I had dinner with my friend Alec on Wednesday, and we had a wide-ranging conversation about curriculum, transforming schools, and going to scale. One thing that Alec discussed was the task as teacher.

In my second year of teaching, I designed a unit on resume writing. On a resume, you are listing your experiences and achievements, but you are also trying to highlight specific strengths that make you attractive to potential employers. While you can't just come out and say that you are hard-working, you can say it between the lines if you choose your words and supporting details carefully.

To encourage students to write their resumes purposefully, I built feedback into the task. The student would list the strengths being highlighted in the resume, a panel of readers would list the strengths being highlighted in the resume, and if the two lists matched up, then the resume had achieved its purpose. Even though I drew my panel of readers from the community, the panel wasn't judging the resumes. Students weren't trying to create the best resume; they were trying to craft a resume out of their experiences and achievements so that their own self-identified strengths shone through.

At first, students struggled. Under work experience, they'd write, "Babysitter, 1993-1996," and nothing else. So, I had to model the process for them. What would they infer about a babysitter who had half a dozen long-term and non-family clients? What would they infer about a babysitter who did the dishes and cleaned up around the house after the baby was asleep? What would they infer about a babysitter who made a fun game out of cooking and eating vegetables? Then we would wordsmith these supporting details as a class, trying to highlight a specific strength through them. Did that last babysitter want to be seen as good with kids, passionate about healthy living, creative, or a problem-solver?

Once students understood what they were doing, they were off to the races. They would revise a single entry a dozen times in one class, asking peers to review and evaluate each attempt. They didn't really need me for much of anything. They would ask me for feedback if I was around, but they weren't trying to please me. They were trying to get a point across to a general reader, and there were plenty of those around. One thing that was fun to see was a student helping another student recognize a hidden strength running through a resume. A student might say, "I know that you weren't trying to highlight this, but I see you collaborating well with others in these three entries. Do you think that's a strength of yours?" The task had taken over as teacher.

In hindsight, I should have done more to build off of the resume writing unit. I used it as a launchpad for the purposeful writing we would do throughout the year, but it was also a fun way for students to get to know one another. We had a number of Cambodian immigrants in the class, and it was eye-opening to learn that some of them had jobs and were significant breadwinners for their families. Students also got into heavy debates amongst themselves over self-perception and action. Can you be a hard worker if your actions don't reflect that? If you aren't a hard worker but you start working hard, do you become a hard worker? Some students also got upset when they couldn't find any recent experiences or achievements from school. Not only did they recognize that it looked bad on their resumes, but they felt that it was bad. At a minimum, I should have used this as an opportunity for goal-setting, giving students an opportunity to update their resumes at the end of the year. What would they do throughout the year to be the person they wanted to be?

A well-designed learning task should be more than a vehicle for teaching, it should teach on its own. In fact, it should take over as the primary teacher once things get going. This sets up a positive dynamic and makes the relationship among teacher, student, and content more balanced. I'm still processing this idea, so expect more examples soon.

## Saturday, February 22, 2014

## Tuesday, February 18, 2014

### Curriculum As Road Trip

I like to take the long view. If I am going to study lessons, observe lessons, or write lesson plans, I prefer to do it in the context of a unit, a yearlong curriculum, or a curriculum strand that spans multiple years. It's hard for me to glean much from a single lesson in isolation.

In a typical lesson, students will make some forward progress.

But what I want to know is how far they'll be in a month.

I often think of curriculum as a good road trip. On a good road trip, you usually have some destination and time frame in mind, but it's also about stopping to explore interesting sites along the way.

When I was teaching in Brookline, I chaperoned the eighth-grade field trip to New York City. Maury, the assistant principal, had been doing the trip for years, and he would turn the kids loose. Sometimes this was inside of an enclosed area, like a museum, park, or zoo, but sometimes it was in a wide-open neighborhood. I remember him turning the kids loose in a twelve block area near Chinatown. They had to travel in groups, stay within the prescribed area, and meet at the rendezvous point in two hours. Maury did this half a dozen times over three days, and not once did a student show up late. To put that in perspective, chaperones were late twice. I thought I trusted these kids, but this blew me away. And it made the trip so much more special for them since they could spend a few hours wandering the big city on their own, spontaneously going into shops or grabbing a snack.

On a different trip to New York City, I was being guided around the city by friends who were native New Yorkers. I had been to New York before, but I had never enjoyed it; the city felt big and impersonal to me. For some reason, I made an effort to study the subway system as we traveled between destinations, and I began to feel as though I could navigate my way back to my hotel if I ever got separated from my friends. I'm not sure if that's what did it for me, but suddenly New York began to feel big and interesting instead of big and impersonal, and I started to relax and have fun.

Trips are a lot more fun when you are free to explore sometimes instead of being led by rope from point to point in one big pack. But to explore an area freely and have fun doing it, you also need to feel comfortable finding your way around.

When I'm designing curriculum, it's as though I'm planning a road trip with my own kids for one last time. I want them to have a blast, I want them to see some sites they've wanted to see their whole lives, I want to share some sites that have been personally significant to me, and I want to prepare them so that they can and will go on road trips with their friends in college and then, eventually, with their own kids. That means making sure they can read a map, navigate on highways and subways, pack light, get through security quickly and easily at airports, change a tire, and be safe at remote motels. I want to be able to drop them off in Amsterdam and say meet me for dinner in Copenhagen in two days.

When curriculum is a road trip:

In a typical lesson, students will make some forward progress.

But what I want to know is how far they'll be in a month.

I often think of curriculum as a good road trip. On a good road trip, you usually have some destination and time frame in mind, but it's also about stopping to explore interesting sites along the way.

When I was teaching in Brookline, I chaperoned the eighth-grade field trip to New York City. Maury, the assistant principal, had been doing the trip for years, and he would turn the kids loose. Sometimes this was inside of an enclosed area, like a museum, park, or zoo, but sometimes it was in a wide-open neighborhood. I remember him turning the kids loose in a twelve block area near Chinatown. They had to travel in groups, stay within the prescribed area, and meet at the rendezvous point in two hours. Maury did this half a dozen times over three days, and not once did a student show up late. To put that in perspective, chaperones were late twice. I thought I trusted these kids, but this blew me away. And it made the trip so much more special for them since they could spend a few hours wandering the big city on their own, spontaneously going into shops or grabbing a snack.

On a different trip to New York City, I was being guided around the city by friends who were native New Yorkers. I had been to New York before, but I had never enjoyed it; the city felt big and impersonal to me. For some reason, I made an effort to study the subway system as we traveled between destinations, and I began to feel as though I could navigate my way back to my hotel if I ever got separated from my friends. I'm not sure if that's what did it for me, but suddenly New York began to feel big and interesting instead of big and impersonal, and I started to relax and have fun.

Trips are a lot more fun when you are free to explore sometimes instead of being led by rope from point to point in one big pack. But to explore an area freely and have fun doing it, you also need to feel comfortable finding your way around.

When I'm designing curriculum, it's as though I'm planning a road trip with my own kids for one last time. I want them to have a blast, I want them to see some sites they've wanted to see their whole lives, I want to share some sites that have been personally significant to me, and I want to prepare them so that they can and will go on road trips with their friends in college and then, eventually, with their own kids. That means making sure they can read a map, navigate on highways and subways, pack light, get through security quickly and easily at airports, change a tire, and be safe at remote motels. I want to be able to drop them off in Amsterdam and say meet me for dinner in Copenhagen in two days.

When curriculum is a road trip:

- There should be destinations to explore.
- The area to explore and the time you have to explore it should be greater each time. You might go from a park in 45 minutes, to a neighborhood in three hours, to a city in two days, to a metropolitan area in a week.
- The scope and nature of the destinations should be staged to help you acquire the skills you need to explore a larger area for a longer time along the way.
- Once you've acquired the skill and confidence, you should be able to break away to explore an area on your own or in a small group. Time and opportunities to do that should be factored into the trip.
- Some of the destinations should be mind-blowingly awesome.
- At some of the destinations, you should be able to look back and see how far you've come. When you reflect on it, you should see that you are doing things that you never could have done in the first week of the trip.
- It should be fun and there should be lots of good company.
- You should feel as though this road trip is preparing you for even more amazing road trips in the future.

## Sunday, February 16, 2014

### Contrarian Root Cause Analysis

Over the next few weeks, I will be describing some of the curriculum that I've developed in detail. My goal is to identify and articulate the design principles that I use. By raising these design principles to the conscious level, I hope to refine them and share them with others.

I have two reasons for working on this. First, it bugs me that I don't understand my own process. When I try to explain how I design curriculum to people, I find myself doing a lot of hand-waving. Second, we need a set of design principles that can guide curriculum designers to design better curriculum. The design principles that we use now result in the production of both good and bad curriculum, most of it bad. It seems like if you have good instincts as a curriculum designer, than current design principles enhance what you do. But if you don't have good instincts, they don't help you at all. I feel like good design principles should help all designers become better designers; otherwise, you aren't capturing something important that good designers are doing.

The most popular framework in use today for curriculum design is

Teaching for understanding is something that is clearly near and dear to me. I want students to make sense of the things that they learn. It's essential. But I almost always disagree with the design decisions that curriculum designers make when trying to teach for understanding. I know that I would be making completely different design decisions to accomplish the same goal. This tells me that I'm applying a different design principle, even if I don't know what that design principle is on a conscious level, yet. It has something to do with learning progressions, but I don't like the design decisions that curriculum designers make when trying to design a learning progression either. So far, I've been using the term "sense-making" as a kind of placeholder for a design principle, but I think it is time to dive in and actually figure out what I'm doing. The best way to do that is to compare and contrast good curriculum with bad.

When McTighe and Wiggins saw how much crap was being produced using

The same thing happened with hands-on learning, cooperative learning, and pretty much every other design principle for good teaching that has ever come along. Someone proposes a great initial idea, and then it stops there. Some individuals may take that idea and refine it on their own, but those refinements are never fed back into the collective consciousness for others to iterate on. We need to stop doing that. I need to stop doing that. So, here we go...

I have two reasons for working on this. First, it bugs me that I don't understand my own process. When I try to explain how I design curriculum to people, I find myself doing a lot of hand-waving. Second, we need a set of design principles that can guide curriculum designers to design better curriculum. The design principles that we use now result in the production of both good and bad curriculum, most of it bad. It seems like if you have good instincts as a curriculum designer, than current design principles enhance what you do. But if you don't have good instincts, they don't help you at all. I feel like good design principles should help all designers become better designers; otherwise, you aren't capturing something important that good designers are doing.

The most popular framework in use today for curriculum design is

*Understanding by Design*, which is based on two design principles: backward design and teaching for understanding. Backward design is simply common sense. Of course, we should identify desired outcomes, determine what constitutes acceptable evidence for those outcomes, and then design learning activities to reach those outcomes. Where it can break down is when designers: (1) don't stretch themselves to select outcomes that force them to iterate and refine their designs, (2) select assessments that don't really provide evidence that an outcome has been reached, or (3) start changing desired outcomes and assessments when a design fails instead of iterating on the design itself. The third breakdown reflects a basic lack of rigor in the application of backward design by the user, but the design principles should be constructed to help the user avoid the first two. Based on the quality of the curriculum that is produced using*Understanding by Design*, that's not happening.Teaching for understanding is something that is clearly near and dear to me. I want students to make sense of the things that they learn. It's essential. But I almost always disagree with the design decisions that curriculum designers make when trying to teach for understanding. I know that I would be making completely different design decisions to accomplish the same goal. This tells me that I'm applying a different design principle, even if I don't know what that design principle is on a conscious level, yet. It has something to do with learning progressions, but I don't like the design decisions that curriculum designers make when trying to design a learning progression either. So far, I've been using the term "sense-making" as a kind of placeholder for a design principle, but I think it is time to dive in and actually figure out what I'm doing. The best way to do that is to compare and contrast good curriculum with bad.

When McTighe and Wiggins saw how much crap was being produced using

*Understanding by Design*, they should have sorted this curriculum into good and bad piles, figured out how the two piles were different, and then used their analysis to refine their theory and practice. We should strive for design principles that cause good design, not just settle for design principles that correlate weakly with good design. I think that McTighe and Wiggins tried to do that at first, but when they couldn't easily increase the yield of good curriculum, they stopped trying and decided to cash in instead.The same thing happened with hands-on learning, cooperative learning, and pretty much every other design principle for good teaching that has ever come along. Someone proposes a great initial idea, and then it stops there. Some individuals may take that idea and refine it on their own, but those refinements are never fed back into the collective consciousness for others to iterate on. We need to stop doing that. I need to stop doing that. So, here we go...

## Saturday, February 15, 2014

### Circular Logic

A few weeks ago, I summarized my thoughts on improving schools in a post titled Pulling It All Together. As I was working on the post, I kept getting stuck because I felt like I couldn't ground each point I was making as I was making it. The point would make sense by the end of the post, but some of the points couldn't quite stand on their own. I finally had to accept that I was constructing an argument that had internal dependencies and couldn't be laid out in a linear structure. The best that I could do was to be clear and concise, giving the reader a chance to stitch everything together in the end.

Here is one point. Not too exciting, is it?

Here are some more of the points. That argument looks like it is about to collapse!

Here are all of the points, assembled and supporting one another.

On Tuesday, my friend Lee was telling me about the machine learning course that he is teaching. His students were using gradient descent to find local minima for a cost function. There are so many variables when it comes to learning that we tend to oversimplify things just to understand them. This can lead us to getting stuck on a local minima or maxima that is really just a blip on the landscape. Instead of throwing away variables, we need to embrace and understand the complexity and interdependencies involved.

In my last post, I wrote that giving students' ownership of the curriculum was necessary but insufficient for designing a good curriculum. There are plenty of things that students want to learn in life that they are unable to learn on their own. I believe that enabling students to make sense of the curriculum is also necessary.

But you really can't isolate ownership from sense-making. I believe that if you enable students to make sense of the curriculum, then over time, students will take ownership of the curriculum. If the school's curriculum does not give them what they need, then these students will simply learn what they need elsewhere. They will have the sense-making skills needed to learn on their own, and they will be driven to make sense of things. Once you make sense of some things, you can't stand not making sense of other things.

Similarly, if you give students ownership of the curriculum, over time, they will want that curriculum to make more and more sense to them. The question is, what happens if the school doesn't or isn't able to respond? In my experience, the students' sense of ownership diminishes if they don't get what they want. They may be happy with choice and relevancy for now, but they will want things to make sense eventually, and something doesn't make sense just because you want it to.

This really isn't a choice between ownership and sense-making. We also shouldn't optimize for both ownership and sense-making. Optimizing each variable in isolation is a mistake. Doing that over and over again is exactly why we are stuck in the mud and unable to gain traction. We should be trying to figure out the direction of the steepest gradient from our current location. I believe it lies primarily along the sense-making dimension, but that's an argument for another day. Namaste.

Here is one point. Not too exciting, is it?

Here are some more of the points. That argument looks like it is about to collapse!

Here are all of the points, assembled and supporting one another.

On Tuesday, my friend Lee was telling me about the machine learning course that he is teaching. His students were using gradient descent to find local minima for a cost function. There are so many variables when it comes to learning that we tend to oversimplify things just to understand them. This can lead us to getting stuck on a local minima or maxima that is really just a blip on the landscape. Instead of throwing away variables, we need to embrace and understand the complexity and interdependencies involved.

In my last post, I wrote that giving students' ownership of the curriculum was necessary but insufficient for designing a good curriculum. There are plenty of things that students want to learn in life that they are unable to learn on their own. I believe that enabling students to make sense of the curriculum is also necessary.

But you really can't isolate ownership from sense-making. I believe that if you enable students to make sense of the curriculum, then over time, students will take ownership of the curriculum. If the school's curriculum does not give them what they need, then these students will simply learn what they need elsewhere. They will have the sense-making skills needed to learn on their own, and they will be driven to make sense of things. Once you make sense of some things, you can't stand not making sense of other things.

Similarly, if you give students ownership of the curriculum, over time, they will want that curriculum to make more and more sense to them. The question is, what happens if the school doesn't or isn't able to respond? In my experience, the students' sense of ownership diminishes if they don't get what they want. They may be happy with choice and relevancy for now, but they will want things to make sense eventually, and something doesn't make sense just because you want it to.

This really isn't a choice between ownership and sense-making. We also shouldn't optimize for both ownership and sense-making. Optimizing each variable in isolation is a mistake. Doing that over and over again is exactly why we are stuck in the mud and unable to gain traction. We should be trying to figure out the direction of the steepest gradient from our current location. I believe it lies primarily along the sense-making dimension, but that's an argument for another day. Namaste.

## Sunday, February 9, 2014

### But Whose Curriculum Is It?

I'm having dinner with my friend Alec in a couple of weeks. Alec is designing an innovation school called STEAM Academy and he has written a number of blog posts on education. I read his blog post on rendering learners legible months ago and loved it. In it, he points out how schooling is designed to steer students down a predetermined path and how we are working hard at exerting even greater control over our students.

I re-read Alec's blog post two nights ago, but this time, it hit me like a ton of bricks. I've been writing that a sense-making curriculum enables students to take ownership of their own learning because, once a student makes sense of something, they can apply it and build on it. Making sense of one thing also motivates you to make sense of other things and helps you develop sense-making skills. But the sense-making curriculum that I've been writing about has been

Based on what I've written about ownership myself, the short answer is no. You can't own a curriculum if you don't have any control over it, and it is hard to imagine how you can own your own learning if you don't own the curriculum. I've been arguing that educators who focus on instruction and student engagement are trying to inoculate their students against the corrosive effects of a nonsense-making curriculum instead of helping students actually make sense of the curriculum, but has my perspective been too narrow? If I take a step back, am I focused on helping students make sense of the curriculum simply to inoculate them against the corrosive effects of a curriculum that is being imposed on them? Should I focus on delivering a student-centered curriculum instead?

I've spent the past two days replaying my experiences with students in my head. I believe that, if they were given the choice, most of my students would choose to be in my classroom and to follow my curriculum. Even if they didn't have to be in school at all, they would choose to come to school to continue engaging in our learning community. That's because our learning community is a special place; it is a place where students discover themselves and their capabilities. In middle school, students are questioning who they will be as adults. Many worry that they are dumb and lazy because others see them as dumb and lazy and that is always how they behave. They may believe or hope that they have the potential for more, but they aren't completely sure. In our learning community, some of that potential is realized. They are productive and valued. They are learning things that prepare them for high school and college and beyond. They see themselves growing as learners and thinkers, developing learning skills and habits of mind that can be applied anywhere. They are happy to come to class because it recharges them intellectually and spiritually.

But they aren't given the choice, and that makes all the difference. I could start offering them the choice mid-year. By that time, they trust me and believe that I have their best interests at heart, so I could steer them to make the choice that I want. But I would know it was a false choice, and they would know it, too. I'm not going to offer them a choice until it is a real choice. I've had a number of students say to me, completely out of the blue, that: "Math class is my favorite class, but math isn't my favorite subject." I think they were trying to tell me something. I can create an environment where they love learning math, but I can't make them love math. That comes from within, and students need to make that choice for themselves. We need to give them that choice so that they can make it.

Before I re-read Alec's blog post, I wrote about where I am now. In that post, I recognized that a sense-making curriculum couldn't reach its full potential as long as it had to align with Common Core standards or high school course pathways. But I thought that I could design a sense-making curriculum within those constraints that would be effective enough to create a tipping point for change, making student ownership of the curriculum possible. Can change precede student ownership of the curriculum or can change only occur when there is student ownership of the curriculum?

For me, student ownership is a mountain and not a compass. It is part of my new normal, and if you end up in a place where students aren't taking ownership of their own learning, then you are badly lost. But optimizing for student ownership does not necessarily lead to good curriculum or better learning. STEAM Academy cites High Tech High as a model for student-centered, project-driven curricula and professional development. High Tech High shares a number of these projects on its website. Well, the projects aren't good. There is little evidence that the projects help students make sense of the curricula or that there is any kind of learning progression across projects. Designing the curriculum may empower students in the short term, but if that curriculum doesn't build understanding and lead them some place interesting, will those students still value that ownership in the long term?

If I had to choose between a nonsense-making curriculum without a learning progression that students control, or a sense-making curriculum with a learning progression that I control, I would choose the latter. And based on my experiences with students, students would choose the latter as well. Of course, our choices don't have to be quite so stark. There should be a way to design a sense-making curriculum with a learning progression and shared control. I'm not sure how to do it yet, but I'm thinking about it.

So, am I prepared to take the Hippocratic Oath for a sense-making curriculum? Alec ends his post by asking that of Sal Khan and personalized education. Could a sense-making curriculum be misapplied to exert more control over students or cause harm? I don't see how. In a sense-making curriculum, students don't just make sense of the curriculum; they make sense of everything. They would recognize the control and resist. At the same time, any teacher capable of designing a sense-making curriculum would recognize and resist it as well. Sense-making is inherently empowering and enlightening. That's why it's my compass and why I can honestly take the Hippocratic Oath.

I re-read Alec's blog post two nights ago, but this time, it hit me like a ton of bricks. I've been writing that a sense-making curriculum enables students to take ownership of their own learning because, once a student makes sense of something, they can apply it and build on it. Making sense of one thing also motivates you to make sense of other things and helps you develop sense-making skills. But the sense-making curriculum that I've been writing about has been

*my*curriculum, not my students' curriculum. Is it possible for students to take ownership of their own learning when the curriculum isn't theirs?Based on what I've written about ownership myself, the short answer is no. You can't own a curriculum if you don't have any control over it, and it is hard to imagine how you can own your own learning if you don't own the curriculum. I've been arguing that educators who focus on instruction and student engagement are trying to inoculate their students against the corrosive effects of a nonsense-making curriculum instead of helping students actually make sense of the curriculum, but has my perspective been too narrow? If I take a step back, am I focused on helping students make sense of the curriculum simply to inoculate them against the corrosive effects of a curriculum that is being imposed on them? Should I focus on delivering a student-centered curriculum instead?

I've spent the past two days replaying my experiences with students in my head. I believe that, if they were given the choice, most of my students would choose to be in my classroom and to follow my curriculum. Even if they didn't have to be in school at all, they would choose to come to school to continue engaging in our learning community. That's because our learning community is a special place; it is a place where students discover themselves and their capabilities. In middle school, students are questioning who they will be as adults. Many worry that they are dumb and lazy because others see them as dumb and lazy and that is always how they behave. They may believe or hope that they have the potential for more, but they aren't completely sure. In our learning community, some of that potential is realized. They are productive and valued. They are learning things that prepare them for high school and college and beyond. They see themselves growing as learners and thinkers, developing learning skills and habits of mind that can be applied anywhere. They are happy to come to class because it recharges them intellectually and spiritually.

But they aren't given the choice, and that makes all the difference. I could start offering them the choice mid-year. By that time, they trust me and believe that I have their best interests at heart, so I could steer them to make the choice that I want. But I would know it was a false choice, and they would know it, too. I'm not going to offer them a choice until it is a real choice. I've had a number of students say to me, completely out of the blue, that: "Math class is my favorite class, but math isn't my favorite subject." I think they were trying to tell me something. I can create an environment where they love learning math, but I can't make them love math. That comes from within, and students need to make that choice for themselves. We need to give them that choice so that they can make it.

Before I re-read Alec's blog post, I wrote about where I am now. In that post, I recognized that a sense-making curriculum couldn't reach its full potential as long as it had to align with Common Core standards or high school course pathways. But I thought that I could design a sense-making curriculum within those constraints that would be effective enough to create a tipping point for change, making student ownership of the curriculum possible. Can change precede student ownership of the curriculum or can change only occur when there is student ownership of the curriculum?

For me, student ownership is a mountain and not a compass. It is part of my new normal, and if you end up in a place where students aren't taking ownership of their own learning, then you are badly lost. But optimizing for student ownership does not necessarily lead to good curriculum or better learning. STEAM Academy cites High Tech High as a model for student-centered, project-driven curricula and professional development. High Tech High shares a number of these projects on its website. Well, the projects aren't good. There is little evidence that the projects help students make sense of the curricula or that there is any kind of learning progression across projects. Designing the curriculum may empower students in the short term, but if that curriculum doesn't build understanding and lead them some place interesting, will those students still value that ownership in the long term?

If I had to choose between a nonsense-making curriculum without a learning progression that students control, or a sense-making curriculum with a learning progression that I control, I would choose the latter. And based on my experiences with students, students would choose the latter as well. Of course, our choices don't have to be quite so stark. There should be a way to design a sense-making curriculum with a learning progression and shared control. I'm not sure how to do it yet, but I'm thinking about it.

So, am I prepared to take the Hippocratic Oath for a sense-making curriculum? Alec ends his post by asking that of Sal Khan and personalized education. Could a sense-making curriculum be misapplied to exert more control over students or cause harm? I don't see how. In a sense-making curriculum, students don't just make sense of the curriculum; they make sense of everything. They would recognize the control and resist. At the same time, any teacher capable of designing a sense-making curriculum would recognize and resist it as well. Sense-making is inherently empowering and enlightening. That's why it's my compass and why I can honestly take the Hippocratic Oath.

## Saturday, February 8, 2014

### Drawing Area

On Monday, Drawing Area won the WGBH Interactive Math Challenge and will eventually become part of the Math at the Core: Middle School collection at PBS LearningMedia.

Derek, a co-organizer of an instructional design meetup I attend, asked me if I'd be willing to share my thinking behind Drawing Area with his instructional design students. I replied by joking that there wasn't much thinking behind it. But, of course, that isn't the case.

In Drawing Area, students find the area of a polygon by drawing the polygon on a grid with rectangles and right triangles. This happens in a browser window. The idea for Drawing Area came from a series of lessons I developed when I was a classroom teacher. For those lessons, students drew their polygons on sheets of graph paper.

To find the area of a polygon, it helps if you can decompose the polygon into rectangles and triangles. However, I found some of my students doing things like this:

This student has decomposed the polygon into three triangles, but the area of the middle triangle isn't going to be easy to find. This student either hasn't understood why he or she is decomposing polygons into rectangles and triangles, or is unable tell at a glance when a rectangle's or triangle's area is going to be easy to find.

You could ask the student to find the base and height for each triangle. And then, when the student can't find the base and height of the middle triangle, ask the student to try again by decomposing the polygon another way. However, that is going to get old pretty quickly.

You could give the student a rule to follow: only make horizontal or vertical slices starting from a vertex. Over time, the student may make sense of the rule and internalize it.

I elected to take a different approach. I decided to draw the polygons on a grid and ask the students to find the number of squares the polygon covered.

When you are counting squares, it is natural to divide a polygon along grid lines. You aren't decomposing the polygon into rectangles and triangles so that you can apply the area formulas for rectangles and triangles; it is simply easier and more efficient to count squares when they are grouped into rectangles (an array of squares) and right triangles (half of a rectangle). This instantly makes sense to students and is something that they come up with on their own.

Once a polygon has been decomposed into rectangles and triangles, some students have a hard time finding dimensions that are not given. This is not an issue when a polygon is drawn on a grid (the student can simply count the number of squares along an edge), but it is an issue when a grid is not provided. What is the length of the base of the triangle?

It is not uncommon for students to pick two numbers in the drawing and add or subtract them. They may see the 12 and the 7 and think: 12 − 7 = 5. It doesn't matter that this makes no sense whatsoever. They know they are suppose to either add or subtract two numbers to find the unknown length.

You could guide the students to focus on the relevant information and eliminate distractors. Since the student is trying to find the length of a horizontal line, have the student highlight all horizontal lines and eliminate the dimensions from all vertical lines:

Is there a way to use the information provided to figure out the length of the middle red line? Some students will make sense of and internalize this over time, but you are still subtly reinforcing the notion that you should be looking for things to add and subtract.

Since the students in my classroom are already comfortable finding the area of polygons drawn on a grid, I decided to leverage that. Can you take this polygon and draw it on a grid? Most students think that's easy. And once the polygon is drawn on a grid, they can find the area.

A student may start by drawing the rectangle to the left, since those dimensions are given.

The student knows that the height of the second rectangle is 6 cm, but the length of the base and its exact position relative to the first rectangle are unknown.

But once a rectangle with a height of 6 cm has been drawn, it can be moved so that its base is aligned with the base of the first rectangle.

Then it can be resized so that the width of the entire polygon is 15 cm.

The right triangle fits right in between the two rectangles, and now any dimensions that the student needs can be determined from the drawing.

After a while, I would encourage the student to predict the dimensions of the individual rectangles and right triangles before drawing them, and then confirm those predictions with the drawing. At no point is the student following rules or doing something that doesn't make sense. The emphasis is on figuring out the number of squares a polygon covers. Using this process, all students can reason through increasingly complex problems:

Derek, a co-organizer of an instructional design meetup I attend, asked me if I'd be willing to share my thinking behind Drawing Area with his instructional design students. I replied by joking that there wasn't much thinking behind it. But, of course, that isn't the case.

In Drawing Area, students find the area of a polygon by drawing the polygon on a grid with rectangles and right triangles. This happens in a browser window. The idea for Drawing Area came from a series of lessons I developed when I was a classroom teacher. For those lessons, students drew their polygons on sheets of graph paper.

To find the area of a polygon, it helps if you can decompose the polygon into rectangles and triangles. However, I found some of my students doing things like this:

This student has decomposed the polygon into three triangles, but the area of the middle triangle isn't going to be easy to find. This student either hasn't understood why he or she is decomposing polygons into rectangles and triangles, or is unable tell at a glance when a rectangle's or triangle's area is going to be easy to find.

You could ask the student to find the base and height for each triangle. And then, when the student can't find the base and height of the middle triangle, ask the student to try again by decomposing the polygon another way. However, that is going to get old pretty quickly.

You could give the student a rule to follow: only make horizontal or vertical slices starting from a vertex. Over time, the student may make sense of the rule and internalize it.

I elected to take a different approach. I decided to draw the polygons on a grid and ask the students to find the number of squares the polygon covered.

When you are counting squares, it is natural to divide a polygon along grid lines. You aren't decomposing the polygon into rectangles and triangles so that you can apply the area formulas for rectangles and triangles; it is simply easier and more efficient to count squares when they are grouped into rectangles (an array of squares) and right triangles (half of a rectangle). This instantly makes sense to students and is something that they come up with on their own.

Once a polygon has been decomposed into rectangles and triangles, some students have a hard time finding dimensions that are not given. This is not an issue when a polygon is drawn on a grid (the student can simply count the number of squares along an edge), but it is an issue when a grid is not provided. What is the length of the base of the triangle?

It is not uncommon for students to pick two numbers in the drawing and add or subtract them. They may see the 12 and the 7 and think: 12 − 7 = 5. It doesn't matter that this makes no sense whatsoever. They know they are suppose to either add or subtract two numbers to find the unknown length.

You could guide the students to focus on the relevant information and eliminate distractors. Since the student is trying to find the length of a horizontal line, have the student highlight all horizontal lines and eliminate the dimensions from all vertical lines:

Is there a way to use the information provided to figure out the length of the middle red line? Some students will make sense of and internalize this over time, but you are still subtly reinforcing the notion that you should be looking for things to add and subtract.

Since the students in my classroom are already comfortable finding the area of polygons drawn on a grid, I decided to leverage that. Can you take this polygon and draw it on a grid? Most students think that's easy. And once the polygon is drawn on a grid, they can find the area.

A student may start by drawing the rectangle to the left, since those dimensions are given.

The student knows that the height of the second rectangle is 6 cm, but the length of the base and its exact position relative to the first rectangle are unknown.

But once a rectangle with a height of 6 cm has been drawn, it can be moved so that its base is aligned with the base of the first rectangle.

Then it can be resized so that the width of the entire polygon is 15 cm.

The right triangle fits right in between the two rectangles, and now any dimensions that the student needs can be determined from the drawing.

After a while, I would encourage the student to predict the dimensions of the individual rectangles and right triangles before drawing them, and then confirm those predictions with the drawing. At no point is the student following rules or doing something that doesn't make sense. The emphasis is on figuring out the number of squares a polygon covers. Using this process, all students can reason through increasingly complex problems:

## Friday, February 7, 2014

### Where to Next?

My career has been a twenty-year journey toward a new normal. On the first leg of my journey, I developed a sense-making curriculum. On the second, I formed a learning community in the classroom. On the third, I discovered what students could do if they were immersed in a sense-making curriculum and a learning community for three years. On the fourth, I coached teachers to use a sense-making curriculum and begin forming learning communities in their own classrooms. On the fifth, I tried forming learning communities among teachers.

I haven't quite finished that fifth leg yet. One thing that I've learned during my journey is that you need to prepare for a leg long before you get to it, and I wasn't prepared for the fifth leg. First, I couldn't articulate how to design a sense-making curriculum, so the teachers couldn't really share in ownership of the work. That is a killer. Second, a learning community among teachers needs a supportive environment. Ideally, it would be part of a larger learning organization, with learning communities at all levels. I never figured out how to engage administrators in the work that teachers and students were doing, so there was always a lack of buy-in at the leadership level.

I fully intend to tackle that fifth leg again. I can't complete my journey without it. But before I do, I want to survey what lies beyond it, so that I can start preparing for the sixth and seventh legs at the same time. This is why strategic planning is so important.

It seems clear to me that, at some point, I need to create a school to demonstrate that a new normal is possible. This school would be a learning organization (adaptive, focused on continuous improvement, learning communities at all levels) and have a sense-making curriculum. By enabling students to make sense of the curriculum, students will climb faster and farther, take ownership of their own learning, and develop the habits of mind and skills they need to continuously test and revise their mental models. These students wouldn't just go on to study at the four-year colleges of their choice, they would go on to become the best thinkers of their generation.

Performance talks, and the performance of this school and its graduates would be off the charts. This would be an Olympic stage: a signal so unmistakably strong that it would cut through the noise. I firmly believe that I can create this school and achieve that level of performance. And I don't say that lightly. My entire career has been a series of tests to prove or disprove this hypothesis.

But I can't create a school by myself. I need a team. Fortunately, I don't need an Olympic stage to form a team; I can go out and enlist people one by one. The hard part is figuring out who the right people are and what evidence will convince them to take me seriously. The right people are few and far between, so I've been following a two-part strategy. While I'm looking for them, I'm providing ways for them to find me.

Vertical Learning Labs is producing curriculum in order to generate income so that I can sustain my work. But these curriculum products are also a trail of bread crumbs leading back to me. If you can look at Drawing Area, Chocolate Chip Cookie Factory: Place Value, Chemistry from the Ground Up, or Teaching a Robot How to Dance without being immediately blown away by what these pieces of curriculum can do for students, then you probably won't fit on my team. These efforts are crude, but I'm looking for the people who can see the genius in them and can see what they can be with refinement. If those people are out there, they should be as hungry to meet me as I am to meet them. That's my working theory for now, anyways. I sure hope I hear more than crickets out there. :)

I haven't quite finished that fifth leg yet. One thing that I've learned during my journey is that you need to prepare for a leg long before you get to it, and I wasn't prepared for the fifth leg. First, I couldn't articulate how to design a sense-making curriculum, so the teachers couldn't really share in ownership of the work. That is a killer. Second, a learning community among teachers needs a supportive environment. Ideally, it would be part of a larger learning organization, with learning communities at all levels. I never figured out how to engage administrators in the work that teachers and students were doing, so there was always a lack of buy-in at the leadership level.

I fully intend to tackle that fifth leg again. I can't complete my journey without it. But before I do, I want to survey what lies beyond it, so that I can start preparing for the sixth and seventh legs at the same time. This is why strategic planning is so important.

It seems clear to me that, at some point, I need to create a school to demonstrate that a new normal is possible. This school would be a learning organization (adaptive, focused on continuous improvement, learning communities at all levels) and have a sense-making curriculum. By enabling students to make sense of the curriculum, students will climb faster and farther, take ownership of their own learning, and develop the habits of mind and skills they need to continuously test and revise their mental models. These students wouldn't just go on to study at the four-year colleges of their choice, they would go on to become the best thinkers of their generation.

Performance talks, and the performance of this school and its graduates would be off the charts. This would be an Olympic stage: a signal so unmistakably strong that it would cut through the noise. I firmly believe that I can create this school and achieve that level of performance. And I don't say that lightly. My entire career has been a series of tests to prove or disprove this hypothesis.

But I can't create a school by myself. I need a team. Fortunately, I don't need an Olympic stage to form a team; I can go out and enlist people one by one. The hard part is figuring out who the right people are and what evidence will convince them to take me seriously. The right people are few and far between, so I've been following a two-part strategy. While I'm looking for them, I'm providing ways for them to find me.

Vertical Learning Labs is producing curriculum in order to generate income so that I can sustain my work. But these curriculum products are also a trail of bread crumbs leading back to me. If you can look at Drawing Area, Chocolate Chip Cookie Factory: Place Value, Chemistry from the Ground Up, or Teaching a Robot How to Dance without being immediately blown away by what these pieces of curriculum can do for students, then you probably won't fit on my team. These efforts are crude, but I'm looking for the people who can see the genius in them and can see what they can be with refinement. If those people are out there, they should be as hungry to meet me as I am to meet them. That's my working theory for now, anyways. I sure hope I hear more than crickets out there. :)

## Thursday, February 6, 2014

### You Are Here

So, where am I now? That is an excellent question.

I got a B.S. in chemical engineering at Carnegie Mellon in 1991, and went to graduate school at the University of California at Berkeley for a year before dropping out to pursue my passion in education. After getting a M.A.T. in math education from Boston University, I started teaching middle school math and science on a two-person team in Attleboro in 1995.

Attleboro was an incredibly creative time for me. The superintendent had banned math textbooks, so I was making up my own curriculum on the fly. I remember designing a unit on fluid pressure and the particle theory of matter. In this unit, students learned by conducting a series of hands-on investigations. One of the initial investigations involved using a digital camera to record video of collisions. By studying the video frame-by-frame (we were able to capture grainy video at 320 x 240 and 5 fps), students applied vector concepts to discover the conservation of momentum. I was appointed to the District Math Curriculum committee and hired to run a physics workshop for teachers over the summer.

In 1998, I started teaching 7th-grade math and science in Brookline. Technically, Brookline was using

While we were getting good results, we were also doing our work in isolation. Imagine that this is a graph of student performance over time. Our students would make higher than normal performance gains using our curriculum, but those performance gains would largely be erased once they were back to using a normal curriculum.

This was still better than a typical intervention. In a typical intervention, there is an initial bump in performance that quickly levels out, and then disappears once the intervention is over. At least with our curriculum, students would make performance gains the whole time they were using it.

On the science side, I was learning to take my curriculum vertical. The math curriculum that Charles and I developed still introduced concepts in isolation; in science, the concepts built on top of each other. I had done this in Attleboro with the fluid pressure unit, but that was a two-month long series of investigations. In Brookline, I was connecting all of the earth and life science concepts in the 7th-grade curriculum in a yearlong series of investigation, using the Big Bang and chemistry as the starting point.

Brookline was partnering with the Virtual High School at the time, and my principal asked me to design an online science course for them. The science course I designed was based around the challenge of programming a spaceship to navigate through a two-dimensional course (up-down, forward-back). The spaceship was essentially a tank of high-pressure gas. You piloted the spaceship by opening and closing nozzles. When a nozzle was open, gas would flow through the nozzle, providing thrust. Over time, the pressure in the tank would drop and the mass of the spaceship would decrease. Students would use experiments to learn the science concepts, and they would use spreadsheets to model the spaceship. All of their calculations would be based on discrete time steps, so calculus was not required and all relationships would be linear. (Students would be able to adjust the size of the time steps, so they would be working with limits.)

The other significant development that occurred while I was at Brookline was the formation of my first learning community. In my first year at Brookline, the students in my homeroom also had me for math, science, and study hall. I didn't know it at the time, but these students had two teachers walk out on them in 4th- and 5th-grade. So, they tested me. They tested me to see if there was anything that they could do to push me away. Somehow I hung in there, and managed to break through with them in December.

For me, a learning community is a community whose primary focus is learning. That means that learning is more important than worrying about making mistakes or looking bad. It means taking ownership of your own learning, approaching new experiences with a sense of inquiry, and pulling together to help other members in the community to learn. These students regularly entered the flow state and tested their own understanding. They wanted to make sense of what they were learning and believed that they could.

In 2001, Charles told me that his wife's school, the Jewish Community Day School (JCDS) was looking for a middle school math teacher. The middle school had less than forty students in it at the time, so I would be the only math teacher in the middle school. Charles didn't think I'd be interested, but I jumped at the chance to see what our math curriculum could do when scaled across three grade levels.

JCDS was very progressive and student-centered, so they were using

I took the math curriculum that Charles and I had developed in Brookline and adapted it for JCDS, using the vertical learning principles I had applied to the science curriculum in Brookline. Being able to build concepts across three grade levels enabled me to design my first sense-making math curriculum. By going vertical and investing in student understanding early on, I helped students climb faster and farther in the long run.

After working with the same group of students for three years, I saw impressive performance gains for the entire three years. When those students left JCDS for high school, their rate of performance growth returned to normal levels, but they didn't lose the gains they had made at JCDS. This indicates that these students were able to build on the understanding they had developed at JCDS, even in environments that didn't natively support sense-making.

After three years of making sense of things in math, these students expected to make sense of things in all subjects, but they were still dependent to some degree on their teachers helping them. Ideally, students should be able to develop the sense-making skills they need to make sense of things completely on their own.

By this point, I had concluded that a sense-making curriculum works. The next step was to see if I could bring it to scale. I left JCDS in 2004 to become middle school math curriculum leader for the Groton-Dunstable Regional School District (GDRSD). The administration at GDRSD wanted the middle school math teachers to adopt a standards-based math curriculum and I wanted to see if I could lead the change process.

The math department was bitterly divided and none of the previous curriculum leaders had been able to achieve any form of consensus. My job was to guide a committee of teachers in selecting a new math program for the middle school by the end of the year. I started capacity-building right away. I wanted everyone to have a deeper understanding of how students learn and how standards-based math programs work (the math wars had kicked up a lot of FUD). We established the criteria we would use to evaluate math programs and started collecting data. As part of the process, I asked teachers to try some different approaches. One of the 7th-grade math teachers who was firmly in the "traditional" camp ended up raving about a functions lesson I had designed for him. He observed students actively taking ownership and reasoning through problems instead of passively waiting for him to tell them what to do. I also secured a commitment from the administration that the committee would select the new math program and not simply make a recommendation to the administration.

In the spring, two clear favorites had bubbled to the surface:

I begged the administration to give the committee one last chance; I felt that we were on the verge of consensus. So, we gathered for one last time at the end of June and I ran through the possible outcomes. We were about to make a decision that the teachers were going to have to live with for the next ten years. We could make the comfortable choice and hope that

We were doing a staggered roll out and building in lots of professional development, so there was still lots of work to be done. I was drawing up budgets and three-year implementation plans, presenting in front of the school committee, working with vendors and consultants, and coordinating everything. It was fun and exciting, but the most exciting thing for me was the potential of creating a learning community among the teachers. The breakthrough we had in June felt similar to the breakthrough I had had with my students in Brookline.

Unfortunately, the administration didn't share my enthusiasm and optimism. My boss, the Director of Curriculum, hadn't experienced the same things that the committee had experienced because she hadn't been there day-to-day, so she assumed that the teachers' buy-in was temporary. She didn't realize that their buy-in was actually at the ownership level; she probably couldn't even conceive of that as a possibility. So, instead of building on their commitment and establishing a learning community where we would all work together toward a common goal, she seized on their commitment to leverage her own agenda.

In my mind, we were removing one script (the traditional textbook) and exchanging it for a slightly better script (

In 2007, I became middle school math and science curriculum specialist in Holliston. I won't go into a ton of detail since I wrote about my experiences in Holliston here, here, and here. My goal was to see if I could implement a sense-making curriculum designed by the teachers themselves and to create the learning community I failed to create in GDRSD.

In my first year in Holliston, I became fast friends with Jessica, the principal of the middle school. We worked closely together and she valued my insights. It was a highly collaborative relationship driven by inquiry. When Jessica became assistant superintendent for the Freetown-Lakeville Regional School District (Freelake), she immediately hired me as her K-8 Math Program Coordinator. I was highly impressed by the team that John, the superintendent, was putting together and I relished the opportunity to work with Jessica again, but this time, at a district level.

Unfortunately, Jessica had other plans. She admitted to me that she only listened to me in Holliston because she was about to flame out there and needed me to bail her out with the staff. Now that she was at Freelake and had carte blanche from the superintendent, she wanted to do things her way. While I can respect that on some level, she should have told me that before luring me away from Holliston. I would have never have gone to work with her under those conditions.

The whole year in Freelake was a complete disaster. Jessica, the superintendent, and the consultant they brought in from UMass Lowell spoke passionately about forming a learning community. I think that they, to this day, genuinely believe that they are true believers of learning communities. But the administrative team at Freelake was no learning community. John and Jessica had their agenda and they used the pretense of a learning community to ram it down our throats. Their goal was to win and then leverage commitments from us and then the teachers. When I objected, the learning community ran roughshod over me. I left when John and Jessica used me to get a group of young teachers to go out on a limb, and then undercut the initiative behind their backs. It was GDRSD all over again, and all though I was wiser and more experienced, I couldn't do anything to stop it. That's when I decided to abandon schools for a while and start up Vertical Learning Labs.

So, where am I now? That is the question that opened this post and it is where I'm going to end. I haven't reached a new normal, yet. I don't even think it is visible from my current vantage point. But I've been to the foothills of the new normal and I'm as confident as ever that it's there. And if it isn't there, I already know that the foothills I'm on are much taller than the tiny cluster of hills that everyone else is on. So this is a good place to be.

I have developed a sense-making curriculum for middle school math and components of a sense-making curriculum for science. The sense-making curriculum for math works for kids. It's been tested and refined. It's also been designed to fit within the constraints of the current system: 50 minute classes/5 days a week, Common Core standards, high school math courses, etc. Even when I designed a sense-making curriculum for JCDS, my priority was preparing students for a seamless transition to the elite high schools in the area. As we move together toward a new normal, those constraints will fall away and I'm excited to see what people can create from scratch.

Other teachers can and will use the curriculum that I've written, and get similar results. A small number of teachers will fly with it right away. The majority will need coaching from someone like me.

I'm working toward articulating a process that other teachers can use to create their own sense-making curriculum. That is a work in progress and I've got a long way to go.

I can consistently create learning communities. I stumbled onto my first one in Brookline, but I've been consciously creating them ever since. It's fairly easy to do in the classroom when I have students in front of me 50 minutes a day/5 days a week. It is harder to do with teachers, whom I may have in front of me only 50 minutes a day/one day every two weeks (10% of the contact time I have with students). I haven't actually managed it with a group of teachers yet, but I have gotten close in GDRSD and Holliston. Doing it with administrators is much tougher because I get much less contact time with them, and when we do have contact, it is usually around their agenda instead of mine.

I'm not yet at a point where I've started to articulate how I create learning communities. In the classroom, I think that a sense-making curriculum is a great start, but other components are definitely necessary.

Finally, I know that I can't convince anyone through words. I've always suspected that, but banging your head against that particular wall for over 15 years brings another level of clarity. The flip side to that is that anyone who has worked closely with me for any period of time walks away with a much deeper understanding and appreciation of what I do. It is rare for me to not win someone over when they experience firsthand what I can do and what I'm about. The question, as always, is: How do I bring that to scale?

I got a B.S. in chemical engineering at Carnegie Mellon in 1991, and went to graduate school at the University of California at Berkeley for a year before dropping out to pursue my passion in education. After getting a M.A.T. in math education from Boston University, I started teaching middle school math and science on a two-person team in Attleboro in 1995.

Attleboro was an incredibly creative time for me. The superintendent had banned math textbooks, so I was making up my own curriculum on the fly. I remember designing a unit on fluid pressure and the particle theory of matter. In this unit, students learned by conducting a series of hands-on investigations. One of the initial investigations involved using a digital camera to record video of collisions. By studying the video frame-by-frame (we were able to capture grainy video at 320 x 240 and 5 fps), students applied vector concepts to discover the conservation of momentum. I was appointed to the District Math Curriculum committee and hired to run a physics workshop for teachers over the summer.

In 1998, I started teaching 7th-grade math and science in Brookline. Technically, Brookline was using

*MathScape*for its middle school math program, but I didn't particularly care for it. I managed to convince another new teacher, Charles, to join me in creating our own math curriculum. The parents in Brookline were very demanding, but they were pleased with the results, so we were supported by the principal. Charles and I also shared a classroom, so we got used to observing and critiquing each other's lessons. We refined the curriculum over two years.While we were getting good results, we were also doing our work in isolation. Imagine that this is a graph of student performance over time. Our students would make higher than normal performance gains using our curriculum, but those performance gains would largely be erased once they were back to using a normal curriculum.

This was still better than a typical intervention. In a typical intervention, there is an initial bump in performance that quickly levels out, and then disappears once the intervention is over. At least with our curriculum, students would make performance gains the whole time they were using it.

On the science side, I was learning to take my curriculum vertical. The math curriculum that Charles and I developed still introduced concepts in isolation; in science, the concepts built on top of each other. I had done this in Attleboro with the fluid pressure unit, but that was a two-month long series of investigations. In Brookline, I was connecting all of the earth and life science concepts in the 7th-grade curriculum in a yearlong series of investigation, using the Big Bang and chemistry as the starting point.

Brookline was partnering with the Virtual High School at the time, and my principal asked me to design an online science course for them. The science course I designed was based around the challenge of programming a spaceship to navigate through a two-dimensional course (up-down, forward-back). The spaceship was essentially a tank of high-pressure gas. You piloted the spaceship by opening and closing nozzles. When a nozzle was open, gas would flow through the nozzle, providing thrust. Over time, the pressure in the tank would drop and the mass of the spaceship would decrease. Students would use experiments to learn the science concepts, and they would use spreadsheets to model the spaceship. All of their calculations would be based on discrete time steps, so calculus was not required and all relationships would be linear. (Students would be able to adjust the size of the time steps, so they would be working with limits.)

The other significant development that occurred while I was at Brookline was the formation of my first learning community. In my first year at Brookline, the students in my homeroom also had me for math, science, and study hall. I didn't know it at the time, but these students had two teachers walk out on them in 4th- and 5th-grade. So, they tested me. They tested me to see if there was anything that they could do to push me away. Somehow I hung in there, and managed to break through with them in December.

For me, a learning community is a community whose primary focus is learning. That means that learning is more important than worrying about making mistakes or looking bad. It means taking ownership of your own learning, approaching new experiences with a sense of inquiry, and pulling together to help other members in the community to learn. These students regularly entered the flow state and tested their own understanding. They wanted to make sense of what they were learning and believed that they could.

In 2001, Charles told me that his wife's school, the Jewish Community Day School (JCDS) was looking for a middle school math teacher. The middle school had less than forty students in it at the time, so I would be the only math teacher in the middle school. Charles didn't think I'd be interested, but I jumped at the chance to see what our math curriculum could do when scaled across three grade levels.

JCDS was very progressive and student-centered, so they were using

*Investigations*in the elementary school and*Connected Mathematics (CMP)*in the middle school. But they were also based in Newton so expectations were very high. The expectation was that all students would take Algebra I in 8th-grade and some students would take Algebra I in 7th-grade, but students had much less time for math because they had to take so many additional subjects, such as Hebrew and religious studies. This meant that using*CMP*in the middle school was going to be unworkable. Most public schools have a hard time getting through the*CMP*curriculum even with extra instructional time and without having to complete Algebra I by 8th-grade.I took the math curriculum that Charles and I had developed in Brookline and adapted it for JCDS, using the vertical learning principles I had applied to the science curriculum in Brookline. Being able to build concepts across three grade levels enabled me to design my first sense-making math curriculum. By going vertical and investing in student understanding early on, I helped students climb faster and farther in the long run.

After working with the same group of students for three years, I saw impressive performance gains for the entire three years. When those students left JCDS for high school, their rate of performance growth returned to normal levels, but they didn't lose the gains they had made at JCDS. This indicates that these students were able to build on the understanding they had developed at JCDS, even in environments that didn't natively support sense-making.

After three years of making sense of things in math, these students expected to make sense of things in all subjects, but they were still dependent to some degree on their teachers helping them. Ideally, students should be able to develop the sense-making skills they need to make sense of things completely on their own.

By this point, I had concluded that a sense-making curriculum works. The next step was to see if I could bring it to scale. I left JCDS in 2004 to become middle school math curriculum leader for the Groton-Dunstable Regional School District (GDRSD). The administration at GDRSD wanted the middle school math teachers to adopt a standards-based math curriculum and I wanted to see if I could lead the change process.

The math department was bitterly divided and none of the previous curriculum leaders had been able to achieve any form of consensus. My job was to guide a committee of teachers in selecting a new math program for the middle school by the end of the year. I started capacity-building right away. I wanted everyone to have a deeper understanding of how students learn and how standards-based math programs work (the math wars had kicked up a lot of FUD). We established the criteria we would use to evaluate math programs and started collecting data. As part of the process, I asked teachers to try some different approaches. One of the 7th-grade math teachers who was firmly in the "traditional" camp ended up raving about a functions lesson I had designed for him. He observed students actively taking ownership and reasoning through problems instead of passively waiting for him to tell them what to do. I also secured a commitment from the administration that the committee would select the new math program and not simply make a recommendation to the administration.

In the spring, two clear favorites had bubbled to the surface:

*CMP 2*and*Math Thematics*. Both programs were standards-based math programs, and I thought both were good choices. The traditionalists preferred*Math Thematics*because the program was structured more like a traditional textbook. The progressives preferred*CMP 2*because it focused more on open-ended problem solving. The administration wanted*CMP 2*, but the committee ended up deadlocking 4-4. With both sides digging in, the administration felt justified in breaking the tie and choosing*CMP 2*itself.I begged the administration to give the committee one last chance; I felt that we were on the verge of consensus. So, we gathered for one last time at the end of June and I ran through the possible outcomes. We were about to make a decision that the teachers were going to have to live with for the next ten years. We could make the comfortable choice and hope that

*Math Thematics*would encourage students to become independent problem solvers, or we could go all-in and take a risk on*CMP 2*. The traditionalists had already acknowledged that the primary benefit of*Math Thematics*is that it made the transition to a standards-based math program smoother for teachers (which is important). The 7th-grade teacher who had tested the functions lesson stood up and decided to change his vote. His 7th-grade colleague stood up and agreed. If*CMP 2*gave them a slightly better chance of encouraging students to become independent problem solvers, than it was worth the risk and greater discomfort for teachers. The committee voted 7-0-1 for*CMP 2*.We were doing a staggered roll out and building in lots of professional development, so there was still lots of work to be done. I was drawing up budgets and three-year implementation plans, presenting in front of the school committee, working with vendors and consultants, and coordinating everything. It was fun and exciting, but the most exciting thing for me was the potential of creating a learning community among the teachers. The breakthrough we had in June felt similar to the breakthrough I had had with my students in Brookline.

Unfortunately, the administration didn't share my enthusiasm and optimism. My boss, the Director of Curriculum, hadn't experienced the same things that the committee had experienced because she hadn't been there day-to-day, so she assumed that the teachers' buy-in was temporary. She didn't realize that their buy-in was actually at the ownership level; she probably couldn't even conceive of that as a possibility. So, instead of building on their commitment and establishing a learning community where we would all work together toward a common goal, she seized on their commitment to leverage her own agenda.

In my mind, we were removing one script (the traditional textbook) and exchanging it for a slightly better script (

*CMP 2*). But how can you believe that teaching from a script is good for teachers when solving problems from a script is bad for students? Many people are able to live with that level of cognitive dissonance, but I can't. I felt like I had betrayed the teachers by unwittingly participating in a bait-and-switch on them.In 2007, I became middle school math and science curriculum specialist in Holliston. I won't go into a ton of detail since I wrote about my experiences in Holliston here, here, and here. My goal was to see if I could implement a sense-making curriculum designed by the teachers themselves and to create the learning community I failed to create in GDRSD.

In my first year in Holliston, I became fast friends with Jessica, the principal of the middle school. We worked closely together and she valued my insights. It was a highly collaborative relationship driven by inquiry. When Jessica became assistant superintendent for the Freetown-Lakeville Regional School District (Freelake), she immediately hired me as her K-8 Math Program Coordinator. I was highly impressed by the team that John, the superintendent, was putting together and I relished the opportunity to work with Jessica again, but this time, at a district level.

Unfortunately, Jessica had other plans. She admitted to me that she only listened to me in Holliston because she was about to flame out there and needed me to bail her out with the staff. Now that she was at Freelake and had carte blanche from the superintendent, she wanted to do things her way. While I can respect that on some level, she should have told me that before luring me away from Holliston. I would have never have gone to work with her under those conditions.

The whole year in Freelake was a complete disaster. Jessica, the superintendent, and the consultant they brought in from UMass Lowell spoke passionately about forming a learning community. I think that they, to this day, genuinely believe that they are true believers of learning communities. But the administrative team at Freelake was no learning community. John and Jessica had their agenda and they used the pretense of a learning community to ram it down our throats. Their goal was to win and then leverage commitments from us and then the teachers. When I objected, the learning community ran roughshod over me. I left when John and Jessica used me to get a group of young teachers to go out on a limb, and then undercut the initiative behind their backs. It was GDRSD all over again, and all though I was wiser and more experienced, I couldn't do anything to stop it. That's when I decided to abandon schools for a while and start up Vertical Learning Labs.

### Wrap Up

So, where am I now? That is the question that opened this post and it is where I'm going to end. I haven't reached a new normal, yet. I don't even think it is visible from my current vantage point. But I've been to the foothills of the new normal and I'm as confident as ever that it's there. And if it isn't there, I already know that the foothills I'm on are much taller than the tiny cluster of hills that everyone else is on. So this is a good place to be.

I have developed a sense-making curriculum for middle school math and components of a sense-making curriculum for science. The sense-making curriculum for math works for kids. It's been tested and refined. It's also been designed to fit within the constraints of the current system: 50 minute classes/5 days a week, Common Core standards, high school math courses, etc. Even when I designed a sense-making curriculum for JCDS, my priority was preparing students for a seamless transition to the elite high schools in the area. As we move together toward a new normal, those constraints will fall away and I'm excited to see what people can create from scratch.

Other teachers can and will use the curriculum that I've written, and get similar results. A small number of teachers will fly with it right away. The majority will need coaching from someone like me.

I'm working toward articulating a process that other teachers can use to create their own sense-making curriculum. That is a work in progress and I've got a long way to go.

I can consistently create learning communities. I stumbled onto my first one in Brookline, but I've been consciously creating them ever since. It's fairly easy to do in the classroom when I have students in front of me 50 minutes a day/5 days a week. It is harder to do with teachers, whom I may have in front of me only 50 minutes a day/one day every two weeks (10% of the contact time I have with students). I haven't actually managed it with a group of teachers yet, but I have gotten close in GDRSD and Holliston. Doing it with administrators is much tougher because I get much less contact time with them, and when we do have contact, it is usually around their agenda instead of mine.

I'm not yet at a point where I've started to articulate how I create learning communities. In the classroom, I think that a sense-making curriculum is a great start, but other components are definitely necessary.

Finally, I know that I can't convince anyone through words. I've always suspected that, but banging your head against that particular wall for over 15 years brings another level of clarity. The flip side to that is that anyone who has worked closely with me for any period of time walks away with a much deeper understanding and appreciation of what I do. It is rare for me to not win someone over when they experience firsthand what I can do and what I'm about. The question, as always, is: How do I bring that to scale?

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