On inefficiency

In the robotics and engineering class and app development courses I teach, there are a lot of group projects. I design the projects to be big enough that a single student cannot do everything.

That said, there are tasks though that a single person can do on his or her own. I always bring up the constraints of time and ask students to frequently reflect on whether the group's time is being used effectively. Three people all building a cardboard prototype for a rectangular box screams inefficiency to me. So does writing a project app from scratch when I have provided starter code to make things easier. 

From an assessment perspective, I want every student to take on every aspect of a project at some point during the semester. All of them should have a chance to write code, wire sensors together, do some fabrication, and test and develop the entire system. For a single project, things don't always work that way. We need opportunities to specialize too. 

I often need to step back within a single project and remind myself: knowing when to focus on one element, when to shift to a new one, and when to zoom out and look at the big picture - this is a skill. This skill develops over time and comes only from experience. Even adults need to be reminded (or forced) to change their perspective to effectively reflect on a process. We also need to be given opportunities to focus on a single task, leaving all others aside.

 Designing, learning, and making are inherently inefficient because the path to the endpoint is uncertain. Building something new and learning something new, are not about efficiency though. Even when we are following someone else's instructions to build a project, we might not have completed that project before. Thinking about efficiency is a useful reminder to make deliberate choices about our time. 

I asked a student about one of the classes this week. He wisely said "Mr. Weinberg, you should take the amount of time you think the project should take, multiply it by two, and then just relax. Give us time."

I often limit the time for projects because I want short design cycles. So far, the only thing that has accelerated progress is being up against a deadline. The learning that happens within that shortened time though is limited.  The rapid progress there is often because students have learned to use their materials.

Learning those materials requires inefficiency to come before it. I need to let that happen. I need to relax there.

Structures and Habits

My courses this year are AP Calculus AB, Robotics and Engineering Technology, and App Development. Given a lot of the work I knew in advance I would be doing this year, I made the explicit decision not to change the Calculus course much from what I did last year.

That leaves Robotics and Engineering Technology and App Development. I wanted both of these courses to be:

  • individualized - students would not all necessarily be working on exactly the same task as others, nor at the same level as others.
  • paced by task and student learning goals, not a unit calendar
  • centered on the process of making and creating 
  • limited in the amount of direct instruction required
  • assessed through documentation and communication of process, not skill level

There is one other critical design requirement that I want to mention.

Almost every course I have taught over my fifteen years has typically followed a gradual release of control model. Students typically start the year by following my directions closely under a lot of structure in the beginning. Then as they understand my expectations and follow my rules, I give a bit more independence to students over time. By the end of the year, we would be a close knit community that knew how to learn together.

I wanted this to be the reverse.

On the first day of each class, I gave students some ideas for what I hoped each of us could celebrate by the end of the semester. I was honest in saying that I didn't know exactly how we were going to get there.

I did say that each project would be an opportunity for students to set some goals, figure out what was interesting to them in the course of completing the project, and make course corrections as they made progress. Short design cycles would be important to doing this. There was never going to be enough time or enough resources to do everything. Playing and brainstorming, research, testing, and evaluation would all lead to some difficult decisions to be made along the way. That, after all, is the engineering process.

I decided that it was important to put this structure in place at the start, or I might just slip back into old habits. I admit after a few months of doing this that I've wavered at times, wondering if I've done the right thing. I've always come back to the fact that this feels like it is just what students need.

A New Chapter

I'm excited to share the redesign of my blog. The new site and name is to reflect my hope to focus on some different things moving forward in a shift in my role at school.

Previously, you've known me as a teacher of mathematics, physics, web programming, robotics...in short, a teacher of lots of things. I've principally been a mathematics teacher through the first fifteen years of my career, and continue to do so by working again this year with students in AP Calculus AB.

The big change is that I am coordinating the STEM program for the high school at SSIS. Thus far, I've designed a fabrication space for the high school and have reworked two classes to be based on the engineering design cycle. I'll go more into detail on both of these courses in upcoming posts. I also spend my time attempting to model the making, design, and documentation process for students and colleagues.

The guiding principle for the engineering classes is that making things is the best way to learn - probably no big surprise for those of you that know me. I'm an engineer by training and a tinkerer at heart. I've learned a lot through my own projects and want to help students experience this for themselves. So far, it is going very well.

Stick around and I'll tell you all about it.

The Computational Thinker's Classroom - Workshop Video

I ran a workshop on computational thinking at the Vietnam Tech Conference this past March. My goal was to give teachers some new ways to think about classroom tasks and the deliberate use of computers to do what they are good at doing.

The general vibe of my talk was consistent with what I've said here in the past. Some highlights:

  • We should be using computers to do the tasks that computers do well. This frees us up to do those tasks for which we are well suited.
  • Insisting on basic skills as the entry point for learning is an easy way to put students on the sidelines. Computers are often how we as professionals answer questions that are important or interesting to us. We should help students understand how to use them in the same way.
  • Spreadsheets, databases, and visual models like Desmos and Geogebra are great entry points for computational thinking. You don't have to be a coder, a mathematics or science teacher, or a technology expert to build these activities for your students.

The video is here:

If you want to do the first three activities yourself and see other resources from my workshop, visit goo.gl/vsT2G6. There is a fourth activity on the page that is mentioned at around 24 minutes in the video that is linked there too.

As always, I'd love to hear what you have to say.

Reminders for Myself

Students can go online and see more than enough videos about completing the square to require me to be the one to write steps for them.

Students can (and often do) seek tutoring outside of class to learn shortcuts to solving the most common problems.

Students can look up code that has been written before.

Students can memorize when I ask them not to do so, and choose not to memorize when I want certain knowledge to be locked in long term memory.

Students can pore over a textbook, often alone, and learn everything that might be tested on an exam. They might understand how to make connections on all sorts of scales, levels, and manners of organization with no input on my part or on the part of another student.

Given that all of these things might be true:

  • My classroom should be a place that maximizes the potential a whole group of human brains all trying to learn something new in the same space. The things we do together should respect the fact that we can do them together.
  • The focus in my classroom should be on the difficult parts of learning. Experiencing and overcoming confusion is a natural part of learning. So is trying something, failing, and learning why that something led to failure. Having good people around during this process lessens the blow. That is why we are there together.
  • I am an expert in identifying the ideal next step in the learning process for an individual, a group, or a class. I am an experienced learner. I've been there. Sharing and calling upon that experience is how I add value.
  • I should outsource instruction for those students that can learn without me. I can teach directly when students need me to do so, but this is not as frequent as I might first think. I should provide as many different resources as possible and encourage students to choose the ones that would best help them make progress. Pride when I am that resource, and disappointment when I am not, are not important. The classroom is not about me.

The structures and systems should not punish students for actions from the first list. The structures and systems in the classroom should support the goals in the second list.

Making Sense of Stories

I love stories. They capture my attention in pretty much any situation in which I find myself, and I don't think I'm the only one. Story telling has always been an easy way for me to capture the attention of students in my classroom. Each story I tell usually shares a snapshot of my life outside of the classroom. In calculus, I tell the story connecting integral calculus to the way I pester my mom by drinking glasses of chocolate milk with increasingly smaller spoons. I tell graduating seniors my story of never feeling like high school was actually over until I experienced eye-lid twitches immediately after my flight took off at the end of the summer en-route for my new college home.

I use stories as pedagogy too; there is something satisfying about talking about number sets as a series of successive inventions introduced to address the mathematical needs of humanity. Counting sheep, signed integers for money, measurement and immeasurable numbers. My intention in doing so has been just, or at least it has felt just up through fifteen years of teaching. The idea is that we start with the most basic elements of mathematics by counting, and then just add complexity as we attempt to account for the rest of what we see in the universe. If we start with the basics, and if we build up our understanding continuously from the basics all the way to the highest levels of mathematics, we are doing right by our students. As our age or number of years in school increases, the complexity increases alongside to match. This, after all, is often what traditional mathematics course sequences have always done.

The concept I confront fairly frequently is how much I disagree with the inverse of this progression. That if we do not start with the basics, then we will not get students to understand increasingly more complex material. This is most often the conversation around students that have gaps in their understanding. We can lament those gaps as teachers, and though my colleagues have always sought ways to help students across them, they can lead to conversations that make me uneasy. "Student A is not ready for X. He can't factor a quadratic."

The main reason I object to this argument is that it leads to a number of issues around course offerings and their structure. I believe curriculum most frequently becomes bloated because of the demands of courses that come after them. Colleges demand X from high schools, so high schools add to their course offerings to match those expectations. This means that high schools demand Y from middle schools, middle schools expect Z from elementary, and so on. I've argued about this mismatch of expectations about the basics across the levels in a previous post.

I am not just concerned about this in the context of mathematics.

My high school US history class twenty years ago made it to the civil rights movement in the 1960s. One could argue that understanding the 1960's requires that we understand the entire story of what happened before it. Maybe we could have moved faster over the entire year so that we could have made it closer to present day, but I don't think my teenage brain would have been able to handle a higher speed.

Must a physics class always start with one dimensional kinematics? Must we do projectile motion algebraically to really understand it?

Stories usually have a beginning, a middle, and an end. If the story of school mathematics always starts with algebra, has geometry and more algebra in the middle, and the end is calculus, students will always be waiting for us to push them forward through the curriculum because as teachers we aknow the story. In traditional timeline based history, we know what happens next because it's the next day or month in time, or the next page in the book. In chemistry, everything is made of atoms, so we have to first build atoms from subatomic particles, then combine elements into compounds, then combine compounds into reactions, and so on.

The other thing that really good stories do, however, is start exactly when and where they need to start. This is not always at the beginning of the action, when things are simple and easy. Good stories expect the audience to trust the medium to provide necessary details along the way. There is backstory, there is foreshadowing and detail and confusion - all deliberately baked in to capture our attention. This is not to say that our job is about entertaining our students. I believe that making sense of what students see in front of them is more important than adhering to a traditional notion of what is basic.

We don't have to construct a car from bolts and sheet metal in order to learn to drive it.

We don't have to understand that water is a polar molecule to understand that it freezes into ice. At some point though, understanding this might help us understand why it ice floats. It's our job to make that knowledge necessary.

The pathways we craft for our students do not have to start at the very beginning of all knowledge or content. They can start with an interesting starting point that leads to questions. They will be confused at first to figure out where they are, what is going on. This is an opportunity to teach knowledge to help students work their way out of this confusion. We can start at the big picture level and dig deeper as increasing complexity demands it. I think teachers broadly understand this on the individual class level, but that this often gets lost in conversations of curriculum or course sequence. We need to be doing more to build our courses to have more experiences like this.

I really think those of us in content based subjects need to talk to our colleagues that teach art. Their courses are often equally dense and skill based, but they take an approach to learning and analyzing that is much more along the lines of being plopped down in an alien environment, shown something novel and unique, and being expected to ask questions. What do you see? How does this make you feel? What questions do you have about what you see? Why did the artist make this choice? How did the artist achieve this result?

There are basics to be taught, but they rarely need to be the starting point.

This is where the biggest shifts in my understanding of this job have occurred over the past fifteen years. Stay tuned.

New Moves: Working With and Within

As I said in my previous post, things have been really busy over here. I made the deliberate choice to turn my attention away from blogging and toward some projects that I’ll be sharing as they develop this summer.

One reason was the realization that I felt I was connecting more to teachers outside my building than I was within. I decided to spend more time this semester walking to have one-on-one conversations with my colleagues. Some of these conversations were around the courses we taught together. Others were from the position of my role this year as department head in mathematics. And still others were about connecting on a personal level with the talented people on the high school team.

Here are a few of the ideas that have arisen from these connections:

  • We are designing a collaborative office space for teachers in math, science, and technology, along with a separate quiet space for deep work and focus.
  • We began a discussion around common language, skills, and curricular connections between mathematics, science, and social studies. Ideas like graphing, precision, and command terms could be presented more uniformly in our classes. This might mean that students don’t have to memorize three different expectations about scaling axes or understandings of the terms “compare and contrast”. We also tried some new approaches to curriculum such as population growth, and flexible ways to connect instruction where it was natural to do so.
  • We explored the need for clear but flexible grade descriptors. This lets students understand what grades mean in terms of their learning beyond a collection of points or fractions out of one hundred.
  • We started looking into a more flexible approach to courses that goes beyond an assumed traditional sequence of knowledge. The story of mathematics from counting to algebra to Calculus, for example, does not always best serve the many public relations issues associated with our subject.

Discussions within the walls of our school to think differently and plan more as a team was a valuable way to spend some of my prep time. I continued to seek balance in the time I spent on school projects and projects at home. This meaningful work did not happen by accident. It takes a commitment of time, and a subsequent decrease in time devoted to other things.

This has resulted a redefinition of what I need from (as well as what I can best provide) my personal learning network. The ideas I get from Twitter and reading blogs still keep me energized and encouraged to try new things in my classroom. Sharing what I do myself has admittedly taken a back seat. I’m looking for ways to help shine light on the great things that others are doing in our school. I’m inspired by what my colleagues have helped students do over the course of the year, and I want others to be inspired with me.

There is a lot more to this change in focus. More on that soon.

From the Archives - Notes Before A Move

It has been quiet over here on the blog. You haven’t missed anything - things are fine. I’ve been running on many cylinders and focusing on some big projects in the works.

I’ve been thinking a lot about the concept of school and why we do what we do. I was reminded while looking through some old files that I had written a long-form article back in the summer of 2010 before moving overseas to teach for the first time. It was an attempt to make sense of the many lines of thought I had about the public school system in general after teaching in the Bronx for six years, and one year at the KIPP NYC College Prep high school. I was not blogging at the time, and did not have a good place to put this beyond emailing it out to some close friends.

I still think it represents my long held belief that we are at our best when we choose to talk and listen to one another. Demonizing one another does little to make progress.

We need a reliable and effective educational system. This fact is obvious to most people. Politicians know that making sound bites that state this fact is necessary to win elections. The difficult part comes when individuals attempt to define precisely what they mean by 'reliable' and 'effective'.

When informing people that I am a teacher, responses are always delivered with a healthy mixture of three main themes: acknowledgment of the difficulty of the job, its importance, and a statement on how teachers are not valued in today's society. What follows is also like clockwork: a sip of a drink, a statement about the “other hand” - at least teachers get summers off and can go home at three. Sometimes I explain other realities of the job (such as grading or the intricacies of lesson planning.) Other times I just nod and accept that most people lack an understanding of how much work is involved in good teaching (both inside and outside of the classroom) or in developing into a better teacher after each day's set of experiences.

As has been said many times before, good teaching is both an art and a science. Teachers will then admit (often when out of hearing range of administrative judgment) that good teaching is an iterative process. There are good days and rough ones, engaging lessons and unintentionally boring activities, and even times when a potentially good lesson fizzles because it meets a particularly fickle developing mind too soon after lunch. While principles of psychology, child development, and principles of cognition can shed significant insight into what should work well in the classroom, teachers are expected to also use a great deal of intuition and experience to figure out what will work best to help students achieve their learning goals and meet standards. Students are, after all, people, not machines.

It is also fairly obvious that the concept of accountability in the educational system is here to stay. This is not in itself a bad idea – given that most people agree about the importance of education, distinguishing an effective educational system from a less effective one is necessary to iteratively reach a system that works well for its students. The devil is again in the details. Teachers, administrators, political leaders, professors, statisticians – they can all be as different in their approaches as there are students in the New York City educational system.

I will now admit one of my own mistakes as a teacher: I have punished an entire class of students for the actions of a few. It never gets me the results I want, and when I have thought about it afterward, it never makes sense. Many students do the right thing on a regular basis – why yield control of the class to the few that least are able to handle it? These individuals often need to be managed in a different way, time, or setting. When I do handle things in this individualized way, as difficult as it can be with a larger class, it always works out in a more positive way for both myself and the involved students.

The logic of a one-size-fits-all solution does not make sense in education. So why is it so common? Our community grapples with the difficulties of reconciling the practical side of accountability with the ultimate goal of educating youngsters to become informed and responsible citizens every day. And yet, we frequently see solutions or policies that attempt to reduce complexity to the singular innovation, classroom structure, or educational program that will fix all of the system's problems.

Furthermore, many people in our field strive on a regular basis to paint a picture of other players as being woefully inadequate, incompetent or immoral, even though these may be a small fraction of the whole. Principals complain about veteran teachers that refuse to try new things and are difficult to fire because of union rules. Teachers that join the profession through alternative routes cry foul when some principals seem concerned only with pass percentages or when a veteran teacher does not take the time to grade nightly homework. A public school parent wonders why his son's new science teacher, who cannot control a class, replaced one with more experience who was fired because he refused to write a whole new curriculum without being paid for the time. A community member might see charter schools as elitist and unfairly funded, but a student attending a charter might just as easily wonder why she could not get the personal attention she needed from her old neighborhood school.

The fact is that the entire spectrum of humanity, from crooks to tragic idealists, are present in our system. There is also a substantial population on the other side of the coin. There are parents that want to help their children with homework but do not know how. There are new teachers that are willing to work long hours to write lesson plans, but do not know that the secret of teaching addition of fractions could be revealed in a minute long conversation with a veteran. Furthermore, there are veteran teachers that have legitimate concerns about policy changes based on their past experience, but their voices are drowned out by others labeling them 'naysayers'.

To frame the debate by assertions from one group on how much another group cares (or does not care) about children and their education is completely unproductive – all of us want the best for the children in our system. There are many innovative, talented, and passionate people that want to work hard in a system to help children make meaningful progress in developing skills for future success. To also claim, however, that moving forward is impossible because of a minority is just as illogical. There are ways to include everyone in the process and discuss how to lead students to develop good character traits and be prepared for their own academic goals.

The primary flaw in the current administrative efforts is in looking for the system that will work for everyone, rather than the people that will make the system work for all. Teachers are often told to differentiate instruction, which means to optimize classroom activities to help and support students of all skill levels to reach specific learning goals. All students are not the same, and neither the paths they follow to to reach their academic and character goals, nor the support they need along the way, will be the same. Why do we look for solutions that are not differentiated in this manner?

The energy crisis will not be solved by just solar power, or wind power, or biofuels. It will be solved by solar power and wind power and biofuels and conservation and the development of new technologies and the adaptation of some old ones. There is no silver bullet; there is, however, a combination of different energy sources that will together bring us a more stable climate, a more stable economy, and a more sustainable lifestyle for people around the world.

Along the same line of reasoning, just creating a system with more charter schools will not solve our problems if the human capital needed to run them is not developed concurrently. Changing the system to one that closes failing schools and replaces them with the same administrators and teachers and conditions that led to its downfall is not the answer. More testing is not the answer, but eliminating testing will not work either.
We need to better support neighborhood schools and the people that work within them and have a system that supports charter schools. We need a union that works to support and protect teachers that might agree with the goals of the administration, but not the methods they use to reach them. We need to study both effective charter schools and effective traditional schools for the successful elements they share. We need to innovate to find ways to emulate the positive aspects of both and invest in people to do the extra work necessary to adapt and run these systems in effective ways. We need to find ways to unite the experience of veterans with the energy of new teachers and alternative certification programs like Teach for America. We need not to spend late nights reinventing the wheel while veteran teachers are eager to be heard.

An earnest effort to invest in and support the people that make these systems work is the other crucial piece that is necessary for the system to improve. Systems that depend on human talent and ingenuity (as education does) cannot be duplicated by simply copying the structures produced by effective educators. One educator may make use of a word wall effectively to improve his or her students understanding, but simply insisting that every classroom have a word wall does not make every educator effective.

A podcast made earlier this year from This American Life, a production of WBEZ in Chicago, described an interesting collaboration between Toyota and GM called New United Motor Manufacturing Incorporated, or NUMMI. Workers from GM traveled to Japan to tour the Toyota plants and explore the structures in place. Many of the workers that traveled were experienced machinists that had spent years doing the same thing over and over again in the plant, and were disillusioned by the mechanical nature of their job. The success of the Japanese system relied on the observations and ideas of individual workers along the assembly line working together and alerting each other when there was a problem. When the assembly line stopped because of a problem, a playful tone would play throughout the factory so that individual workers would know which station needed assistance. Floor managers would work to divert workers to assist the troubled station until the issue was resolved. The end result of this system was a higher productivity, higher quality product, and increased pride on the part of the workers constructing the cars. The American workers were energized by the visit and left Japan inspired and ready to apply the lessons learned to the factory floor back in the United States.
Initially, management was excited to call upon the new energy of the returning workers. These managers attempted to copy the exact structure of the plants in Japan, down to the alignment and arrangement of the individual machines on the shop floor. They opted not to invest the same energy and money in establishing the systems that supported the people in the assembly line. Penalties were instituted for halting the assembly line, and workers would snitch on each other to enhance their reputations with managers. In the end, the same problems experienced by American plants before the collaboration still occurred. What remained was an unhappy workforce, and a factory that looked just like the plant in Japan, but with none of the productivity.

Cookie cutter solutions appeal to the preference for simplicity built into the human mind. They are shortcuts, which are dangerous if used without understanding what is cut out for the sake of speed. Charter schools do a lot of good for the students that attend them, but that does not mean we need many more charter schools - there are both effective and ineffective ones. Research that shows that Teach for America corps members can help students make progress on a level comparable to teachers with more experience, but that does not mean we need more Teach for America corps members and fewer traditional teachers.

These represent individual pieces of the solution to the difficulty facing us in reforming the educational system to work better for its students. The key is to figure out how to make the most of all of the different talents and capabilities of all of the people in our system to do this. This is not about stating which group is the greatest obstacle to progress. The system will only improve if we figure out how best to inspire and support the people working within it. Each of us knows what is at stake.