**Week Twelve Essential Question: **How will I demonstrate impact on student learning as a result of my differentiated lesson?

Here are the first five Alaska Mathematics Practice Standards and my thoughts on how Minecraft can be used as a tool for differentiated student learning in alignment with each standard.

**Make sense of problems and persevere in solving them.**

Minecraft offers problem solving challenges to everyone from the first time user to the most expert gamer. In the MinecraftEdu Tutorial World, players discover how to maneuver around and dig, build, and craft in Minecraft through experimentation, with very minimal direct instruction provided through information posted on walls and signs. Tutorial World is designed so that you learn how to play Minecraft by playing Minecraft. There’s no penalty for making mistakes; you don’t “die” if you do something wrong. You can try something over and over until you accomplish that task, and then try it some more if you want to improve your skill. Or move on to the next challenge; it’s all self-paced, so it’s up to you.

Once you’ve mastered the basics, you can play in Survival mode where your ability to survive and thrive depends on discovering strategies to provide yourself with food and shelter while defending yourself against various enemies and hazards. Even in the digital world, survival and material success are both pretty powerful motivators. In Creative mode, you are immune to all damage and have unlimited resources and the ability to fly, thus freeing yourself up to create fantastic structures. Curiosity and creative energy are the primary motivators here.

My limited observations of students in Minecraft has indicated to me so far that almost all students will persevere at tasks in Minecraft. Whether they persevere at the task the teacher has set or some other (off-task) objective of their own invention is another question, but in the classes I’ve observed, every student remained engaged with Minecraft even when they were off-task from the Minecraft assignment given by the teacher. I can’t say the same for textbook or workbook assignments in any class I’ve ever observed.

I have observed some students, myself included, reluctant to enter into Minecraft. I watched my own son play for at least two years before I ever mustered the courage to take the mouse and keyboard myself and see what I could do. I have seen a few students sit rapt beside their partners while their partners controlled the mouse and keyboard. The observing students were interested and engaged, talking with their partners and making suggestions; they just weren’t actively maneuvering an avatar in the Minecraft World. In each case, I managed to persuade the reluctant observer to take the mouse and keyboard and learn how to look around, move around, and build and dig within just a couple of minutes. I strongly recommend sending every student through Tutorial World, in control of his or her own avatar, to help students overcome their doubts about their Minecraft abilities.

Ideally, first time players would have a mentor nearby who would give little hints and tips whenever the novices showed signs of frustration, and who could answer questions without giving away too much. I think it is very important for the mentor to say and do as little as possible to leave most of the problem solving and discovery up to the new player. This allows the new player the satisfaction of true accomplishment and provides a big confidence boost, especially for reluctant players.

**Reason abstractly and quantitatively.**

Some of the various subparts of this standard include:

- represent a situation symbolically and/or with manipulatives
- represent a situation symbolically and carry out its operations
- create a coherent representation of the problem
- make sense of quantities and their relationships in problem situations
- consider the quantitative values, including units, for the numbers in a problem

Minecraft is an ideal “digital manipulative” for reasoning abstractly and quantitatively. Students can represent situations symbolically, from simple geometric shapes to complex engineered structures including working machines and computers (using special redstone blocks to create circuits). The uniform cube size of blocks in Minecraft makes them ideal for keeping track of units and quantitative relationships.

**Construct viable arguments and critique the reasoning of others.**

Because Minecraft offers students a concrete visual way to represent their thinking and their solution to a problem, it provides an excellent platform for students to present their arguments and critique each other’s reasoning. For example, if you give students the challenge of constructing a bridge, students can build their bridges, explain their designs to each other, and critique each other’s designs. Students can use screenshots to show their work, or students playing in the same multiplayer World can tour the World together to view each other’s structures.

**Model with mathematics**

To me, this standard presents the most obvious fit to Minecraft (next to persevering in problem solving). Here are some of the subparts of this standard:

- identify important quantities in a practical situation and map their relationships using such tools as manipulatives, diagrams, two-way tables, graphs, and formulas
- apply mathematical knowledge, make assumptions and approximations to simplify a complicated situation
- analyze quantitative relationships to draw conclusions
- reflect on whether their results make sense
- improve the model if it has not served its purpose

Several sixth grade students at one of our local middle schools have taken on the challenge of modeling in Minecraft a real world problem that requires a real world creative solution: a massive debris flow, a sort of slow moving landslide, is plowing inexorably toward the Dalton Highway and the Alaska Pipeline just south of the Brooks Range. Colin Osterhout created a World that simulates the terrain in the area of the Monster Lobe, and Technology teacher Ray Imel has guided the students in developing their ideas for potential solutions to the problem. The students are now exploring ways to model the debris flow itself with Minecraft blocks, and to model the structures or strategies that might protect the highway and the pipeline. Because it is relatively easy to modify their creations, students can engage in a recursive design process to refine their models. While Minecraft cannot mimic reality perfectly, it invites students to reflect on the most relevant elements of the problem to model and gives them an exercise in recognizing and articulating the limitations of their model and what real world adaptations they would need to make.

**Use appropriate tools strategically**.

Here is an opportunity for students to demonstrate not only good problem solving ability but also common sense and maturity. While it may be mightily tempting for some students to deploy the TNT blocks with abandon, chances are that is not the best strategy for most problems. Some students will do it anyway if they have access to TNT, but I think given time and good instruction, most students will learn to assess the properties of the different blocks available in Minecraft and make good strategic decisions about which blocks to use where. As a basic example, a block of sand will crumble if unsupported underneath, whereas a block of stone will not.

Minecraft may be offered as an option for demonstrating understanding in a differentiated classroom. Sometimes it will be an excellent choice; other times it will be a very inefficient one. It is good for students to have the freedom to weigh those decisions and accept responsibility for their choices.

**And another important mathematics practice: collaboration**

When students engage in Minecraft in a multiplayer World, they can work together on the same structures, and they can observe each other’s work in progress. Minecraft also includes an onscreen chat feature, and if the students are in the same classroom together, chances are high that they will talk to each other aloud about what is going on in Minecraft. In every class visit that I have made, students have supported each other through this communication. The whole class quickly identifies the Minecraft masters, and although these students may not be the ones who usually have high social standing, their expertise in Minecraft is clearly valued and respected. I have been continually impressed by students’ willingness, even eagerness, to share their expertise as well as their new discoveries. I have also been impressed with the clarity and conciseness of their instructions to each other. Somehow Minecraft seems to lend itself to good communication. I’ve also noticed how keenly students attend to each other’s instructions, often picking up on the gist of the new information so quickly that they are able to solve the rest of the problem themselves before they’ve heard the whole explanation.

The buzz of collaborative problem solving in a classroom engaged in Minecraft is so exciting. It makes you want to think of new ways to use Minecraft, just to keep that buzz going.