Saturday, May 21, 2016

Ten Teen

My two and a half year old daughter did several things with numbers yesterday that I had never heard her do before.

We were out on a walk, and someone walking two dogs passed us.

(That was my count, anyway.)

"Five!" Mia exclaimed.

"Where do you see five?" I asked.

"Five dogs!" she answered, pointing back over her shoulder.

Then she looked ahead to another dog that was approaching.

"Six!" she proclaimed.

Two new things here:

  1. I had never heard her use a number greater than 2 to describe the total quantity in a group of objects. She has said "two books" and "one moon," but nothing over two that would show that she understands that a bigger number can be a total quantity. (We math teachers call that cardinality.)
  2. She said "five" and then she said "six." I know this doesn't sound like a big deal. But it was the first time I had heard her count on, without starting at 1. 
Sadly, the dogs passed so quickly by that we never had a chance to see if there had been 5 dogs or 2 in that first group. (I am pretty sure I was right, though.)

Later, at dinner, she stretched her hand up in the air and started counting at 4.

"4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 18, 19, ten teen," she said.

"Yes!" I said. "We really should have a number called 'ten teen.'" 

"I don't think she knows about 13 and 14," my husband said.

Mia, overhearing him say "fourteen," immediately started counting at 40.

"40, 41, 42, 43, 44, 45, 46, 47, 48, 49, forty-ten!" she said happily.

"Yes," I said. "And the name for forty-ten is fifty!"

"50, 51, 52, 53, 54, 55, 56, 57, 58, 59, fifty-ten!" she continued.

"Yes," I said. "And the name for fifty-ten is sixty!"

What is so cool here is her understanding that there is a repeating pattern to our number system. She has only heard someone count above 30 about 3 times in her life, I would guess. But she has internalized something about the counting pattern.

And so we continued on to ninety-ten, at which point I told her ninety-ten was called one hundred, even though I wasn't sure if that was the right thing to say, since something big changes at 100. She's only 2 and a half, though, so I told her it was 100 without getting too complex, and we kept counting together until we got tired of the game. 

Then I dictated notes to my husband, who jotted down on the back of an envelope what had just happened while I held our wiggly ten month old with one hand and tried to finish my dinner with the other.

Wednesday, September 26, 2012

Mistakes

Today we were solving 8 + 3 + 2.

I asked what answers the students had found.

"12," someone said.

"15," Maggie said.

I recorded both totals on the board. "Any more answers?" I asked.

No more hands went up.

"Who will defend their total?" I asked. I pulled a name out of my cup of names. It was Jaylin.

"I know that 8+2 is 10," he explained. "And 3 more is 13."

I wrote down his solution on the board.

"Who else wants to defend their answer?" I asked. Then I saw Maggie's hand up. I called on her.

"I made a mistake," she said.

"What was your mistake?" I asked.

"I thought it was 15," she said. "But I counted wrong. It's 13."

I smiled at her.

"Wow, Maggie," I said. "You have to be really brave to say 'I made a mistake' like that."

Suddenly, Maya raised her hand.

"Yes, Maya," I said.

"I made a mistake," she said.

"What kind of mistake?" I asked.

"I thought it was 15, too," she said.

I smiled at her.

"Maya, Maggie made a mistake today. I'm not sure if you did or not, but that's okay. There will be lots of other days for making mistakes."

Tuesday, June 26, 2012

Dangers of the Pacing Guide

In the past few weeks, I have been working on a project to align our district's math curriculum with the new Common Core standards.

Since I have always taught at a pilot school, I have in many ways been sheltered from the mysterious workings of the Boston Public Schools. As part of this project, I have caught a glimpse into what teaching is like for many teachers in the district.

On the first day of the project, we were told that we would need to understand the new math standards, then think about what might help children learn them, identifying materials and resources that could help teachers introduce the material.

"You mean we don't just follow the Pacing Guide and go through the curriculum as it's written, from start to finish?!" asked one teacher.

That's exactly what we mean, the leaders replied. A collective gasp traveled the room as teachers shook their heads, wondering how they would do such a thing.

In my mind, this is what teaching is -- knowing what you want your students to think about or get better at, then figuring out how to help them do so. This, along with paying close attention to how your students make sense of the world, is the heart of the intellectual work we do.

But most of the teachers in the district aren't in the habit of doing this anymore. When it's time to teach math, they reach for a Daily Pacing Guide that tells them exactly what lesson to do on, say, November 13th. While the pacing guide has a few floating days for when your students need a little more time, there isn't much room for flexibility or you'll be (gasp!) off the pacing guide. Reading is the same but a little worse, since they use not only a Daily Pacing Guide, but also a generic, scripted curriculum.

What's the outcome of this? Teachers are forgetting how to intellectually engage with their students' thinking and their work, think deeply about what might begin to move them to the next place, and plan a lesson.

I guess this is the logical outcome of the profession becoming more scripted and "teacher-proof" in recent years. I shouldn't be surprised. What shocked me was the teachers' increasing dependence on the pacing guide. Many teachers want the pacing guide. When I suggested that it might be a disservice to professionals to ask them to blindly adhere to such a document, many looked askance. This is what their job has become. They are forgetting how to do it any other way.

Tuesday, June 5, 2012

What insects need to live

One of the objectives of our second grade insects curriculum is that students should learn that insects need 4 things to live.

You know them, right? Quick! Name them!

I'm sure you got it right, but in case you didn't, here are the 4 things: food, water, air, and space.

In the past few years, we've started writing learning targets for our lessons, so that both the teachers and the students know what they are supposed to learn. One of our learning targets is this: "I can list what insects need to live." If you can list those 4 things, you get it right. If you can't, you have missed your target.

(We write more interesting learning targets than that one. But it is easiest to write and assess objectives that involve remembering facts, and hardest to write and assess objectives that involve thinking and analysis. This is one danger of objectives.)

A few weeks ago, in an inquiry group for science teachers, we took a deeper look at some student work having to do with this learning target. We looked at one student's observational drawing of a milkweed bug habitat, and we looked closely at partial transcripts of science discussions from two classrooms.

We noticed, when using the Collaborative Assessment Conference to look at the drawing, that while the student had painstakingly labeled, with arrows, the insects' food, water, and air holes, when she wrote the word "space," she drew an arrow pointing to the word "space" itself. Her label was pointing at itself.

This prompted us to think about how abstract "space" is. Who decided insects need space, anyway? What does that mean? Do they need a space to live in? Do they need just enough space for their bodies so they don't get squished? We began to eye our list of four needs with some suspicion.

In the science talk transcripts, the students dug deeply into the idea of what insects need to live. That's not what the discussions were intended to be about -- the teachers had asked where insects live. But as students shared ideas about where they live, they naturally started to talk about what they need to survive. They talked about food, and that insects live in places where they can get the kind of food they need. They talked about protection -- insects live under logs because it is dark and safe and hard to find them.

Then one student said that insects need each other to survive.

We, the teachers, thought hard about that. It made us wonder: What does "live" mean? Does it mean that an individual insect lives? Or does it mean that a species survives? If it's the latter, they most certainly do need each other. 

The second graders, though, weren't thinking about reproduction. They were thinking about safety. They were pretty sure that some insects protect each other. If that was the case, didn't those insects need each other to survive? (If you're not sure about this, check out this video of fire ants making a raft so they can survive a flood in the jungle.)

[The students in one class designed an experiment to see if insects need each other to live. They took one mealworm and put it, alone, in a habitat with food, water, air, and space. It died. The mealworms die easily, so this is hardly incontrovertible evidence, but the second graders were pretty convinced.]

The more we thought about it, the sillier this learning target seemed to us. Do the curriculum writers have any idea of the diversity of insects on earth? Those insects need very different kinds of things to live in very different places. What is really interesting about insects is how they live in certain places so they can get what they need to live -- an idea the students began discussing almost immediately. This seems like a Big Idea about insects (and all living things) that could lead to all kinds of thinking and analysis, instead of just memorizing four things that insects supposedly need to live. 

This is one of the many stories that make me think we should always word our objectives as questions, not as answers. What do insects need to live? There are many answers, and we could investigate them all year.

Thursday, May 31, 2012

What I Learned at Harvard

It's been a year since I last wrote a blog post -- a year in which I haven't been teaching, but have been learning instead. My year of graduate school is at an end, and so I'd like to share the biggest thing I learned at Harvard:

We only really learn the things we figure out ourselves.

This actually seems so obvious to me that I'm a little embarrassed to write it down, but from looking at the world around me, it appears it's not so obvious.

This big take-away can be phrased in other ways. You can't make anyone learn anything they're not ready to learn. People don't learn anything if you tell it to them. You can't really teach anybody anything -- you can only guide them in exploring ideas.

It seems to be a more or less controversial statement depending on how you say it. And I'm not sure all those statements really mean the same thing, or are always true. But I do know a few things.

I know that the person who does the talking, the one who explains, is the one who learns. "Learners talk and teachers listen," as my wise Professor Duckworth wrote on my journal this year, and she's right. If I hear someone explain something that makes sense to me, I kind of understand it, but I don't really own it until I explain it to someone else -- or, better yet, to several other people. Even then, it's very possible I won't remember it a few weeks later. If I really want to learn it, permanently, I have to experience it, struggle with it, and figure it out myself.

Here's another part of this that I cannot believe I never figured out in all my years of teaching, and no one ever told me (or maybe they told me, but I didn't learn it): students only learn what they DO.

In other words, as I've heard said at least one hundred times this year, "Task predicts performance." The idea is well explained here, but what it means is that we only learn to do what we practice doing. If we practice a procedure until we have memorized it, we are only learning to memorize a procedure. If we work with a team to solve a construction problem with blocks, we are learning about constructing buildings, and learning to solve problems in teams. If we sit and listen to a teacher talk, we are learning to sit and listen to a teacher talk, but nothing more. We only learn to do the things we do.

The obvious problem here is that when we think of what it means to be a student, we think of students sitting and listening to the teacher. And when we envision a teacher, we envision someone standing in front of students, talking. According to what I've learned this year, in this scenario the person doing the learning is the teacher, because the teacher is the one talking and thinking. The students are learning to sit and listen.

This was brought home to me a few weeks ago. I'm part of a group that has Harvard professors come and speak with us for one hour on Friday afternoons. It's a chance for us to hear about different professors' work, even those whose classes we didn't get to take.

Until last Friday, the visits were almost indistinguishable. The professor would announce, "I'm just going to talk for 20 or 30 minutes, and then we can have a conversation." They would open up a powerpoint presentation with 40-60 slides, talk for 50 minutes, then entertain 2 or 3 questions before leaving.

A few weeks ago, Steve Seidel, a truly great teacher, came to speak with us. He brought 15 slides, and only got through 7. He told us about some thinking he'd been doing lately, with some quotes from Frederick Douglass that had pushed his thinking. He asked what the quotes made us think. Then he told us he had to give a talk soon, and would we think about the topic of his talk, and maybe connect it to the Douglass quotes, and tell him our thoughts. He took careful notes of each person's ideas, and thanked us for helping him plan his talk.

It was the polar opposite of the other Fridays, and I was struck by how much more useful it was. Unlike the other talks, I can still remember what we talked about, and I suspect I'll remember it for some time. Most importantly, Steve came to listen, think together, and to learn from us, and the result was that we thought and learned, too.

All of this thinking about how people really learn -- by doing and talking, not by listening -- and how to teach -- by listening -- has me trapped in a new quandary. All around me, I see people "teaching" by telling people things -- Harvard professors, elementary school teachers, and myself, on a pretty regular basis. But I don't think people are learning much this way.

Teachers, policy-makers, administrators, and academics need to learn that this isn't how people learn. And my instinct is to tell them this, to say, "You know, no one's gonna learn that if you just tell it to them."

You can see my problem, of course. No one will learn this from me telling them, because that's not how people learn. Teachers won't change their practice, and school leaders won't change their priorities, because I (or some other little pipsqueak) come along and says that people don't learn this way. People have to learn it for themselves, when they're ready to learn it. They'll be ready to learn it when they experience it, or closely watch their students and observe it. And there's no way to make that happen quickly.