The Five Levels of Buy-In

I hate the term buy-in, but decided to use it for this post because it is a term most people know. While googling to see if I should use a hyphen in buy-in or not, I happened to stumble upon this rant contrasting buy-in with ownership. It's worth a read and I think it is spot on. (I especially enjoy how he also tears apart the idea of best practices.)

When you do use the term buy-in, you are essentially talking about convincing people to adopt your idea as if it were their own. That should raise red flags. It is disingenuous and more than a little patronizing. But, by definition, a new normal isn't something that people are going to arrive at on their own or through any kind of incremental analysis. You have to start by convincing them to try a new practice that they don't believe in. As you are tacking up wind, you need to start with buy-in, but you eventually want to transition to ownership. If teachers don't take ownership of these new practices, then you aren't shifting core beliefs and those new practices are going to disappear once you stop pushing them. That's not a new normal.

The level of buy-in is one of the compasses I rely on to do this work. If buy-in is increasing, then I am making progress. If buy-in is decreasing or stagnant, then I'm in trouble. Here are the five levels of buy-in (in reverse order) that I look for:

Resistance

This level is fairly self-explanatory. I am flat out refusing to do what you ask.

Sabotage

On the surface, I am doing what you ask. In fact, on the surface, I am cheerleading for the change. But behind the scenes, I am undermining everything you are doing. I have two goals here. One is to co-opt the change process so that I can mitigate it. The second is to insulate myself from any blame when the change process fails. This way, I can say, "I did everything that you asked me to do and it didn't work. Now what?" This makes you look bad and makes it less likely that you'll try to change something else. Failing to detect sabotage and call it out also makes you look weak and desperate for any kind of win.

Compliance

I'm not trying to make the change fail, but I don't actively support it either. At this point, I'm just doing the minimum I can to keep you off my back. If you accept compliance, then it indicates that you are also going through the motions and don't really believe the change will have a lasting or significant impact either.

Professionalism

I have a lot of personal integrity and want to do the best job that I can. This means that I will do whatever you ask me to do. It also means that I will continue doing anything on my own that I think a professional should do. However, I don't necessarily believe that the change is going to have a lasting or significant impact.

It is hard to be critical of this level of buy-in, but it is insufficient when trying to change core beliefs and establish a new normal. Lots of teachers feel an affinity for the Understanding by Design process. As a professional educator, I should be designing backwards from enduring understandings. But when the process does not yield better outcomes, they don't question it. They don't say, "This should have worked, but it didn't. What did I do wrong? I need to dig in and figure this out, and keep at it until it does work." Instead, they feel like they did their jobs and did it well, but things just didn't pan out.

A teacher that goes beyond professionalism and expects a change to yield better outcomes will engage in inquiry and take risks, similar to what I did when my gratitude journal wasn't quite working.

Ownership

This change is one that I want, I have some say in what this change ultimately looks like, and I am part of the group trying to bring it about. I tend to be driven by some goal rather than the change itself. I am trying to implement a change to bring about some outcome. And I am committed to making this happen, so I am prepared to make sacrifices and put myself at risk.

This is the level you need to see if you are going to bring others onboard. If it is just you driving things, then it feels like you are doing this for yourself and not for the organization or some greater good. You can't reach a tipping point if others don't take ownership.

Changing Beliefs and Practices

My goal is to establish some new normals for teaching and learning. This means adopting some new practices. But the old practices that I am hoping to replace are rooted in core beliefs. So, in order to get people to adopt new practices, I also need to get them to adopt new core beliefs. Which do I work on first?

I have had this debate many times with my friend and former colleague, Ginny. I think that we both agree that you need to change practices before core beliefs. To change a core belief, you need firsthand evidence, and you will only get that firsthand evidence if you try something different and get unexpected results.

One of the milestones in Algebra I is learning how to find the equation of a line given two points. The summative assessment for the seventh-grade functions unit we developed in Holliston included this problem:

Find the slope, y-intercept, and equation for the line that passes through (-9, 2) and (6, -4).

Start by finding the slope:

Then substitute the slope and one of the points into the slope-interecept form of the equation for a line to find the y-intercept:

Finally, use the slope and y-intercept to write an equation for the line in slope-intercept form:

Most teachers firmly believe that finding the equation of a line given two points is hard. They regularly see high-performing eighth-grade students struggling with it. Learning it requires a student to memorize a number of steps, and many students are either unwilling or unable to do that.

I, on the other hand, believe that this process is fairly intuitive and accessible to most sixth-graders. You may have noticed that the summative assessment for the sixth-grade functions unit we developed in Holliston contained this problem:

Find the rule to predict the area of the colony on Day x.

Day	Area (cm2)
0
5	32
9	52
13	72
17	92

Okay, we are giving the students four points on the line here, but that doesn't change the nature of the problem.

Start by finding the rate of growth. The bacteria colony is growing at a rate of 20 square centimeters every four days, which is 5 square centimeters per day.

Then find the area of the colony on Day 0. To do that, we work backwards. From Day 0 to Day 5, the colony grew for five days. At 5 square centimeters a day, it grew 25 square centimeters. So the area of the colony on Day 0 must have been 7 square centimeters. (A student also could have counted backwards by 5, finding the area of the colony on Days 4, 3, 2, 1, and then 0.)

Finally, write a rule to predict the area of the colony on Day x.

If the colony starts with an area of 7 square centimeters and grows at a rate of 5 square centimeters per day, then on Day x, the colony will have an area of 5x + 7.

Within a week, we had close to 100% of all sixth-graders doing this type of problem, including special education students in our substantially-separate math class. More importantly, they viewed this problem as trivial and did not feel as though they needed to memorize anything to figure out how to solve it.

By convincing the sixth-grade math teachers to try a new curriculum with new instructional practices, we were able to generate firsthand evidence that caused some of them to reconsider their core beliefs about the difficulty of tasks and what students can and cannot do. It was a small shift, but it was enough for me to build on and introduce even more new practices. Presenting this evidence at the professional day in January to the rest of the department caused a stir, but it did not really move any of the seventh- or eighth-grade math teachers. Because feedback is so noisy in educational systems, it is very easy to dismiss secondhand evidence.

My overall strategy in Holliston was to build working relationships with the math teachers and to encourage a few individual teachers to try some new practices. Because teachers would be experimenting with new practices without a change in core beliefs, none of those new practices could be that radical. However, the new practices had to be powerful enough to generate short-term evidence that would register above the noise. If the firsthand evidence was too powerful to ignore, then a small shift in core beliefs would occur and I could then suggest a few slightly more advanced new practices. This would lead to another small shift in core beliefs and more advanced new practices. I would essentially be tacking into the wind. As evidence mounted and core beliefs shifted, more teachers would take ownership in the work and, together, we'd be able to convince more teachers to take that small first step.

Function Junction, Part 1

I was talking to my coach Sarah this week when I realized that I haven't been doing a very good job of telling my backstory. There are things that I've seen, done, and learned in life that no one, not even my closest friends, really know about. These are things that make me who I am and fuel my vision.

I was the math and science curriculum specialist at the Robert Adams Middle School in Holliston, Massachusetts from 2007 to 2010. In the fall of 2008, I worked with the 6th-grade math teachers to develop and implement a new functions unit. In most middle school math programs, students learn a little about slope in pre-algebra. But their first real introduction to functions is in Algebra I, where they are expected to master a number of discrete skills, including:

• Using the slope and y-intercept to graph a line
• Writing the equation for a line in slope-intercept form
• Finding the slope and y-intercept of a line given two points
• Working with linear equations in point-slope form
• Working with linear equations in standard form

All of these skills should sit on top of a single conceptual framework, but because very few students enter Algebra I knowing anything about slope, there really isn't time to develop a conceptual framework and then get students to mastery in the time allotted. Instead, we are forced to ask students to learn each skill in isolation.

In Holliston, about 60% of our students take Algebra I in eighth-grade, and only half of those students do well on the functions chapter test. I would describe functions as a significant pain point for the eighth-grade math teachers; they really wanted their students to do better on this key concept, but they didn't know how to make that happen.

I decided to target the functions pain point in 2008 for five reasons:

• I didn't have a very good working relationship with the eighth-grade math teachers and alleviating this eighth-grade math pain point would be a big step toward establishing one.
• Functions is something that we could do completely in-house in the middle school. We could introduce functions in sixth-grade without relying on any help from the fifth-grade math teachers based in the elementary school, and we could have everything wrapped up and tied in a bow by the end of the eighth-grade, so we wouldn't need the high school math teachers to do anything different to take advantage of what we had done.
• The math teachers all recognized that procedural approaches weren't working and wanted students to have a conceptual understanding of functions.
• If we could help students develop conceptual understanding and double the number of students reaching mastery, then people would notice and applaud the work we were doing. It would also go a long way toward changing some of the core beliefs held by the middle school math teachers themselves.
• The functions pain point isn't something that any one teacher can successfully tackle on his or her own. This would reinforce the fact that I wasn't pointing my finger and saying that individual teachers weren't doing their jobs. It would also highlight the good things that could happen if we set aside our egos and worked together as a department.

I spent about a month working with the sixth-grade math teachers to design a four-week functions unit for sixth-grade. We did this work after school and during their prep periods. As curriculum specialist, I had no say over how they spent their prep periods, so this was a purely volunteer effort. When we finally implemented the unit in November, I spent some time modeling lessons and coaching teachers in their classrooms.

Here are some of the problems we used in the summative assessment we gave at the end of the unit:

3) At the start of an experiment, a bacteria colony has an area of 22 cm2. It grows at a constant rate of 3 cm2 per day. Fill in the table and come up with a rule for predicting the area of this bacteria colony on Day x.

Day	Area (cm2)
0
1
2
3
4
28
55

4) Bob uses the following rule to predict the area of a bacteria colony on Day x:
area = 21 + 4x. How fast is the bacteria colony growing? What was its area at the start of the experiment? Explain how you can tell by looking at the rule.

5) Find the rule to predict the area of the colony on Day x.

Day	Area (cm2)
0
5	32
9	52
13	72
17	92

Use the graph to answer problems 7-10 and the bonus:

7) Which bacteria colony is growing at a constant rate? How can you tell just by looking at the graph?

8) When is Bacteria Colony B growing faster than Bacteria Colony A? How can you tell just by looking at the graph?

9) What was the average growth rate per day for Bacteria Colony B between Days 4 and 7?

10) Describe the growth of Bacteria Colony B over time. Explain when it is growing faster or slower, when it is shrinking, and when it is staying the same size.

11) Bonus: Write a rule for the growth of Bacteria A over time.

We spent a professional day in January analyzing the results of the summative assessment as a department. 85% of the students scored a B or higher. The seventh- and eighth-grade math teachers were floored by both how well the students did and the quality of their written responses. We estimated that 75% of the students had a solid conceptual understanding of linear functions and could fluently translate among tables, equations, graphs, and written descriptions as long as functions were presented in a real-world context. 55% of the students completed the bonus correctly even though we had never asked them to write an equation from a graph with a fractional rate of change before, and another 20% understood what they needed to do, but just made a procedural error somewhere along the way.

One of the sixth-grade special education teachers worked closely with us as we developed the sixth-grade functions unit. She used a pared down version of the unit with the students in her substantially-separate math class. (A substantially-separate math class is for students with math learning disabilities so severe that it has been determined that their needs cannot be met in a general math class.) Her students loved the unit and got 75% of the pattern, relationship, and algebra questions on the state test correct when they only got 45% of the questions in the other four strands correct. The state test was administered in May, about five months after she taught the functions unit.

In 2010, I developed the seventh-grade functions unit with the seventh-grade math teachers. By this time, the first group of sixth-graders that had taken our sixth-grade functions unit were now seventh-graders. The seventh-grade math teachers had been excited by how well these students had done on the sixth-grade summative assessment, but they were anxious about how much those students would actually retain. We decided to start the unit with a warm up activity designed to re-activate what the students had learned sixteen months ago.

Although the students said that they had forgotten everything about functions from sixth-grade, the warm up activity demonstrated that the conceptual framework for functions they had developed was still there, and everything came flooding back to them.

Here are some of the problems we used in the summative assessment we gave at the end of the end of the seventh-grade unit:

A plant is growing at a constant rate. Use the table to answer problems 1-5.

Day	Plant Height (cm)
0
20	17
28	23
36	29
44	36

1) What is the rate of growth of the plant? Explain how you found it.

2) What is the starting height on Day 0 of the plant?

3) Write a rule for the height of the plant (y) after x days.

4) Use the rule to find the day when the height of the plant will be 80 cm. Write the rule and show all steps.

5) Create a Plant Height vs. Time graph.

Use the following rule to answer problems 6-8: w = 50m/3 + 100 where w = gallons of water in a tank and m = minutes.

6) Use the rule to fill in the rest of the table. Show all steps.

Minute	Water in Tank (gal)
0
10
15
	620
	800

11) Graph: y = 3x/4 − 2

13) Write an equation for the given graph.

In problems 14 and 15, graph the two given points, then find the slope, y-intercept, and equation for the line that passes through those two points.

14) (-9, 2) and (6, -4)

15) (-8, 2) and (-5, 10)

16) Explain how you found the slope for the graph in problem 14.

17) Explain how you found the y-intercept for the graph in problem 15.

18) Challenge: Find the point (x, y) where the two lines in problems 10 and 11 would cross if they were on the same graph.

We found that the 75% of the students who had developed a solid conceptual understanding of functions in sixth-grade were able to pick up immediately where they had left off and build on what they had learned. In fact, the seventh-grade math teachers found that they had to do very little teaching in order to get students to generalize from real-world contexts to abstract x's and y's, or to introduce fractional rates of change. However, the 25% of the students who were shaky after sixth-grade got left in the dust.

I left Holliston after the 2009-10 school year, but the plan was to develop a new functions unit in eighth-grade. The 75% of the students with a solid conceptual understanding should have easily been able to extend what they knew to linear equations in standard and point-slope forms. This means that all of the eighth-grade Algebra I students (instead of less than half) should have mastered linear functions before moving on to Algebra II in ninth-grade, saving the high school math teachers 3-4 weeks of re-teaching time. And the students that didn't take Algebra I should have been much better prepared for Algebra I in ninth-grade. All of this should have then opened the door to a district-wide conversation about collaboration and curriculum and instruction.

Within the middle school math department, I was hoping that the success of this conceptual approach to functions would lead to a willingness to work together and to try new instructional strategies. Up until this point, getting teachers to try some new curriculum hadn't been too difficult, but getting them to accept coaching was like pulling teeth. And new curriculum was substantially less effective without the necessary coaching and shifts in practices. My next goal would have been to analyze what we were doing and then to try to increase the percentage of students developing solid conceptual understanding. If you've been reading my blog, then you know that the first step is to design a curriculum that breaks down tasks to intuitive subtasks. I think we did that in the sixth- and seventh-grade functions units. The next step is figuring out how to help students learn how to perform those tasks. We got to 75%, which is excellent for our first try, but now we needed to push that up to 95%+. Doing that would mean challenging even deeper core beliefs and forcing more changes in how we operated as a middle school and district.

The Environment for New Normals

New normals come out of left field and strike like thunderbolts. We don't see them coming, but they seem stunningly obvious in hindsight. Going into the 1968 Olympics, everyone thought that the best technique for the high jump was the straddle. All it took was the performance of a single high jumper with a radical new technique, the Fosbury Flop, to sweep the straddle into the dust bin of history. Four short years later, at the 1972 Olympics, the Fosbury Flop was the new normal.

Meanwhile, there hasn't been a new normal in teaching and learning in my lifetime. I don't think there's been one in centuries, maybe even millennia. Again, I'm not talking about the institution of schooling; I'm talking about the intimate interaction among teacher, student, and content as seen from one foot away. At that distance, a teacher working with a student on multi-digit multiplication in the middle of a busy class looks the same as a tutor working with a student after school, a parent working with a child at the kitchen table, or a teacher working with a student in a one-room schoolhouse on the prairie in the 1870s. The tools may be different, but the basic strategies and techniques remain the same.

Is it possible to pull off a Fosbury Flop in education? I'm not sure, but I sure hope so. I think there are better techniques in teaching that are still undiscovered, and we need something that can shake our understanding of both teaching and learning to the core. Comparing the landscape of high jumping in the 1960s with the landscape of education today may help us understand how to bring about the new normal we need.

Variation and Experimentation

To arrive at a new normal, there needs to be some level of variation and experimentation that occurs at the bottom and bubbles up to the top. In the 1960s, all of the best high jumpers were busy refining the straddle technique, and it is very doubtful that any of them were going to break away to try something radically different. It took Dick Fosbury, an unknown high schooler at the time, to gamble and invest five years in a completely unproven technique.

If Dick Fosbury had experimented with the wrong technique, the flop would have failed. If Dick Fosbury had quit after four years before perfecting his technique, the flop would have failed. If Dick Fosbury had suffered a career-ending injury, the flop would have failed. If Dick Fosbury had lacked the physical gifts to jump higher than 2.13 meters (7 feet), the flop would have failed. New normals emerge because of individuals, but relying on a single individual for a new normal is not a good bet. Ideally, you want a thousand high jumpers working to perfect the straddle technique, and you want a thousand high jumpers working to find the next technique to replace the straddle.

It is hard for me to evaluate the level of variation and experimentation in high jumping in the 1960s because I don't know how many other kids were perfecting radical high jumping techniques in their backyards. What I do know is that the level of variation and experimentation in public schools has decreased significantly since I became a teacher in the 1990s. The standards movement led to a number of top-down reforms. Curriculum standards were removed from local control and transferred first to the state, and now to the national level. There has been a massive drive for consistency. It is now considered unacceptable for two fifth-grade science teachers in neighboring classrooms to each be doing their own thing. The goal is for everyone to collaborate and standardize curriculum and practices. Twenty years ago, half of the math teachers in Massachusetts were using math programs that were either home grown or cobbled together from multiple sources; today, virtually everyone uses a monolithic math program purchased from a major publisher.

To be fair, the variation that existed before the standards movement wasn't very productive. New normals didn't arise from this experimentation, and many of the experiments were pointless and yielded poor results. But you can't discover new normals without variation and experimentation, and those experiments cannot be centrally curated. After Dick Fosbury won the US Olympic Trials in 1968, the trials were held again because the US Olympic Committee still didn't believe in the flop and didn't want Fosbury on the team. If every high jumper on Dick Fosbury's high school track team had to standardize on a single technique, I don't think that Fosbury could have persuaded anyone in 1963 that his technique was superior and should be adopted by everyone.

Supervision and Coaching

When Dick Fosbury began working on the flop, he was a member of his high school track team. This means that his coaches and teammates were watching him jump. They could see both his technique and the heights he was clearing. Initially, his coaches wanted him to switch back to the straddle. But at some point, they could see that the flop was working for him (Fosbury eventually broke his high school's high jump record and placed second at the state meet) and started to give him tips and feedback to improve his technique as best they could.

On the other hand, teaching in schools largely happens behind closed doors. No adult really knows what you are doing. One of the motives behind the push for consistency across classrooms is to de-privatize teaching and to get teachers talking and sharing strategies and practices. Past efforts to break down walls include lesson studies and the formation of professional learning communities, but none of these efforts have been successful. Very few school districts employ coaches, and most teachers view coaches as nuisances rather than helps. Supervision consists of the principal coming by to observe a lesson twice a year every two years.

To get a sense of what supervision and coaching looks like in schools, imagine a high school track team where every member of the team practices in isolation. Twice a year, the athletic director, a former javelin thrower, swings by to check on you and to write a report for your file. Four times a year, the whole team gathers, but you may not do any high jumping on those days. And in October, you finally receive your scores from the state meet (the one formal competition of the year) that was held in April.

A Single Metric for Performance

Dick Fosbury made a lot of adjustments to the flop before he won the gold medal at the Olympics in 1968. One of them was learning that he had to adjust his point-of-takeoff as the high jump bar was raised. While making these adjustments, Fosbury was able to gauge whether his technique was improving or getting worse by observing the heights he was clearing. He was also able to compare his performance against established benchmarks, such as the high school high jump record and the world record. Without this data, would Fosbury have been able to improve the flop? Would he have persevered for five years? Would the US Olympic Committee have allowed him on the team? Would he have convinced the world his technique was better?

We don't have a single metric for performance in education. Even the most ardent supporter of standardized testing wouldn't argue for a single metric. Instead of adjusting our technique to jump higher, we are forced to adjust our technique to optimize the vertical force we exert at the point-of-takeoff or the curve of our back. We hope that will translate to higher jumps, but we don't really know. We also have no idea how our performance compares with the teacher across the hall, the teacher in the next town over, or the teachers in Shanghai.

Noisy Feedback

Feedback in educational systems tends to be extremely noisy. Part of that is because there isn't a single metric for performance, so one metric may indicate that you are improving, while another may indicate that you are getting worse. But feedback also suffers from lag and the number of variables in play. When you experiment with a new technique, it can take days, weeks, months, or even years before measurable student outcomes emerge. This makes it difficult to tease out the effect of the new technique from the effect of other intervening factors. It's like sitting at a console and mashing on buttons. After a few hours, you start to see some things happen, and you have to figure out which button, or sequence of buttons, caused which thing to happen.

The existence of numerous variables that are difficult to control for also contributes to noisy feedback and makes it hard to compare results across multiple trials. It's as though some high jumping competitions are occurring in sand with a strong headwind, while others are on spongy surfaces indoors. Because of this, research studies often contradict each other and we have to rely on meta-analyses across studies that often draw faulty conclusions. Many of these studies conclude that procedural techniques are more effective for teaching math. But drilling down, you will find that most teachers in these studies had more experience using procedural techniques and were ill-equipped to use the conceptual technique being studied. The longer, more in-depth studies that may tease out those effects carry much less weight in a meta-analysis, and these meta-analyses drive policy decisions.

The Olympic Stage

Dick Fosbury had the opportunity to win and demonstrate the Fosbury Flop in front of an audience of millions, including thousands of his fellow high jumpers. I can't think of anything comparable in the educational world. There are TED talks, but those are curated and you don't really have the same opportunity to demonstrate the performance of a new technique. Finland shocked the world by finishing first or second in math, science, and reading on the 2006 PISA, which caused educational researchers and policymakers to flock to Finland. But the educational techniques used in Finland were selected by someone at some point. Dick Fosbury didn't have to pass through any similar gatekeepers. He just had to jump higher than anyone else.

Incentives and Competition

The best high jump recorded using the flop is less than 5% higher than the best high jump recorded using the straddle. Yet, that tiny performance gain was enough to convince the entire world to switch from the straddle to the flop. Teddy Rice would argue that competition creates a sense of urgency that causes us to seize on incremental performance gains, no matter how small. I don't disagree with him, but I don't agree that the failure of schools to seize on similar incremental improvements is evidence that schools don't compete. I just think that the basis for competition is a little different.

While Dick Fosbury was developing the flop, the rest of the world was engaged in an arms race to perfect the straddle. The world was shocked by the Fosbury Flop not because the world was complacent, but because it was suffering from a case of tunnel vision. Hundreds of high jumpers were competing to be the best, and it looked like perfecting and mastering the straddle was the way to get there. When Fosbury won the gold medal at the 1968 Olympics, he showed everyone that there might be another way. A few high jumpers tried it and won. A few more tried it and won. New records were set, and soon the number of high jumpers trying the flop was a tidal wave. The transition was fast.

Let's contrast this with what happened when Finland topped the charts on the 2006 PISA. Finland didn't surprise the world because it used a new technique; it surprised the world because no one was expecting Finland to be at the top. Educational researchers and policymakers immediately flocked to Finland to see what they could learn, but the reports coming back were garbled. No one could tell which buttons Finland had pushed or if Finland's results could be duplicated by another country operating under another set of conditions.

I can guarantee you that if another country – such as Brazil – had taken lessons learned from Finland and started climbing up the rankings in 2009 and 2012, the world would have noticed and reacted urgently. But that didn't happen. Instead, Finland has fallen in the rankings and it is looking more and more like its performance in 2006 was more noise than signal.

The same thing happened in the 1990s with the TIMSS. This time the darlings were the Singapore math curriculum and lesson studies from Japan. Although widely adopted, neither technique has achieved much long-term success. The Fosbury Flop didn't become the new normal because Dick Fosbury won with it; it became the new normal because high jumpers across the world began to win with it. So far, there has been a disappointing pattern of that not happening when new techniques are adopted. This pattern of failure and the lack of a strong signal makes schools reluctant to jump on the next new thing.

Even worse, in education, we aren't making incremental progress on the techniques that we do have. In the United States, ideas such learning by doing, focusing on problem solving and critical thinking, cooperative learning, personalized education, community service and educating for social responsibility, and performance assessments were all widely practiced by the progressive education movement in the late nineteenth century. Our best teachers today are not practicing those techniques at a higher level than the best teachers were a hundred years ago. The state of the art has not moved much at all.

Instead of competing to raise the bar, it feels like we are competing to get more teachers to the bar. It makes sense when there are so many underperforming schools and teachers that could be doing so much better if we could just get them to apply the techniques we already have. And competing to be the best is pretty hard when there is so much noise in the system and we don't have a single metric for performance. But I still believe that schools will compete to be the best if something rises above the noise and they become convinced that a new normal is possible. Dick Fosbury did it with a 5% performance gain in high jumping in 1968. It is going to take more than that to do it in education in 2014. I guess it is up to us to figure out what that is and then to make it happen.

The Fosbury Flop

In 1968, Dick Fosbury shocked the high jumping community by winning the Olympic gold medal in high jumping with the Fosbury Flop. The dominant technique at the time was the straddle. Thousands of high jumpers around the world were competing to squeeze as much performance out of the straddle as possible, and incremental improvements were quickly adopted and studied. But by 1972, 28 out of the 40 competitors in the high jump at the Olympics were using the Fosbury Flop, and the last world record set using the straddle was in 1978. The normal in high jumping before 1968 was the straddle; after, it was the flop.

My goal as founder and Chief Learning Officer of Vertical Learning Labs is to create a new normal in teaching and learning. My goal isn't to disrupt the institution of schooling, but to change how we think about teaching and learning at a one-to-one level. In my opinion, everyone is using the straddle technique today. This includes every classroom, our best teachers, charter schools, private schools, one-on-one tutors, homeschoolers, MOOCs, Khan Academy, flipped classrooms, camps, after school clubs, Finland and Singapore, parents at home in a teachable moment… we are all using the straddle. Researchers are studying expert straddlers and policymakers are trying to figure out how to get everyone to use those best practices, but none of that is good enough. We need a flop.

You don't arrive at a flop through iteration and incremental improvement. Advocates of procedural and conceptual learning are on neighboring hills sniping at each other. Each camp wants to pull everyone else uphill. Up their hill. Meanwhile, the flop is a mountain sitting miles away that towers over both of them. How do we get there?

Dick Fosbury developed his flop in complete isolation. He tried to use the straddle, but felt that the technique was too difficult for him to master. So he started from an outdated version of the scissor. It took Fosbury five years to refine the flop to the point where he could win the Olympics. In the early years, his coaches tried to talk him out of it until he began showing improvement and setting personal bests.

As a student of new normals, I have four questions when it comes to the Fosbury Flop:

1. Would the flop still have appeared if Fosbury hadn't developed it?
2. Was winning the Olympics necessary for the flop to gain traction and take over?
3. How obvious is the flop in hindsight? How much better is it than the straddle?
4. Is there another flop waiting in the wings to become the next new normal?

It appears as though the development of the flop happened just as high jumping was transitioning to softer landing zones that made it safer to land on one's back, neck, and head. The flop wasn't actually feasible at world record heights until the 1960s. And Fosbury evolved the flop from an existing technique that was popular at one time. So it is possible that there were other high school high jumpers experimenting in the same way, but Fosbury was the first to get noticed because he was the first to win with the flop on the world stage. On the other hand, Fosbury had to put up with a lot of crap. The results from his initial experimentation weren't promising and everyone was telling him to go back to the straddle. I'm guessing that Fosbury only stuck with it because he knew that he would never be world champion using the straddle, and he wanted to be world champion enough to persevere. It would be interesting to know how many other high jumpers in the world were experimenting with radical techniques, and how many of them were close to breaking out when Fosbury did. One in a thousand? One in ten thousand? One in a million? Is there a tipping point when a new normal becomes inevitable?

I don't think that Fosbury had to win the Olympics in order for the flop to become the new normal. Even if Fosbury had only won bronze, I think you would have seen a lot of floppers at the 1972 Olympics. The flop didn't take over because the high jumping establishment instantly saw it as superior; the flop was still received skeptically after Fosbury's win. But enough individual high jumpers (probably the ones in the second tier who realized they weren't going to make it to the Olympics sticking to the straddle) were willing to take a risk and start using it, and they found success. It's when floppers besides Fosbury started winning that the flop became the new normal. What if Fosbury had still won the NCAA championship in 1968, but hadn't made it to the Olympics? Clearly, Fosbury had to win on a stage large enough to encourage a critical mass other high jumpers to try the flop, but how large that stage needs to be is very unclear.

The last world record set with the straddle was 2.35 meters. The current world record set with the flop is 2.45 meters, a difference of less than 5%. Knowing how quickly the Fosbury Flop became the new normal, I was expecting a greater difference. However, in athletics, a difference of 5% is probably the difference between an Olympic champion and a good college athlete, so I shouldn't be surprised. Usually, new normals are obvious in hindsight; that is how and why they become new normals. As a non-high jumper, it isn't obvious to me that the flop would be superior to the straddle. And apparently, there is considerable debate about this within the high jumping community. Some feel that the straddle is as good as the flop, but that the flop is much easier to master. So, while an expert straddler will jump as high as an expert flopper, there will be a hundred expert floppers for every expert straddler.

I think that the world needs a new normal in teaching and learning, and I think that my approach to curriculum design can produce that new normal. I've already done what Fosbury did and refined my process in isolation; I'm just waiting for my Olympic moment. What will it be? How large does it need to be? The student outcomes I see from my curricula are much more than 5% better than what we achieve with our current curricula, but we don't see the same rewards and willingness to take risks to be 5% better, so the deltas need to be greater to reach a tipping point in education. Still feeling my way to next steps, but I like this analogy. I should have a problem description and environmental analysis soon. After that, my goals and strategies. Stay tuned!

Building Understanding

You would think that most curriculum would be designed to build student understanding, but that isn't the case. Many people, including teachers and curriculum designers, continue to advocate procedural learning over concept development. This is partly due to a natural bias to teach the way we were taught, but also partly due to the build up of anecdotal evidence suggesting that concept development is either less effective or less efficient than procedural learning.

How is that possible? How could memorization be a more effective way to learn something than understanding it? Understanding definitely pays off in the long run. Students who rely on memorization eventually get stuck while students who understand what they learn are able to move on to more advanced studies. The problem isn't that building understanding is ineffective, it's that curricula designed to build understanding are ineffective. I would argue that if we were actually building understanding with our curricula, then it would quickly become our new normal because it would be so much more effective than what we are doing now.

Let's consider the laws of exponents:

In a procedural approach, students are given the laws to memorize, and then asked to apply those laws in dozens of practice problems. To avoid interference, each law is typically introduced on a separate day. While students will still have to pick out which law to apply for a given problem on a cumulative test, few problems will require the student to apply more than one law at a time. At most, a student may be asked to simplify an expression like this:

When a procedural approach is taken, the expectation is that students will be introduced to these laws in pre-algebra, but that they won't remember them beyond the test. The laws will then be re-taught in Algebra and Algebra II, and only mastered in Algebra II after students are applying them on a daily basis. This means that we are relying on brute force and repetition to get students to mastery, and we aren't expecting the low-performing or learning disabled students who will never get through Algebra II to master these laws at all.

In a conceptual approach, the laws of exponents are first introduced by deriving them, and demonstrating how and why they work:

The theory is that if you can derive a rule and explain it, then you understand it. However, once a student can do that, the curriculum then returns to the traditional path: each law is practiced in isolation to minimize interference and mastery is not expected until two years later in Algebra II after students are applying the laws on a daily basis. So even though we are teaching for understanding, we are not expecting a different outcome. This is why many people see concept development as a waste of time.

I don't believe that curriculum designers are simply going through the motions or paying lip service to building understanding by slapping a different introduction onto the traditional procedural approach; I think that they don't know what else to do. We want the students to apply the laws of exponents. They understand the laws of exponents (at least well enough to explain and justify them). So what else is there?

The problem is that curriculum designers are conflating the laws of exponents with the task that students need to perform. Because of this, they view the derivation of the laws simply as a bridge to the laws themselves, and once the students understand the laws, they think their job is done. The goal isn't to understand the laws of exponents, but to understand how to simplify exponential expressions well enough to debug things if something goes wrong or to reason through things if something new and unexpected pops up. To get there, the steps in the task needed to be explicit and grounded enough so that students can try things out, and problems need to be complex enough so that students need to try things out. We don't want automaticity and abstraction at this point.

To launch into a complex problem, students need to understand their goal and a set of basic tools and strategies for reaching that goal.

So what does a student need to know and be able to do to perform this task?

The student needs to know that, in order to write an expression in simplest terms, he or she must be able to identify, re-group, and count all of the factors in the expression.

To re-group and count the factors, the student needs to be able to interpret exponents, which means that the student needs to know what an exponent is and apply that definition to write out the factors in an exponential expression using multiplication:

To do that, a student needs to be able to identify the base for an exponent. Our expression has six exponents. What is the base for the second exponent (6)? Is it 3a or a? What is the base for the fifth exponent (3)? If you are fluent with exponential expressions and the laws of exponents, you may be able to pick out bases intuitively, but how would you figure out a base if you couldn't see it right away?

To identify the base of an exponent, you need to apply the rules for order of operations. To make this easier, let's make each operation in the expression explicit (another sub-task that students need to be able to perform that we don't teach):

Now I can tell that the base of the second exponent (6) is a and not 3a because I wouldn't multiply by 3 until after I've evaluated the exponent.

Once all of the exponents have been written out as multiplication, then the factors can be re-arranged (commutative and associative properties of multiplication) and re-grouped using exponents.

While this process may seem more complicated than memorizing and applying the laws of exponents, all we are doing is making every step explicit. If you were to attempt to solve the same problem using the laws of exponents, you would find yourself going through the same process. You may not be aware of some of the steps because they are so automatic and you are doing them in your head subconsciously, but they are there. Making them explicit actually makes it easier for students who don't yet have that level of automaticity. It also makes it easier to catch any errors you may be making.

A common error is treating coefficients like exponents. When students are adding exponents, they instinctively want to add the coefficients:

And when they are multiplying exponents, they want to multiply the coefficients:

Their pattern recognition causes them to hone in on the numbers and to start operating on them instead of thinking in terms of factors. Thinking in terms of the laws of exponents encourages students to go straight to computation. You identify which law applies, and then you add or multiply.

Stepping back and explicitly thinking in terms of factors instead should help students catch and correct these errors:

1. What factors are there in this expression? A 6 and two a's, and a 3 and five a's.
2. Can I re-arrange and group any of the factors? I can re-arrange the factors to group the a's, so now I have a 6, a 3, and seven a's.

The laws of exponents don't enter the student's thinking at all except as a short cut for combining two a's and five a's.

1. What factors are there in this expression? Four 3's, four groups of five a's, and four groups of two b's.
2. How many a's and b's do I have? Four groups of five a's is twenty a's and four groups of two b's is eight b's.
3. Can I re-arrange and group any of the factors? Nope.

Again, the laws of exponents only serve as an efficient way to count factors.

When building understanding, we need to be clear on the tasks that we want students to perform. We don't want them to derive or apply the laws of exponents. We want them to simplify expressions containing exponents. When we do that, we uncover critical sub-tasks that students need to be able to do, such as identify the bases of exponents. If a student cannot identify the base of an exponent, the laws of exponents are not going to help, and the student will be unable to complete the task.

The mistake that many curriculum designers make is thinking that breaking down a task represents a form of scaffolding. Scaffolding are supports that we put into place when building a structure, but that are removed when the structure is complete. That is not at all what we are attempting to do. The sub-tasks that we identify through a task analysis represent what students need to know and be able to do; they aren't a bridge to a higher level abstraction that will eventually replace the sub-tasks, but a foundation for reasoning and problem solving that enables abstraction.

The Prison of Core Beliefs

There have been and continue to be attempts to establish new normals in curriculum design. None of them have been particularly successful, and I will argue that none of them will ever be successful as long as they fail to change expectations for student performance. Right now, when we teach something, most teachers expect that a third of the students won't get it, a third will get it just well enough to pass the test, and a third will get it and understand it well enough to hold onto it. We think of that as normal.

Every once in a while we will be encouraged to try something different, but when we try something different and the results end up basically the same, it only reinforces what we believed and expected in the first place: some students get it and some students won't, and there is nothing that we can do to change that. If you truly believed that, how long would you bang your head against the wall trying to alter reality before reverting to the status quo? Jumping to a new normal is going to take years, if not decades. And much of that time will be spent wandering alone in a fog with no sense of direction. If we want people to commit to and complete that journey, then we need to arm them better.

Standards

The big push over the past 30 years has been the standards movement. The basic premise of the standards movement makes complete sense: establish standards for what students should know and be able to do, test students against those standards, and use that assessment data as feedback for continuous improvement. The No Child Left Behind (NCLB) Act set a goal for 100% of our students to reach proficiency by 2014, and sticks and carrots were put into place to make sure that the system responded with urgency.

The standards movement has been fairly successful at taking the slack out of the system. Our lowest-performing districts, schools, and teachers got a serious wake up call, and we have now raised the floor on student performance. By taking out the slack, I mean that people are finally doing the things that they should have been doing all along. By redoubling our efforts, we have shifted our classrooms from an expected 33% | 33% | 33% break down in student performance to 25% | 40% | 35%. While that is nothing to sneeze at, it isn't sustainable and we have run out of ways to push performance higher.

To achieve the shift to a 25% | 40% | 35% break down, we threw massive resources at the problem. And what the people on the ground have taken away from all that effort isn't that the 8% that moved from don't-get-it to get-it-just-well-enough-to-pass-the-test are more capable than we originally thought, it's that we only got a few more students over the bar by lifting them up and over it ourselves. Because once we stop lifting them, they will be right back where they started in the don't-get-it camp. Core beliefs have not changed at all.

The standards movement is at a crisis point. We are bringing the common core and a new regime of national tests online, but student performance has largely plateaued and timelines for goals are being pushed back. The big question is: What happens when we can't afford to continue throwing sticks and carrots at the system? Will anything survive or will the old slack return? In order to become a new normal, something has to be so compelling that we keep doing it even after someone stops pushing it. It has to become internalized, and I'm not sure if anything from the standards movement has become internalized. Just imagine what would happen if state testing (or it's replacement) went away tomorrow.

Understanding by Design

The curriculum design process with the greatest mindshare today is Understanding by Design. Again, the basic premise makes complete sense: start with an enduring understanding and then design a curriculum to achieve that enduring understanding. An enduring understanding is intended to be an audacious goal that galvanizes us to bring everything to the table. But it presumes that the tools needed to achieve this goal are known and that iteration is sufficient to find what we need.

One of my favorite television shows is Kitchen Nightmares where Gordon Ramsay visits failing restaurants and helps their owners turn things around. As much as I enjoy the show, Gordon Ramsay has it easy. Models for highly successful restaurants are out there and can be studied. We know what makes for a great restaurant. The same can't be said for great curriculum. This means that, to turn around a curriculum, you need to try a lot of things that have never been tried before and most of which aren't going to work. Even worse, if you do try something that will eventually work, it probably isn't going to work the first dozen times you try it because you are new at it. That takes perseverance.

Unfortunately, what usually happens is that we try a few things, they don't work and we don't come close to reaching our audacious goal, and this ends up reinforcing our core belief that some students will get it and some won't and that this outcome is normal and to be expected. Or we pick a goal that sounds audacious but really isn't. Either way, the status quo is maintained and nothing new is discovered.

Power Standards

Power standards were a popular approach to curriculum design, but they have fallen out of favor, largely because the approach proved to be ineffective. I actually adopted power standards for a few years and still think that they provide a useful framework for thinking about curriculum, but they definitely aren't enough to create a new normal on their own.

The basic premise behind power standards is that some standards are more important than others and that we should focus on the most important ones. Again, perfectly logical. One of the nice things about using power standards is that teachers need to come together to decide which standards are power standards (a rule of thumb is that only one third of the standards are power standards). The criteria for being a power standard are endurance, leverage, and readiness. If well-faciliated, these conversations could lead to a much deeper understanding of the standards themselves.

I like power standards because of the emphasis on leverage. Some standards are frequently leveraged to reach other standards. For example, you need to understand order of operations in order to understand how to simplify expressions. If the curriculum designer understands that and can build that into the curriculum, then simplifying expressions will end up making a little more sense to the student. This is part of what we do when breaking down tasks in a task analysis.

Understanding by Design gives you a distant landmark to shoot for, but no compass. Using power standards, the landmark is a little closer and you do have a rudimentary compass in leverage, but the compass can be very hard to read and there is little driving you forward to brave the fog. How confident are you that leverage will lead you to a place where all students will get it? If you are unsure, it is that much easier to turn around and go back to climbing the mountain you know.

Adaptive Learning

One of the hot trends today is injecting big data into the standards movement. The basic premise is that we aren't closing the loop because: (1) formative assessment data is not getting to the teachers, so teachers aren't able to adapt their instruction to the needs of their students; or (2) formative assessment data is getting through but teachers don't have enough resources at their fingertips to respond at a granular level. Either way, technology is riding to the rescue. Soon, a computer will be able to collect highly detailed formative assessment data from a student, and then match that data against a database of world-class curricula to tailor a learning program for that student in real-time.

Great, except the world-class curricula sucks and will continue to suck until we have a curriculum design process that can take us to a new normal. Where is the world-class curriculum for teaching students to use prime factorization to find greatest common factors and least common multiples? If there is something out there that actually makes sense to students, I haven't seen it. This is why one-on-one tutors and elite private schools end up using the same basic curriculum that everyone else uses: there aren't any better alternatives and more data isn't going to change that. Why isn't there urgency to create something better? Because our curricula is giving us the outcomes that we expect and consider normal.

Student Engagement, Multiple Representations, and Discovery Learning

In the interests of time, I'm going to lump all of these approaches to curriculum design together. Imagine that you are designing a curriculum to help students learn how to use prime factorization to find greatest common denominators and least common multiples. How would any of these approaches help you? Until you've broken these tasks down to sub-tasks that are intuitive or build on sub-tasks students have already mastered, any true form of discovery learning would be impossible and all you'd be doing is leaning on student engagement or multiple representations to help students memorize a procedure. These approaches can't help you until you've taken that fundamental step first.

In many ways, focusing on student engagement first feels like you are putting all of the onus on the student. As the curriculum designer, I'm not going to make the effort to break this down in a way that makes sense to you; instead, I'm going gamify it or put it in a context relevant to you in the hopes that you will be able to overcome the dysfunctional curriculum and make meaning of this yourself. Focusing on multiple representations first feels like throwing stuff against a wall and hoping that something sticks. Do multiple representations, but only after you've done your job as a curriculum designer and found a path I can take to understanding. Discovery learning can be guided or unguided. If it is guided, learning should be guided by a curriculum that makes sense. If it is unguided, I think you are asking a lot from the student to re-create mathematical discoveries it took the human race thousands of years to discover.

The Math Edublogosphere

Finally, there are a group of bloggers that seem to advocate an entirely different approach to curriculum design, one that focuses on mathematical thinking. I say seems to because I've had difficulty engaging with this community. My sense is that they have settled on a new normal that is different than the normal most people are on and also different than the one I'm advocating. One of the most influential bloggers in the group is Dan Meyers. It also sounds like their thinking has been heavily influenced by the Interactive Mathematics Program (IMP), a problem-based math curriculum for high schools. I became aware of IMP when I was student teaching at Brookline High School in the 1990s, but I was not impressed by it.

I may try to blog more of my thoughts on the math edublogosphere at some later point, but I thought it was worth giving you a small taste of what they do. Here are two classic problems that I'm linking to through Bryan Meyer's Doing Mathematics blog.

In this problem, students are asked to investigate the number of squares a single square can be divided into. The squares don't all have to be the same size. Through their investigations, they identify patterns and then develop rules.

In this second problem, students investigate a number of questions, such as: Will the dot always hit a corner? How many sides will the dot hit before hitting a corner? Students are able to generate and investigate their own questions. Eventually, patterns are identified and rules developed.

While I appreciate the kinds of thinking that students are asked to do in these problems, I don't sense any kind of progression (new problems don't build on top of earlier problems and problems don't appear to get any richer or more complex). There also seems to be a separation between these problems and the curriculum these teachers use to meet the standards. While I'm not particularly interested in climbing the mountain this community is climbing, I am curious how they got there. Like I said, reaching a new normal is very hard.