Computational thinking

Now that I have a year under my belt, I would like to think that I'm a little wiser. I know how to be really, really inefficient while planning lessons. Goal number one of next year: be a little less inefficient.

A chief cause of the hours I would spend planning a poor lesson was an overload of ideas and resources. I would spend far too long reading through ideas, half starting, and thinking. Then I'd run out of time, underplan an inquiry-based activity, and run a bunch of copies of worksheets. During the lesson, I'd get frustrated by the students' lack of initiative and interest (caused by a lack of support and clarity).

And repeat, day after day. Lots of time spent planning lessons that could have taken ten minutes to plan.

I would like to be a little less inefficient.

My plan is to focus on one specific framework. Instead of trying to do many different things because their cool, I want use a more focused set of ideas to both give my teaching more consistency and my planning more efficiency.

Framework: Computational Thinking

What is computational thinking (CT)? Combine critical thinking with the power of modern computing. This is not trivial – it is a significant shift in how we develop students' ability to solve interesting problems.

There are several ways of breaking down CT. Google and ISTE both offer definitions and resources. Some computer science curricula, Exploring Computer Science and CS Principles also offer approaches and resources, but are more computer science centric. The point is that there are resources available and many smart people who think this is a valuable approach.

But, to make this really clear, I think it's best to present an activity, and contrast a more traditional approach with a CT approach.

Activity: Review solving linear equations

Traditional approach: Model solving a few. Perhaps have students justify the steps to underline the idea of equality. Then have them practice – either alone or in groups. You could mix it up and play the mistake game if you're feeling different, or play a row game.

CT approach: Write a linear equation on the board with one unknown. Have students tell you how to solve it, step-by-step, but be an absolute pain in the ass. Do only exactly what they say. Make them justify their steps. Ask if you're done after every step. Do a couple of problems like this.

Why? You're going to focus on solving linear equations as an algorithm. Ask the students to write an algorithm to solve any given linear equation. Explain what you mean by an algorithm – a very precise step-by-step set of instructions that a trained monkey could use to solve an equation.

Teaching in Wisconsin

The Background

In the past year and a half, teachers in Wisconsin have been in and out of the national spotlight after our governor's attack on collective bargaining rights. The bill sparked massive protests for weeks around the state capitol, and ultimately passed through a budgetary process. The law that was passed, known as Act 10, severely diminished the powers of unions and increased contributions to benefits. This was a leading cause of the unsuccessful recall election that took place recently.

After Act 10 became law, there was a great deal of uncertainty about how districts would use their new powers. As it turns out, my district is going to be the first one to really put them to use and experiment. It was announced after spring break that in the future, nearly all high school teachers now are teaching the entire school with no prep period. In the core departments, this lead to approximately one out of every four teachers in the department being laid off. The remaining teachers will receive a bonus stipend of $14,000. In many respects, we now have a spotlight on us from across the state.

My Experience
I don't write all of this to complain. I simply want to relate my experience of becoming a new teacher and completing my first year during this time as I think we are at a crossroads in education in Wisconsin, in more ways than one - how we teach, how we're judged, and what society believes about teachers.

The climate has been decidedly negative. Very few people encouraged me to become a teacher, but more people than I count have questioned me. Or simply told me it's a poor choice. These voices have been inside and outside of the school, and the story they have been telling is the same: "You don't want to get on this train. It's breaking down and heading toward a cliff. There are better things to do with your life."

Perhaps. There are changes coming, definitely. I doubt the wisdom of many of them, but I also know that this where I am supposed to be.

Teaching is a strange profession. It seems that people either (a) think we're doing a truly noble service, or (b) think we're parasites who deserve less than what we earn. I have a lot of support - parents, students, friends, and community members who genuinely thank me for my daily work. And then I balance that with the looks of condescension and judgment, or people shouting "f@#$ you" out of their car window at me on my walk home because of a pin on my bag.

At the end of the day, and the end of the year, I haven't decided how I feel or what I think. There's not a single way that I feel about teaching in Wisconsin right now. I love teaching - I know that - but teaching in Wisconsin right now is too complex to relate without several hours and a few pints. I don't know how long I'll be able to deal with the negativity and pressure.

It's hard serving in a community that proudly voted nearly 3:1 for a governor that has extremely little respect for educators. I try to remind myself that I'm here for the students, but it is going to be my blood, sweat, and tears that make these new changes successful. What I fear is that my success is going to be used as proof of the validity of their ideas, even though they have handicapped me in an insulting manner.

But that's not going to stop me, because I love this state. We have an amazing tradition of progressive thinking and high quality education (see: The Wisconsin Idea). Further, the people of this state are genuine, friendly, warm, and hard working, even if that doesn't seem to always be reflected in our politics. Politically, we are severely divided, and I am clearly in the slight minority. There are many, many people with us, but just a few more who disagree with us.

I don't know what the future holds. I'm anxious about the teacher evaluation system that is now being piloted in a number of schools. I'm anxious that Wisconsin's commitment to a nation-leading public education system is slipping. I'm anxious about the quality of minds and characters who are going to volunteer to teach in this climate.

I'll be here next year. I am committed to this state and want to believe that Wisconsin will keep bending toward justice (great article by John Nichols). But I do have some serious doubts now, and that is new.

An equation is a problem...

I have been teaching algebra 2 for about three weeks now, and I've noticed some serious deficiencies in my students' understanding of algebra. We have been reviewing the basics - solving linear equations and inequalities, graphing, and working with absolute value. Students are consistently making the same mistakes - their typical response is a vacant "oh", followed by a quick fix, and I'm struggling to help them understand what is happening.

I've been scratching my head, rather anxious about our prospects of success. Our algebra 2 course is essentially a class about the major functions of mathematics - polynomial, rational, radical, logarithmic, exponential, and trigonometric. For each unit, we do the same set of things - graph, solve, and model.

After working with them for a couple of weeks, I developed a suspicion that they don't really understand what we're working with - specifically, the equals sign. They can somewhat reliably graph and solve basic equations, but I've seen little evidence that they understand what these actually represent.

So, I took five minutes from class yesterday and had them answer a few questions. Here are the questions with some typical responses:

• What is an equation?
• A problem that can be solved mathematically.
• Something that has an end solution through multiple applications.
• A problem you solve to get an answer.
• It is a sequence of #'s and variables, and your job is to find the right answer to it.
• Numbers or letters used to represent or solve something.
• What is a graph?
• A grid where you plot points.
• A typically square thing you draw a line on.
• Where points are plotted and to show increase and decrease.
• A graph is a visual equation.
• A graph is like another way of showing your work when you solve an equation.

While there are some glimmers of hope in there, I think this is going to be a barrier for us. Students will not be able to reach the depth of understanding that I desire unless they understand what that damn equals sign actually means. And I think this boils down to looking at operators, relations, variables, constants, and expressions. Maybe not using that language, but building on those ideas.

So, here's my plan. I'm going to students do an open sort with the following:

• Relations: =, <, >, ≤, ≥
• Operators: +, -, ÷, ×
• Variables: x, y, z
• Constants: 0, 1, 2, 3
• Expressions: 3x + 4, 5 - 1, 4ab
• Equations/inequalities: 2x ÷ 5 = 4, 2 - y < x, 5a ≥ 8b, 1 + 1 = 2

After the items have been sorted, I'll encourage student to create a hierarchy of their groups. I really want to focus on the groupings - what do things have in common, how are they different, and what do they represent.

In the end, I'm hoping that my students have a better understanding of equality as a relationship, and that an equation is simply a statement that two expressions have the same value.

I would really appreciate any feedback before I give this a go!

The Mulligan

I don't love the block schedule. I'm not sure I even like it, and I'm not sure it's good for teaching math.

But, as a first year teacher, there are two significant benefits:

1. Reduced number of preps
2. I get a mulligan halfway through

I'm pretty excited about #2 right now. Now that I have half a school year under my belt, there are about a million things I want to change, and some of the changes just work better when you get a new class. Here's a short list of changes I'm thinking about:

• Change the purpose of the openers
• Start student portfolios
• More mid-block formative assessments
• Make whiteboarding and sharing an everyday part of class
• Better cooperative group activities with individual accountability
• More emphasis on communicating reasoning
• Preparing for student mistakes instead of helping them avoid them
• More consistency is the handling of assignments
• Focus more on connecting with student
• Focus less on the real word justification of the mathematics
• Connect mathematical reasoning to students' lives more often
• Follow through with consequences more consistently
• Make better use of our weekly trips to the computer lab

The new term starts next Tuesday. While I'll certainly try to work on all of these, I'm going to pick two or three over the weekend to really set my sights on and reflect on in more detail. More to come later.

Becoming A Better Mathematician

A year ago, there were two Project Euler problems that really gave me headaches (#26 and #34, if you're really interested). I remember spending hours on them to no avail. This was frustrating, especially with how I work. I ended up skipping them and moving on to other problems, but that kind of thing doesn't sit well with me.

So I took them up yesterday, and surprisingly, solved both without a terrible amount of trouble or time. I could chalk this up to simply taking a break and seeing the problem in a different light - which has worked for  before - but I think it's more than that. Teaching high school mathematics has made me a much, much better mathematician.

While this certainly gives me a personal sense of accomplishment, I'm more interested in the specific things that have made me a better mathematician and how I could use these in my teaching. Reflecting on my work yesterday, there were a few significant changes in the way I was working:

• Make big problems small
• My go-to approach is to plug some stuff in a small example, see how it works, and look for some kind of pattern.
• Slowing down
• I was solving for slowly - once I had an idea that I thought might work, I took the time to think/write out my reasoning before getting started on the solution.
• Starting over
• I was much more ok with completely scrapping something and starting in a new direction.

These are nothing revolutionary. Far from it. They are things I've heard and read before, and things I (sometimes) try to incorporate into my teaching. But there is something about experiencing this first-hand that really drives it home.

What's my take away? This needs to be a more conscious part of my teaching. It's not going to change a student in a day. It might now show up on a test. But at the end of the year, if I've done my job right, there will be a whole new level of problems that a student will now have the ability to take on. The process is slow, but without fruit.

I also need to keep doing mathematics. Whether it's inside the classroom or out, it's not an indulgence - it's a professional development necessity.

New Year's Resolutions

1. Run - three to four times a week. It makes me a happier, healthier person. I just need to commit to the time.
2. Read - at least one book a month.
3. Blog - one new post a week, even if I don't feel like I have much to say. Because when I start writing, I find that I always do.

School of One

I've recently been asked to help develop a pilot "School of One" program in our district. For those of you not familiar with the project, take a look here. Basically, here's how it works.

1. Student comes into class and looks at their "playlist" - their options for what to do today.
2. Student makes their choice. This might be small group work, tutoring on a computer, direct instruction, etc.
3. Student gets started.
4. Student takes short formative assessment.
5. Teachers feed results into algorithm for all students.
6. Algorithm output lessons and activities to be prepared.

And repeat.

The more I think about School of One, the more ambivalent I am. There are some really amazing ideas and opportunities here, not the least of which is that students are given a higher degree of control and power over how they spend their time. To me, this is the benefit. There are others, to be sure, but I think that they all really revolve around this. Choice allows education to become more personal, more meaningful.  Instead of being instructed exactly the same way as your other 29 classmates, your path is unique, based on who you are, what you're good at, and what you want to do.

I am excited to be involved, but not without some concerns and doubts. Rather than approach these as reasons not to help, I'm looking to these as the points I'll want to make sure are addressed by our work. It is the reason I am writing this post and the reason I hope you will help!

Feedback and assessment
As feedback has been one of the items I've been focusing on this year, this one concerns me. The only assessments built in are the short formatives given to student at the end of each lesson. The results are then fed back into the algorithm. If the student has demonstrated mastery, they move on. If not, they'll have to do a lesson based on the same objective again. Students involvement in this process is minimal, and there is essentially no feedback given to students. I don't like the idea that we just have a student spend another full lesson on the same content without any feedback other than the fact that they didn't get it yet. We need to do better than that.

The algorithm
This algorithm is basically supposed to work like Pandora or Amazon's suggested items. Based on your history, the available resources, and people like you, the algorithm suggests the lessons that will be the most productive for you. Without a doubt, a clever idea. There's a lot of faith placed in the algorithm, and yet remarkably little is shared and public about it. It was developed by a for-profity ed company, Wireless Generation, which is now owned by the News Corporation. That in itself scares me a bit, but I can get past that because we're almost certainly not going to be able to use it.

What scares me about the algorithm is its potential to render a teacher's observations and professional judgment inconsequential. I do not want the role of the teacher to become something like a machine operator. The entire process needs to be within our control, which includes the inner workings of the algorithm. My fear is that the central piece of School of One, the algorithm, is a proprietary blackbox.

The algorithm needs to be open source. It needs to be available to anyone and everyone, free, and without any restrictions. This process and how lessons are sequenced and chosen cannot be a proprietary secret if we really think that this model has the potential to change how we teach. Do not make this simply a tool that teachers use. Make it one they control.


The big picture
Each day's lessons are chosen based on a fairly specific roadmap of objectives that need to be covered. Even though the students path will be personalized, I'm a little anxious that we're not going to be taking students off of the path enough to really show them the world. Mathematics is much, much more than a series of facts and processes. It's a way of making sense of the world. I'm not sure how we're going to roll this in, but it will be a failure if we don't.