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.
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 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.
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.