An Unusual Math Lesson on Practice

We sittin’ here, I supposed to be the franchise player, and we in here talkin’ about practice. I mean, listen, we talkin’ about practice. Not a game, not a game, not a game. We talkin’ about practice. Not a game. Not a, not a, not the game that I go out there and die for, and play every game like it’s my last. Not the game. We talkin’ ‘bout practice, man. I mean how silly is that?”
-Allen Iverson 

Practice. If you’ve read some of our recent posts, you know that Vena Cava educators are big on understanding practice, which we also call Habits. In many ways, education is about teaching students how to learn, and the way to learn is to transfer more and more skills (and knowledge) from your conscious mind to your subconscious mind by doing the skill (or drawing upon the knowledge) over and over again. Right? I don’t consciously think about riding my bicycle anymore, because I’ve learned how to do it from practice. I don’t think about completing the square, because I’ve done it enough that I can just use it as one step in reasoning through a more complex logical problem. Allen Iverson, back in his heyday, didn’t think about shooting a three. He had practiced shooting three’s way too many times in his life to think about it, and that’s why he thought attending practice wasn’t important (what he missed, of course, was a team spirit. Every time we play with new people, we have to learn their habits. Check out his Career Highlights and Awards – you’ll be impressed. But then… check out how many times his team won a championship). 

Well, here’s my recent lesson on practice. Perhaps you can use the same one yourself, or take the outline and adapt it to your own purpose and style. 

I start off with an innocent question: Can you learn from just watching a YouTube video? The typical response is that some students give an immediate and defensive “YES!” – but most students are in the land of “ehhh… yes? no? I don’t like watching Khan videos…” 

I would say (as I tell students) that the proper answer to that question would be another question: What are you trying to learn? It seems to me that it is completely possible to learn from just watching a YouTube video, as long as what I am trying to learn is very basic. However, as the task begins to increase in complexity, I think you have to begin to do more than just watch. 

I then walk over to my closet that I am lucky enough to have as a teacher who rides his bike to work most days and say “for example, what if what I am trying to learn is slightly more complex? I’m not talking about rocket-surgery here. What if the learning is how to tie a bow tie?” I pull one of my bow ties out and begin mimicking a YouTube video that explains how to tie a bow tie, working through the process and explaining what I am doing until I have a perfect bow. 

I give the tie to one lucky student (because for some reason all of them want to try it) and ask them to complete the task. We watch for a minute as the repeatedly mess it up. 

In order to tie a bow tie, you have to practice along with the video. Then you have to practice some without the video. And then you have to practice some after it has been a day since you tried it. And then you have to practice some after it has been a month since you tried it. And then… you get the point. 

Of course, the next step is to relate it back to math (or whatever content you are teaching). You know how to do that. But nonetheless, I’ll describe the three ways I did it today with my three different classes. 

 

Freshman are studying linear systems, but we are starting slowly with a much-needed regrounding in why. A couple of days ago, I asked them to find the slope of a line that we know goes through two points – for example the (x, y) coordinate points (-1, -2) and (5, 9). Many of them unfortunately had the curse of knowledge… they said they didn’t know how to find the slope because they knew there was a formula they needed, but they didn’t remember what it was. AHHHH!!!! How frustrating as a teacher! To find the slope, just get a ruler and your graph paper notebook and draw the graph! Then, count how many spaces up the second point is from the first, and divide it by the spaces to the right – that’s the rise over run aka slope! You don’t need the equation that you can’t even remember! 

Now, imagine that you (freshman), actually did all of the practice you were supposed to do in 8th grade with graphing lines… It’s really repetitive practice, right? Drawing the same coordinate plane (WITH a ruler) over and over again, plotting the points, and counting spaces gets tedious. You would probably have developed your own ‘shortcut’ that went something like this: you just divide the difference in y-values from the difference in x-values. That would have been your own way of stating the equation “y-two minus y-one over x-two minus x-one”, and I bet you would have remembered it far better because of the practice reps you did than you remember the equation your middle school teacher told you to memorize that you now don’t remember. 

Sophomores are studying completing-the-square, and although we go through the why of completing the square quite heavily, at some point they also need to just practice doing it. Well, about a week ago I had them do a practice page in one of our main books. Yesterday, I gave them the same page over again, asking they they focus on completing the process without notes and on the clock (under 1 minute per problem). Because I teach 10th and 11th grades at the same time, I went to go do the formal lesson for 11th and left them to their work. When I came back, almost everyone had realized it was the same page they did a week ago and ceased to work on it because “we’ve already done this page.” As you can imagine, my bow tie lesson with them was about this occurrence yesterday. Without going into more details, I told them that they all had better ace this Friday’s quiz… if that means they need to do some extra practice at home on top of the new homework, then so be it. 

Juniors are studying rational functions, and I intentionally have them try the homework using only the descriptions and examples from the textbook before I teach them anything about it. We used our bow tie lesson to talk about ‘how to read’ a math text. You can’t just read – you have to read with graph paper next to the text and a pencil in hand! That is the only way you can follow along, combine your own knowledge to make sense of new knowledge, and understand. How else can you make sense of a rule like: 

Screenshot 2020-01-15 at 4.51.53 PM

Finally, seniors are learning how to do data analysis in Excel. For them, the lesson goes right along with a concept of which I am constantly trying to convince them: that part of learning Excel is just playing with it a lot in low-stakes situations until you learn the fundamentals. For example, if I wanted to program a spreadsheet to analyze how changing the number of times the loan is compounded affects the total payment, I could use the formula A=P(1+r/n)^nt. A very common mistake (after forgetting to include necessary parenthesis in the formula code) is to simply forget to add a * in-between the P and the parenthesis – because of course that is typically implied in mathematics. When programming, however, we have to tell the computer exactly what we want it to do… so catching a mistake like that can take much longer than we are used to. You know how to get good at catching it? That’s right, “We talkin’ ‘bout practice!” 

-mmm

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