it a little better, I would have had Socrative ready, or have asked ahead of time if the teacher had mini-whiteboards available to use. I just came across this blog post comparing Socrative & InfuseLearning. I'm wondering if many of the students were using Internet Explorer and that was the issue?
- Checking homework... I didn't spend any time in class checking their homework from the night before, which is a normal routine for the class. Where does this fall in this lesson, if at all? Should homework even be checked (I never did, students were responsible for checking their answers and their performance would show on their quizzes).
- The Google Form Opener and Closing really provided valuable feedback for me (the teacher) and [the opener] allowed for some great partner/group/class analysis and discussion. I think that is a valuable use of technology that enhanced the lesson.
Opener (2-3 minutes)
Students understood "half mast" and for the most part (with the exception of the student mentioned above) followed the rules.
Students had no problem getting on InfuseLearning and signing in. Once I selected a question to push out to them though, nothing showed up on their screens. We tried it multiple times throughout the period to no avail. I tried it when I went back to my office and there were no issues. So, I'm wondering if there is some sort of limit with how many students can be in a room at once (we only had about 36 I believe) or if IE was an issue?
Warmup (10 minutes)
The Google Form warmup went great. Students got started and factored 3 problems, all of which were Perfect Square Trinomials. I used conditional formatting to code the "right" answers as green. However, I only coded one way of writing the answers correct, and left some other "right" answers not green. This led to a great thinking time for the students of "which answers up there NOT in green are actually right, and why?"
I then showed them something like (x+2)(x+2)=8 and asked them to use the Zero Product Property to solve it. The majority of the students didn't fall for my trick question (it's not equal to zero) and FOILed out the problem and tried to subtract 8 from both sides in order to solve it.
I changed the equation to be (x+2)^2=8 and asked them to solve it. Some of them still tried to FOIL it back out, but then I showed them that when we have something "quantity squared", we can take the square root of both sides to solve it.
Because I couldn't do any of the InfuseLearning activities noted above, I tried to have the students write down their ideas, share with a partner, and then I would pick some to share out to the class. Not ideal (I think whiteboards would have been an improvement from this), but it worked ok. When watching the video back, I still was not fully happy with how I moved on in certain instances instead of probing further.
I showed them numbers like 9,16,25 and asked them what they were called (Perfect squares), and then said that it's because they can be written as 3^2, 4^2, 5^2 (as "something" squared). So since (x+2)^2 is just another "something" squared, it is also a Perfect Square. However, since it comes from a Trinomial, it is called a "perfect square trinomial" (PST)
For #7 above, most of the students could answer "yes" or "no" after we clearly defined what a PST was, and then I asked them to start thinking about what the 3rd number in a PST always was (a perfect square). Not too many of them could give a reason WHY their answer was "no" - meaning, if it's NOT a PST, what number would make it become a PST? We ended up discussing and modeling that together as a class, which made this section go a little longer than planned time-wise, but necessary.
*I had VLookup put in the spreadsheet ahead of time so I could see which students still needed to submit. This was definitely helpful (and more helpful if I actually knew the student names!). It would have been neat to show the students the results coming in, but I didn't want them to see their classmates' answers and just copy. Because this was their first experience with GForms, it might have been good to have them do a "non-math" or "non-right answer" form first so they could see how the results come in.
Concept Introduction (5 minutes)
This was the next step building off of what they did in the previous section. Without a third number to confuse them, could they come up with the 3rd number themselves? When we went over one of them, I said that I didn't think what they gave me was the right answer (even though it was) and I wanted them to convince me they were right. This would have worked much better had I had a way to get an argument from EVERY student, and not just the 2-3 students I called on. I learned about the "Convince me" from a Steve Leinwand presentation I went to this week; it's next on my "to blog" list so I'll write more there.
Visual Introduction (5 minutes)
I wanted to make sure to hit up the visual learners and show them the conceptual reasoning behind the "formula" most of them already knew (cut the middle # in half and then square the result). I think it's important for students to understand that what they are really doing is "completing a square" when doing this process. Same thing, I was going to have the do an InfuseDraw question and actually fill in a square for me so we could look at the results - bummed that couldn't happen. Whiteboards would have worked as well, although w/ InfuseDraw I could have projected all the drawings up there with no student names for some deeper analysis.
Mathematical Solving Introduction (10 minutes)
I asked the students to factor and solve the equation. Most of them realized they couldn't factor it and tried the quadratic formula. I told them they couldn't use the quadratic formula but needed to solve it. This led us to seeing how we could convert the equation to a PST, and however we changed the equation on the left we had to compensate for it on the right (this is different than how I used to teach it - I used to have the students "subtract 4 from both sides. Then add 9 to both sides."). It was fun playing a little bit of devil's advocate, trying to do some things wrong and having the students try to convince me otherwise. Again, I wish Infuse would have worked or I had another way to get answers from all the students rather than just had them "discuss it" (which some partners did better than others) and then call on different students.
Practice and Extension (15 minutes)
I ended up going over 1 more and then students only had 2-3 minutes to practice another one. They didn't get to do the peer teaching I wanted them to. In addition, I really wanted to get to the challenge activity, but we didn't. If I was teaching again on Monday, this is where we would start because I think it's a very valuable part in the cycle of learning.
Exit Ticket (5 minutes)
Students were only given about 3 minutes instead of 5, so I'm disappointed I wasn't more strict on the time with getting them started on this. About 2/3 of the students submitted it before the end of the period, and the others were told they had to finish submitting it at home. They didn't get their hw assignment until they submitted the exit ticket, which I thought was a neat idea.
I thought this was a great exit ticket because it guided the students step by step through the process and allows me to see exactly where they are going wrong. It also gave them the chance to give feedback on the lesson. If I was teaching on Monday, there are several things I would go over on Monday based on what they wrote.
Same thing as the class opener, I had the VLookup formula put in already so I can tell which students submitted the form. As of right now (Sunday morning), there are 11 more students to submit, but there were 3-4 students absent on Friday. Not bad considering I gave them 2 minutes less than they should have had.
Put in confirmation of Google Form for students to get after submit.
Once they hit submit, they were given the practice problems to try. I believe I gave them 5 where they just had to find the 3rd number, 3 where they had to solve it completely, and 1 problem that my fellow exposed them to the previous day in a more "problem solving" opener that I wanted them to see that they could now solve mathematically. That whole cycle/connection with starting with the conceptual we need to work on, but with the time we had in planning I think it was decent for a first round.
Next steps - completing the square when 'a' is not 1!