Goodness, it’s been quite a long time since I’ve talked about teaching. Sorry about that! Part of it has been because I wanted to wait and get some results before I presented what I was doing, but also it’s just been really hard for me to write about. There’s just so many angles! My work is this huge intersection between culture, education theory, engineering, and mathematics… maybe “cognitive science” is a catch-all? Anyway, all of these fields are deep and rich discussions on their own, but when I try to talk about them all at the same time my mind starts to explode.
So here goes nothing! I’ll start where my last teaching-related post left off: the second grading period.
Over the course of the first grading period. I had been noticing that just about every one of my students had some sort of weakness in following directions. For some, it was subtle, and it was hard to tell how was much of their problem was due to them “not understanding my accent” or “my way of doing things” (as was always their excuse) and how much was a weakness in that skill area.
So to find out, I tried to set up an experiment.
I put the class in groups of four, gave each student a piece of paper, gave each group a slip of paper with ten simple instructions printed on it, and then went to the school office to wait. These were the instructions:
- Put your first name in the upper left corner of your paper
- Put your the date in the lower right corner of your paper
- Put your last name in the lower left corner of your paper
- Put your grade level in the upper right corner of your paper
- Draw a square in the center of your paper
- Draw a circle inside the square
- Take your paper to the office
- Clap three times
- Give your paper to Mr. Husmann
- Go back to class and sit quietly
It was fun to wait there in the office for the kids to trickle in. After fifteen minutes or so a group walked to the office and tentatively walked in. I just sat there, and they looked confused. Finally, the leader of the group tried to hand me his paper. I looked at the paper and back to him.
Me: “Why are you giving this to me?”
Student: “Uh, we’re finished”
Me: “No you’re not”
Student: “What, why?”
Me: “You haven’t followed all the instructions”
Student: “Yes we have” (points to the work)
Me: “No you haven’t”
Student: “Well what should we do then?”
Me: (big smile) “Go back and read the instructions!”
A little while later, they came back grinning, clapped three times, and gave me their papers. Then other groups started coming and started to figure out the clapping instruction from each other.
Even though the groups were helping each other, there still were some pretty funny slip-ups… one group didn’t realize that I needed three claps and kept clapping one time and trying to hand me their paper. I wouldn’t move. But my favorite was the student that tried to show off. He walked to the office doorway, set down his paper, clapped three times, proudly shouted “I PASS!!”, then picked up his paper, and went back to class. He never handed it in. We all had a good laugh about that one when he realized his mistake later.
When I looked over the papers after, I was pleased to see that most groups did a pretty good job of following the other instructions. Still, some errors managed to propagate through the class. One common one was that students would put their date and last name directly under their first name and grade level instead of putting those entries in the corners at the bottom of the page. Some of the shapes drawn weren’t right either, but I didn’t count that as an instruction error: it turns out some students simply don’t know their shapes.
It was a fun test, but I don’t feel satisfied. Mostly, I feel like I was just testing my students’ attention to detail. Although this is a weakness for my students, I’m not sure that it’s much different from a similar group of American students. (Any American teachers want to try?)
Intuitively I’m looking for something a little bit more mysterious than attention to detail. The skill I’m trying to pinpoint is the ability to get a new device and read it’s manual to learn how to use it. The ability to follow directions to do or create something you’ve never done or seen before.
I was recently working with one of my top students and stumped the student on a problem that does a good job of showing what I’m talking about:
Round 78 to the nearest ten. Now round 64 to the nearest ten. Use digits and a comparison symbol to compare the rounded numbers.
My student knew how to do everything on this question, but was still stumped. (Yes, the question is worded a little bit awkward, but that was the language that the book was using and the student was used to. He had all the tools to solve the problem.) So I worked with the student like this:
Me: “Read the question again”
Student: (reads question)
Me: “How many things is the question asking us to do?”
Student: “I don’t know”
Me: “Well, tell me what the question is asking us to do, and we’ll count.”
Student: “Round 78 to the nearest ten”
Me: “Good! That’s one.”
Student: “Round 64 to the nearest ten”
Me: “Good! That’s two.”
Student: “Use digits and a comparison symbol to compare the two numbers”
Me: “Good! That’s three. Any more?”
Student: “Uh, no.”
Me: “Great, that’s right! Well, can you do the first thing?”
Student: “Round 78? Yeah that’s easy – 80.”
Me: “Excellent! Write it down then”
Me: “Ok, how about the second thing?”
Student: “64 to the nearest ten is 60.”
Me: “Yup! Write that down too.”
Me: “How about the third thing?”
Student: “I have no idea.”
Me: “Ok, read it out loud”
Student: “Use digits and a comparison symbol to compare the rounded numbers.”
Me: “Still don’t know where to start?”
Me: “Ok, lets break it down. Do you know what digits are?”
Student: “Sure: 0, 1, 2, 3, etc.”
Me: “How about what comparison symbols are?”
Student: “Yeah.” (draws <, >, =)
Me: “Point to your rounded numbers”
Student: (points at paper)
Me: “Ok can you use digits and a comparison symbol to compare the rounded numbers?”
(Side note: Notice that I did not steal the student’s epiphany — the student did all the thinking work and I just facilitated. This is my teaching philosophy: in order for a person to learn something, THEY must make the discovery. It means they get that endorphin rush which is not only one of the best “highs” in the world but the most powerful memory cementer and personal motivator.)
So while this mysterious skill requires a certain amount of attention to detail, you can see it’s a little more than that. To me it’s a part of a larger category of skills that are essential in math and science. Let me show you another one of these related skills that I have yet found a name for, by creating a fictional situation that illustrates an extreme absence of this skill:
- I write 1+1=? on the board.
- I show students what it means and how to find the answer.
- Students practice and get comfortable with adding any two numbers. (2+3, 4+1, etc.)
- I write 1+1+1=? on the board.
- Students freak out. “You’ve never taught us this before!!” “How are we supposed to know how to do this???” (They have no idea where to start and will not even try to make an educated guess what to do.)
This hasn’t happened in my classes with something as simple as 1+1+1, but it’s come close.
(edit 4/11/14: To clarify, the “skill” I’m looking at here is to have the thought process that goes, “oh, the plus sign means add the two numbers together, so it looks like having a second plus there means I’ll have to add one more number to my answer” rather than “oh crap this problem looks completely different from what I’ve seen before so I have no idea what to do and that’s that”.)
But as you can see, these skills that I’m trying to isolate are absolutely essential in math and science… in fact, you might call them the pillars of mathematical and scientific thought: they allow you to operate within a consistent external framework that you apply to a novel problem or situation. If you can’t do that, you will never own your own math and science… you will always be regurgitating someone else’s thinking or worse, memorizing procedures.
While I have seen these same weaknesses in children I have worked with in America, it seems more severe and widespread here in Liberia. There could be a number of reasons for this, including recovery from the war, malnutrition, interrupted education (I think these skills might be related to literacy), etc. But when I visited The Gambia a while ago (I’ll tell you why in a future post), and talked to education volunteers there, it sounded like their students had similar weaknesses.
My theory is that these skills are weak across the board in Africa, because they are not cultural values, and so aren’t practiced. African culture, being “high-context“, emphasizes using personal relationships to acquire information rather than independently finding answers using external, standardized, and codified systems. (Western, “lower-context” culture prefers the latter). There’s nothing wrong with living life either way, but if you want to do math and science, you need to be comfortable operating in external/standardized/codified systems, because that’s what makes modern math and science tick.
You might argue that other high context cultures do math and science just fine. Japan for example, has one of the highest context cultures and yet is a leader in math and science. How do they do it? I don’t know, but I’d love to find out because I think that information could be hugely applicable here. It looks like in Japan’s history there was a huge country-wide modernization effort to respond to the growing challenge of the west in which they figured many of these things out. Does anyone know anything about this that can share in a way I can understand? (I’m no history person…)
So, I hope you can see that I’m not saying Africa is doomed to be weak in math and science because of their culture — not by a long shot. What I’m trying to say is that I believe that if we can find ways of isolating and exercising these building-block skills we might create an explosion of math and science capacity in Africa. I think with just a little effort in the right places, some big stuff could start happening. (And I believe this sort of intervention is also needed in America’s education system as well, which I think is developing similar problems, but for different reasons).
So I began to brainstorm ways of practicing these skills. I thought about what I experienced in life that strengthened this category of building-block math and science skills. I thought back to playing with Legos, origami, solving puzzles… and then it hit me. There’s been one single activity and pursuit that has been the most instrumental in developing my abilities in following instructions, attention to detail, interfacing with external, standardized, and codified systems, abstract thought… all these building-block skills of math and science. Any guesses?
Yup, it’s computer programming. I’ve been programming ever since the third or fourth grade when my father got me a computer and told me, “we’re not buying you any games, so if you want any, you better program them yourself”. And so I did. It was probably the single most influential thing my parents did for my education (and brain development!). (Thanks Dad!)
So now fast forward here to Liberia. Guess what I was doing during the second and third grading periods? That’s right, in an attempt to strengthen these mysterious skills and practice arithmetic in a non-boring way with my students, I taught my students how to program.
And no, I didn’t need computers.
(more to come)