This afternoon, @davidwees shared a link to an intriguing article in the following tweet:
Sadly, the article is for subscribers only, but the web site does provide a very brief summary that was enough to get me thinking today:
“What We Know
- No evidence that different curricula give different outcomes.
- Limited evidence that ordinary CAI improves learning.
- Strong evidence that using effective teaching strategies can make a difference.”
With what little insight this gives me into the article as a whole, I couldn’t agree more. I’ve been writing digital math curriculum for 5 years, and in that time I’ve had the privilege of visiting numerous classrooms to see our lessons in action. Based on these observations, I believe teachers have a much greater impact on student learning than any curriculum materials in their hands.
If you’ll recall, my first team and I were very passionate about how we conceptualized the lessons we wrote. We poured our hearts and souls into making them the best we could. However, our curriculum is not designed to do the job for the teacher. It has a role in delivering content for sure, but so does the teacher through a variety of factors including classroom layout, routines, questioning techniques, and instructional pacing, to name a few.
There are two caveats here. First, I make no claims that the lessons written by my team will deliver amazing results if taught well. I would like to think they do their job well, but I am clearly biased. Second, I’m not claiming, in general, that curriculum materials make no difference with regards to student learning. Given the choice between an old-school textbook or any one of a variety of other curriculums such as Investigations in Number, Data, and Space or, ahem, our curriculum, I will gladly take either of those over an old-school textbook. I might, perhaps, still be able to get good results with an old-school textbook, but the job is going to be much easier for me using instructional materials that match my beliefs about how people learn and the ways in which I engage with my students.
So thinking through all of this today reminded me that I have some pretty extensive observation notes that I took during several classroom visits four years ago. I read through them again this evening, and I think four years ago I was clearly seeing a lot of what I’ve just been talking about.
That got me thinking. Why not share my notes here? That way others can “see” what I was seeing. I also figure it helps me share more about my job like I promised in my first post during this blogging challenge. So for the next few days, I’ll be posting notes from various site visits I’ve done to see our curriculum in action.
In case you’re worried, nothing in these notes gives any identifying information about the school or the teacher. Also, I recognize that having a stranger observing in the classroom can put some teachers on edge. So I can’t generalize that what I saw in my observations is indicative of how these teachers teach normally. However, I still feel the observations are valuable, especially since I saw patterns as I observed in multiple classrooms.
Sadly, my notes do reveal some warts with regards to a few of our lessons back then. Thankfully our curriculum has gone through a round or two of upgrades over the past few years, so I don’t feel as bad since I know they have been tweaked and improved over time.
Other than fixing some language mistakes, I’m leaving these notes as they were written. I don’t want to change the voice of the “me” from four years ago. The “me” from four years ago is in italics. The “me” from today is in regular text providing a bit of commentary.
To give you some background about this first observation, I was observing a multiplication lesson in a 4th grade classroom. The topic of the lesson was introducing students to the doubling and halving multiplication strategy.
If you’re not familiar with it, here’s a simple example: Let’s say you don’t remember the product of 6 × 7. What you can do is halve one of the factors, like 6, to get the expression 3 × 7. You might have this product memorized, or you might quickly be able to count by 3s or 7s to get 21. From there you just need to double that product to find the product of 6 × 7. This is a very handy strategy, but also a very sophisticated one. In this lesson the students are meant to explore the idea of halving a multiplication expression by halving an array.
As you’ll see, the lesson does not go smoothly, partly because of issues with the lesson, but also because of issues with the teacher’s delivery.
Students got their computers from the laptop cart with minimal disturbances.
The iPad was just introduced a few months before this observation. At this point laptops were the primary tech device in classrooms.
The routines in this room were not as smooth as others I’ve seen, but students managed to get computers and log in without any prompting.
The teacher started the lesson by projecting the Knight Game on the board and having the students take turns coming up and filling in the missing blocks. The students quieted down and participated readily.
The Knight Game is basically a matching game. The students would be given a number, and they had to select different arrays containing that quantity of objects.
This game was actually in the Prior Knowledge section of the lesson. The teacher chose to play this game instead of a Bingo game that was actually the intended Warm Up activity. Considering she didn’t have a full class period to teach the lesson, I think it was a good choice to start with this game instead.
Students’ computers were open in front of them during the game. I saw classes at other schools where students lowered the screen to a 45 degree angle while the teacher was teaching. This isn’t sufficient because I saw many students accessing internet games and music even with their screens lowered. The students just sat low in their seat to see their screens. Someone on my team made a good suggestion that students lower their screens, but also turn their computers so they face away from the students.
The computers had software to prevent students from accessing external sites, but in nearly every school I visited, these elementary students broke through it in no time.
The teacher had the students come up one at a time to fill in the missing parts of the bridge. This was slow and very time-consuming.
This game could have been a great review of arrays and the meaning of multiplication, but the teacher never questioned the students about why they chose the answers they picked. A lot of good discussion and review was missed.
When she did help students, instead of asking them to think about the multiplication shown in the array, she just said, “Count the circles to help you find your answer.” The student would count 12 circles and then pick an answer that had 12 in it.
It was obvious that the teacher was not familiar with the big picture of the multiplication unit (or this lesson for that matter). Had she known, she could have used better messaging with the students throughout the lesson.
After playing the game, the teacher moved into the Engage activity. Unfortunately, this was the time that the DTP froze and she wasn’t able to load the activity she needed.
DTP stands for Digital Teaching Platform. This is the name of the software that delivers our content.
The teacher decided to wing it on the white board, while waiting for technical help. While the tech person fixed the technical problem, the teacher demonstrated how the problem 7 X 4 could be solved using the doubling strategy.
This didn’t seem effective because she had to work on a small white board that was on an easel in the corner of the room. The students were far away at their desks. It would have been better to call the students up to sit on the carpet around the easel so they could see and be more immersed in the conversation.
Once the DTP was up and running again, the teacher played the opening movie where Robin shares the doubling strategy with Andy.
I’m assuming because of the time she’d lost, the teacher chose to skip discussion of the movie. Instead she simply told the students they would practice the doubling strategy in the Explore activity.
Students opened the Explore activity and got to work. This was a disaster. The first screen in the activity has students working with the graphic organizer. It became clear in the first minute or two that the students in this class had never used the graphic organizer before.
This is a tool used in many lessons in our curriculum. The fact that it was new to these students showed me that this teacher had not used our curriculum that frequently with her students.
They were supposed to drag something from the bank, but the students had no idea what the bank was or where it was on screen.
They were also supposed to duplicate what they dragged from the bank. The students figured out the duplicate button, but many had no idea why they were duplicating. They just did it and went on answering questions.
Some students answered the questions on screen without ever interacting with the graphic organizer at all.
The teacher stopped the lesson after a few minutes. I thought she was going to demonstrate how to the use the applet. Instead she reviewed the meaning of the term double. This was important, but it did nothing to help the students succeed with the interactions they were unsure of how to do on screen.
Most students seemed to ignore the text in the questions, and instead they just solved the multiplication problems that were shown. This meant they were not engaging with the big ideas of the lesson.
I went computer to computer listening to students and helping them use the graphic organizer. When one student got to a screen that asked her to explain how she used Robin’s doubling strategy, the girl said, “I didn’t use that.”
After a few minutes, the teacher stopped the class and told them she was going to open up the rest of the activities for them to do including the Independent Learning, Mastering Skills, Take It Further, and the games.
As students finished the Explore activity, they moved on to the next activity. I saw that some students would start the Independent Learning, but then they would close it and move to the game instead.
This seemed to be a common problem in the schools I visited where the teachers opened up too many activities at once. Without proper classroom management routines, the students were free to jump from activity to activity, not really caring what they completed or how well they completed it.
The teacher skipped the Summarize activity altogether, preferring instead to have the students work independently through the various activities she had opened for them.
This concerned me so I offered to do the summary. The teacher agreed. I had the students stop their work and join me on the carpet so we could go through the Summarize activity of the lesson.
I’m not going to pretend that I pulled off a fantastic summary. I completely winged it, but I did make an effort to address the concerns I saw as the students were working and I tried to bring some closure to the lesson.
I did feel that the Summarize activity (and lesson as a whole) was too challenging as designed. The students saw that the halved fact was related to the original fact, but they lacked the ability to do the halving and doubling themselves by the end of the lesson. Also, when the lesson transitioned from multiplying by 6 to multiplying by 8, it jumped into the example of 8 X 7. Unfortunately when we halved this to 4 X 7, that multiplication fact was still too hard for many students to solve mentally so the usefulness of the strategy was lost on them.
I did go back and explore the lesson after this experience. I understand its goals a bit better, but it’s clear that it requires a fair amount of planning and a lot of finesse for teachers to pick up and teach it well.
I feel that more time should have been spent on how to halve a fact rather than verifying that the halved fact equaled the original fact. The verifying step was too advanced and didn’t translate into a practical mental math strategy for solving multiplication problems through doubling.
At this point I would normally say “Whew!” because there’s so much text, and to acknowledge those of you that made it all the way to this point in my post, but I only wrote a small chunk of the text today. The rest I just copied and pasted which is sort of like cheating, but whatever. Anyway, this wraps up my first lesson observation. I look forward to sharing another one tomorrow.