Transformations with Scratch

Students need to do more

I don't mean problems. I mean building. Creating. Writing. Designing. I think it can be amazing [read: tragic] how little students actually produce in a typical math class - no wonder math is often perceived as abstract and disconnected from the real world.

Having students do more is good for about a million reasons. They provide a firm foundation to build on their prior knowledge and experience, formulate questions, climb the ladder of abstraction, and experience how math is connected to the world they live in. And the best part? The result of their growth is concrete. It's not a completed worksheet, or a good grade on a test. Maybe it's a video, or a presentation, or a programmed simulation, or whatever. The point is that it is something much more real.

Challenges

That all being said, there are reasons why projects aren't the norm in math. I know some schools have taken bold steps and are letting going of pre-determined curricula in place of project-based learning and student-driven inquiry, but they're the minority. And not my school.

In a typical public school, I think these are the main challenges for using projects in math: 

1. Finding projects that fit the unit.
2. Student expectations of what math class is.
3. Presenting the projects to students.
4. Assessing the projects.
5. Instructional time.
6. Planning time.

My plan is not to solve all of these challenges this year. My hope is to create some space and a framework that allows me to insert projects more frequently.

First project: Transformations with Scratch

I participated in a CS4HS workshop this summer and was introduced to Scratch. The best way to learn what it is is to play with it. Go ahead, it's a free download, cross-platform, and fun.

The first project of the year for my geometry students is going to be creating a 30 second animation with Scratch. I like this it introduces programming as well as gives students a deeper experience with transformations. 

Here's the handout for students that I will use. The front side presents the task and details to the student; the back contains the rubric by which the projects will be assessed.

Scratch project

I could greatly use some critical feedback before I give this a go. Design, language, rubric, whatever. The "product" part of the rubric definitely needs improvement, but I'm having trouble describing what it is that I want students to produce.

After this project, I plan on tweaking the setup and then using this as my template for the rest of the projects. Hopefully it will making creating new ones quicker and easier!

Geometry summer curriculum work

This summer our department was given some curriculum hours to develop/reshape our geometry courses in light of the Common Core State Standards (CCSS). I'll assume that you know something about this - I just want to share the process we went through and where we are currently.

At the beginning of the summer, we had a consultant give a short workshop for math teachers in our district. To be perfectly honest, I didn't find it incredibly helpful - possibly because I'm not that long removed from my certification program, where the CCSS were the only standards that we worked with.

But, I did take one quite useful idea from the workshop - a process for breaking down the standards into something that we can get a better grasp on. I turned that process into a sensibly designed Google Docs template to facilitate our summer work.

So how did this work? Well, as a starting point, we decided to base all of our work of the suggested "pathway" from appendix A of the CCSS for mathematics. Within each unit, we looked at the different clusters. We decided that, for the most part, we're going to teach mini-units based on clusters.

For example, here is the first cluster:

Reading through this it makes sense, but this is where is becomes more real. How we turn this into what we're teaching? We considered just making these our direct standards, but there was some messiness there. Concepts overlap, others would be difficult to assess, and so on.

This is where breaking them down became quite helpful. For each cluster, we created a document that broke down each standard into the what and how. Looking at these all together, then, we would create our standards. We used some standards pretty much directly. Others we would combine, tweak, and interpret. Some standards we decided were things we would do/teach in class, like G-CO.4, but we wouldn't make them standards for assessment.

For the above cluster, this is how we broke the standards down, and these are the standards we developed:

1. Geometric definitions
   Identify & precisely define angle, circle, perpendicular, parallel, & line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
2. Transforming figures Reflect, rotate, and translate figures.
3. Identifying transformations Identify sequences of transformations that carry a given figure onto another.
4. Transformations as functions Describe a transformation as a function in the coordinate plane.

Now these are standards that I'm more confident that I can teach and assess.

What we're currently working on & where we're going

We're done with everything above, and we're finishing writing small formative assessments for every standard. We're then going to pull them together, tweak them, and create the summative assessments. Our school implements a 80% summative, 20% formative grading policy, so we're somewhat forced to break things down like this. I probably wouldn't otherwise.

This was all rather mundane work, and I have a hard time calling it "important", especially considering what we might have done with our time otherwise. However, whatever gripes you may have with national standards, and I have several, we are legally obligated to teach them, are students are going to be judged on how well they know them, and we're likely going to be judged on how well our students do. So, in some manner of speaking, this was important work to complete.

There's clearly something missing from this model. It treats math as the sum of the standards, when it should be so much more than that. At the beginning of the summer, we were hoping to include a "cluster question" within every cluster of standards that would be an interesting problem, application, project, or whatever that uses the main idea of the cluster. We didn't have time to develop them, but those could help.

Incorporating the practice standards will help. I'm going to try to use them daily to guide my teaching. But what I really want to do is use this work as the base for turning geometry into a project-based course. We'll have a solid grasp of what our students need to learn, along with some of the how. With this foundation laid, I think we could do something really special while respecting our commitment to teach the standards.

Transforming geometry

I never wanted to teach geometry. It bored me in high school, and I could never get myself particularly excited about the side splitter theorems or, well, anything about it. Ick.

So naturally, geometry was and is one of my main course assignments as part of my first teaching position.

Goal: make geometry interesting to teach and learn. Or, at least suck less.

There are two reasons that this might actually happen - The Common Core State Standards and computational thinking.

Common Core

 The first one is that the Common Core State Standards (CCSS) changed the focus of high school quite significantly by giving transformations a central role. Our department made the decision to embrace this direction and go with it. This summer we've been taking the suggested sequencing from Appendix A, and then interpreting and translating this into a curriculum that we feel we can teach. If you want to a gander/copy/steal, our work is here (and still changing):

• Unit 1: Congruence, proof, & constructions
• Unit 2: Similarity, proof, & trigonometry
• Unit 3: Extending to three dimensions
• Unit 4: Coordinate geometry
• Unit 5: Circles
• Unit 6: Applications of probability

Now these alone aren't going to make geometry awesome, but I think that they do provide an improved sequencing and emphasis than a traditional geometry course. I'm also just getting a start on writing some assessments which is highlighting how different the approach is. I'll post more about that later.

Computational thinking

This one has me much more excited. I already wrote a post about what it is and why I've decided to use it. At a high level, think of computational thinking as combining critical thinking with the power of computing, an incredibly relevant approach.

Now that may not sound like it has much to do with high school geometry. High school geometry is traditionally a very abstract course where students are first introduced to mathematical rigor and proof. Unfortunately, we can fall into teaching geometry as a means to end (teaching proof), and we lose some of the utility and concreteness of geometry. After all, geometry is shapes!

So with that motivation, I want to consistently incorporate computational thinking practices into geometry. I want to make geometry a more hands-on and practical course. I'll still teach proof & rigor, but I want students to associate geometry with geometry rather than proof.