Minecraft: Soma Cube

I recently came across a very interesting puzzle called the Soma Cube. It was invented by a Piet Hein, a researcher who was feeling bored during a lecture by Werner Heisenberg in the 1930s.

The puzzle is a 3 x 3 x 3 cube made up of seven pieces. Six of the pieces are all possible arrangements of four individual cubes, not counting rectangular prisms. I gave my students centicubes and asked them to see if they could come up with all 6 unique pieces:

This led to rich discussion about piece A and B. They are mirror images of each other and there is no way to rotate or twist piece A to look like piece B, or vice versa. (Fun fact: this property is called “chirality“)

Once we made the pieces, we attempted to assemble the Soma cube. This tasks takes a lot of patience, some luck and a good head for working systematically. For example,

• How do you know you are not attempting a previously failed solution, just rotated?
• Is it possible to be “one cube” away, change a single block, and complete the puzzle?
• How do you document your solution?

Some students completed the cube three or four times, and others eventually gave up and followed a guide. I saw that some students who followed the guide ended up creating their own unique solutions once they saw that it was possible.

Indeed there are around 250 unique solutions to the Soma cube, as well as an entire library of alternative shapes you can construct from these pieces:

One question that came up frequently was “How do we share solutions?” This was a good question. It is not easy to take apart a structure built with centicubes layer-by-layer as opposed to piece by piece. One idea I came across in a text book was to teach students the idea of a height-map.

A height-map allows you to see a 3D object in a flattened 2D view. What if instead we replaced the heights with the colours of the blocks themselves? Then, anyone who wanted to recreate a student’s solution could simply copy over their colour pattern and build the blocks from the ground up. I wondered what the best way to do this would be…ENTER MINECRAFT!

I created a Minecraft world and called in “Soma World” (download link). It gives students a world where they can build their Soma Cube solution in a collaborative and easy way (much easier than if they didn’t have access to this technology) and share their solutions.

The engagement and interest in this topic was off the charts. As time went on, I made characters inside the world of my students who had become Soma Cube masters (I think at one point a student had come up with 14 unique solutions to the cube!)

Minecraft allowed me to think about my learning outcomes from a SAMR perspective. Let’s pause and have a look at what SAMR can tell us about using Minecraft in this context:

• Substitution:
  • “Use Minecraft to build a Soma Cube by yourself.”
    • As you can see, this adds almost nothing new to the experience. In fact I would argue this detracts from the core learning of using your hands and eyes to feel, turn and join blocks into coherent shapes. Abstracting this important task into simple taps on glass is a poor substitute.
• Augmentation:
  • “Use Minecraft to build a Soma Cube collaboratively with a friend”
    • Teamwork is a critical outcome woven through every skill strand in the curriculum. Minecraft is not essential for collaboration but watch students work together inside a world and you will see incredible levels of engagement and teamwork.
• Modification
  • “Re-create your Soma cube in Minecraft. Take pictures to show each face and then write an instruction manual in Minecraft. Share your book with a friend. Swap cube instructions and try to build each other’s solutions.“
    • Ok! Now we have a task that asks our students to transfer their knowledge from one setting to another setting: IRL to Minecraft. Then, we ask them to select what parts of the cube are relevant and create instructions. This is about as far as I got with my students for this mini-project.
• Redefinition
  • “Code an agent in Minecraft to build your Soma Cube Solution”
    • We never got this far, but as you can see the ability to climb up the SAMR ladder is easy when you are using software that encourages emergent play. Coming up with ideas for “redefinition” is often challenging, and it should be! By virtue of the fact that redefinition tasks should be “previously inconceivable”, creating learning experiences that redefine what is done in the classroom takes trial and error.

Once students finished the world they were very proud of themselves and each one came away with deep knowledge about the content. As I teacher, I also had an assessable piece of work: the student’s exported PDF journal. These were constructed with rubrics we made before hand and allowed me to give direct feedback to my students.

You don’t have to print out their work in the digital space, and there is probably arguments to be made for reasons why you shouldn’t. However I have found that there is nothing quite as engaging as written feedback from a teacher, even for work that is almost 100% digital.

In fact, when you do this your students will also start to view Minecraft the way you do, as a learning tool. This has lots of benefits as you progress down the road of incorporating Minecraft into your classroom.

@jessesblack