Monthly Archives: July 2018

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 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.