Minecraft and the Alaska Math Practice Standards

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.

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Digital citizenship and classroom management

Week Eleven Essential Question:  What technology will I use to allow students to demonstrate they have met the standards targeted by my rubric? What are the classroom management considerations that I must address?

As you probably know by now, Chip, Colin, Nathan, and I are exploring how we can use Minecraft in the classroom.  I believe that students can use simple video tools such as Screencastomatic to show and describe what they have created in Minecraft to model with mathematics and solve real world problems with simulation tools.  There are a lot of other possibilities, too, but I am weary of considering new tech tools.  I’d like to think and write about classroom management for a while instead.

Without good classroom management, there is a lot of potential for the Minecraft experience to go wrong.  The Minecraft wiki has a whole page on griefing, or willfully antisocial behaviors in multiplayer video games.

One approach to preventing students from destroying each other’s Minecraft constructions is to (virtually) physically separate them.  I suppose each student could play in a single player world.  In a multiplayer world, players cannot jump over fences, but fences can be destroyed with axes.  In MinecraftEdu, the teacher can place special blocks that could protect structures or keep players apart.  In my own demo world, Proportion World, I used “build disallow” blocks under the models I constructed so that students cannot alter or destroy the models.  But, by definition, students cannot build over “build disallow” blocks, so those blocks can’t protect the students’ structures.  Teachers could use the special MinecraftEdu border blocks to create a separate area for each student and then teleport the student into that area.  That may be the best short term solution for something like allowing students to build a model for a math problem.

But I believe that much of the true educational power of Minecraft lies in the potential for collaborative problem solving, and all of these methods of isolating students prevent collaboration.

So what to do?

I’ve added some links to some articles and blogs that address the question of classroom management in our Pearltrees.  Here are my own thoughts, inspired by what I have read and from my own teaching experience.

I think Minecraft offers an exceptional opportunity for students to learn digital citizenship.  As with most truly worthwhile undertakings, this is not a quick or easy process.  It could begin, as it did in Joel Levin’s class, with one student protesting another student’s actions in the Minecraft world.  Joel used this “teachable moment” to launch a class discussion about acceptable behavior in the virtual world of online communities.  I believe students are more likely to adhere to a code of conduct they create, and I think the whole process of devising and revising a code of conduct is a valuable educational endeavor. Over time, students might even create their own constitutional government for their Minecraft world.

Carol Tomlinson identifies several principles of differentiation, including respectful tasks, quality curriculum, and teaching up.  I think most of the management problems that might occur in Minecraft would be avoided if these principles are fulfilled, but that may be easier said than done, depending on the class profile.  The ideal Minecraft project would be intriguing and relevant to the students and would provide enough challenge to stimulate and motivate them, but not so much as to frustrate or intimidate them.

Easier said than done…

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My diigo library (weekly)

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My diigo library (weekly)

Posted from Diigo. The rest of my favorite links are here.

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Unpacking standards: Differentiating through student product

Week Ten Essential Question:  How can I differentiate through student product in my classroom?

This week I attempted to create a rubric that could be used to assess student learning through project-based use of simulation games such as Minecraft.

First, the Alaska Standards I chose to unpack in my rubric:

Standard for Mathematical Practice 4.  Model with mathematics:

In grades 9-12 mathematically proficient students will:

  • apply mathematics to solve problems in everyday life, society, and workplace
  • identify important quantities in a practical situation and map the relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas
  • consistently interpret mathematical results in the context of the situation and reflect on whether the results make sense
  • apply knowledge, making assumptions and approximations to simplify a complicated situation, realizing that the final solution will need to be revised 
  • analyze quantitative relationships to draw conclusions
  • improve the model if it has not served its purpose

Writing Standards for Literacy in History/Social Studies, Science and Technical Subjects grades 6-12:  Production and Distribution of Writing

6.  Use technology, including the internet, to produce, publish, and update individual or shared writing products, taking advantage of technology’s capacity to link to other information and to display information flexibly and dynamically

Here’s a link to my rubric:

Rubric for Simulation Modeling with Math

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Proportion World

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My diigo library (weekly)

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Riptides and Pearltrees

Week Nine Essential Question:  How can I use Pearltrees to differentiate content in the classroom?

Colin and I both got a late start on this week’s assignment to learn how to use Pearltrees.  We didn’t plan to collaborate, but a conversation that we had been having over Twitter and e-mail drifted into a Google Chat while each of us was getting started with Pearltrees.  Pretty quickly we figured out how to link to each other, and then we started sharing discoveries back and forth.  Colin saved me a lot of work by posting several great links from his diigo library into the MinecraftEdu team pearl.  It was very cool to see the changes happening to our Pearltree in real time as we were each working simultaneously on different parts of it.

I realized afterward that we had just had our own differentiated learning experiences.  Colin caught on to how to add pearls much faster than I did, and his work freed me up to add some comment pearls.  We both worked on reorganizing and had some hands-on learning about joining teams, deleting pearls and links, etc.  We worked at our own pace, learned from each other, and were able to focus on the aspects that were most interesting and useful to us.   Here’s a link to my Pearltree.

I think Pearltrees would be a great graphic organizer for students.  I can imagine using it for K-W-L.  A team of students could start by creating a central pearl identifying a key topic.  They could add pearls to it listing what they already know (K) about that topic, including links to useful websites, images, etc.  Next, they could link pearls from what they know to what they want to know (W)– questions that they have, related topics they’re curious about, etc.  As team members explore each other’s pearls, they would probably think of new questions and interesting topics to add.  For the final stage of the project, the students could research some of their questions and new topics and add whole new Pearltrees with what they learned (L), and maybe even create new teams based on new shared interests or questions.

As happened with Colin and me, I think there would be natural differentiation in this process and in the content students explore.  Students would be free to add pearls anywhere they had questions or particular interests, and students could share knowledge and resources with each other by adding more comment pearls and weblink pearls.

I think working in Pearltrees simultaneously and seeing the realtime changes to the connections would be motivating for students.  I also think they would enjoy the power to collaborate and share expertise and questions with each other.  A paper K-W-L chart can be a useful graphic organizer, but I think a K-W-L Pearltree would be so much more dynamic and engaging.

Life in the MOOC

Well, I felt like the swimming lessons were going along nicely, and I was learning to paddle around and do some pretty cool things out there in the big cyberspace ocean.  I was really looking forward to the UAS spring break week– no new homework assignments for a week, and I could maybe even get ahead a little during the peace and quiet while my kids were at school.  And then their spring break was the next week, so we’d have some good family time together because I’d have all that work done ahead of time.  Ha!  Want to make God laugh?  Tell Him you’ve made plans.

My daughter caught a nasty virus at the beginning of our UAS spring break, and I spent pretty much the whole week taking care of her.  Of course I was rewarded for my efforts by coming down with the same virus myself just as she was recovering.  And somehow I never do accurately gauge just how much time my Girl Scout volunteer commitments are going to take… so the past few weeks have been a blur of illness and Girl Scout cookies.

Add to that the enormity of Project 2 and the Week Nine Pearltrees project and the looming prospect of Week Ten and the final project, and I feel like I’ve been caught in a riptide that has pulled me underwater and is dragging me out to sea.  I just want to catch my breath!  And maybe lie on the beach for a while. I wish!

I have continued to learn about Minecraft.  My son showed me how to generate a flat world in the regular Minecraft game, so I started building Proportion World there.  Then I discovered that there are some special teacher blocks in MinecraftEdu and decided to start over building Proportion World in MinecraftEdu.  So unfortunately, progress has been slow, but I think when I am done, I will have a useful world that I can share with Nathan and other teachers to use for teaching proportions and three dimensional scale relationships.  It won’t be fancy, but I think it will still be very engaging and memorable for students to complete their math lesson in MinecraftEdu.

Meanwhile, Colin has done amazing things in MinecraftEdu.  He figured out how to import a Google map into a MinecraftEdu world, and he set up a server so that those of us included in the MinecraftEdu trial version can visit his Douglas Island/Juneau world.  In an amusing coincidental connection to my blog theme, I seem to find myself underwater most of the time there because I’m still not that great at maneuvering around in Minecraft.  Oh well.  Learning to swim in yet another world.

I can’t wait to have some time to visit my classmates’ blogs and explore their projects for Assignment 2.  I hope that will happen soon.  So much to learn!


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My diigo library (weekly)

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Playing the game: meeting standards and differentiating instruction

Week Eight Essential Question:  How might video games enhance my students’ learning?

Revelation:  Minecraft is a geeky game.  Maybe you already knew this.  It became apparent to me when I encountered students who denied having ever played the game but demonstrated obvious proficiency in the MinecraftEdu tutorial.  It might be geeky, but it’s still a game, and being given a whole class period to play a computer game was a novelty for these high school students.

I had the privilege to be a guest in Nathan Adams’ high school classroom when he introduced the MinecraftEdu Tutorial World to two of his classes.  In the Tutorial World, the students learned how to navigate through Minecraft and how to dig and build by completing a series of “hands-on” challenges.  All of the students, from the genuine novices to the professed experts, were engaged in the tutorial challenges.  We could most easily observe that they had mastered the building skills; we could see the structures that they built.  The students also demonstrated perseverance in problem-solving as they used trial and error to figure out how to navigate through the Tutorial World, communication and collaboration skills as they asked for and gave help to each other, and spatial reasoning– a key skill in Minecraft.

Nathan, Colin, and I have been talking about ways to use Minecraft in the classroom to meet Nathan’s instructional goals.  Colin is working on creating a Minecraft map of Douglas Island that Nathan and his students can use to model and explore ecosystems.

My plan is to use Minecraft to create a proportional reasoning challenge for the students in Mr. Adams’ prealgebra class.  I have been learning how to play in Creative Mode in Minecraft to create “Proportion World.”  In Proportion World, students will first take a tour of a couple of sets of proportional models that I am building.  Each pair of models is accompanied by signs that describe the scale relationship between the models.  The next part of the challenge will be for each student to build a scale model of a given structure.  The final challenge will be for each student to build an original structure, build a scale model of that structure, and post signs to describe the scale relationship between the two.  After all students have completed the challenges, the whole class will tour the world together, and each student will give a live oral presentation to the class describing his or her models and problem-solving process.  I think I can create a scoring rubric that ties the Proportion World challenges to several Alaska Standards for Mathematical Practice and Content.

Minecraft can be used to meet all of the Alaska Standards for Mathematical Practice K-12 (2012):

  1. Make sense of problems and persevere in solving them
  2. Reason abstractly and quantitatively
  3. Construct viable arguments and critique the reasoning of others
  4. Model with mathematics
  5. Use appropriate tools strategically
  6. Attend to precision
  7. Look for and make use of structure
  8. Look for and express regularity in repeated reasoning

The challenges I am creating in Proportion World will meet the Alaska Standards for Mathematical Content (2012) for Ratios and Proportional Relationships:

  • Grade 6:  Understand ratio concepts and use ratio reasoning to solve problems.
  • Grade 7:  Analyze proportional relationships and use them to solve real-world and mathematical problems.

and Geometry:

  • Grade 6 and 7:  Solve real-world and mathematical problems involving area, surface area, and volume.
  • Grade 8:  Understand congruence and similarity using physical models, transparencies, or geometry software.

I must give credit to my sixteen year old son Sam as a key member of my PLN for this whole MOOC experience, and especially for simulation and video game expertise.  Since he was in kindergarten, he has enjoyed escaping into virtual worlds in his downtime, the more complex, the better.  He’s not the kind of person to let video games interfere with his responsibilities, so I’ve never had to monitor or limit his screen time.  To tell you the truth, I’ve never really paid that much attention to what he has been up to until I started taking this class.  Recently he has been helping me learn how to play some of these games (including Minecraft).  Now I marvel at his virtual world accomplishments.

The second game I explored for Week Eight is Zoo Tycoon for PC (Microsoft Corporation, 2003).  It’s not a new game; I think I gave it to Sam for his birthday some time when he was in elementary school.  He popped the disk in my laptop the other night and started creating a new zoo, and within a couple of hours, he had a profitable enterprise going.  Zoo Tycoon is a simulation game, sort of like The Sims, where you start with a bare piece of land and a budget, and you have a whole array of categories from which you can purchase structures, animals, and habitat features for your zoo.  Guests start visiting your zoo, generating income but also demanding services (food, drink, restrooms, etc.), so the game becomes a challenge of planning, estimating, budgeting, cost/benefit analysis, spatial reasoning, artistic creativity, and more.

I invited my thirteen year old daughter, who is not a big video game fan, to try the Zoo Tycoon tutorials with me.  In a short time, she had figured out the basics of the game.  I think she would have no trouble going on to develop a successful zoo.  As far as classroom application, I think the game would be good for mental math and all kinds of accounting skills, but I’m not sure exactly where it would fit in the middle school curriculum.

Tracie recommended the third game I explored this week when I asked in our Twitter chat if anyone knew of any good algebra games.  Lure of the Labyrinth is a free online game designed to develop prealgebra skills.  The website has an excellent section for educators explaining how the game fits with curriculum standards and how to implement the game successfully in your classroom.  It also features two modes of play, Play Game and Play Puzzles.  In the Play Game mode, the students work their way through a series of challenges to achieve the overall goal of rescuing pets from monsters.  In the Play Puzzles mode, students just solve the individual puzzle challenges, focusing on particular prealgebra skills without engaging in the pet rescue story plot.

As a digital immigrant, I am amazed at the way all of these games are designed for the player to learn how to play by playing.  I find myself constantly wondering where the help button is.  It takes real patience, perseverance, and clever reasoning to figure these games out.  I definitely have not been giving kids enough credit!  What’s great is that the games are engaging and motivating enough that kids will do what it takes to solve the puzzles.  When those solutions involve skills and concepts that match our curriculum goals and standards, I think we should embrace games in our classrooms.  And we should learn from the games themselves how we can make the rest of our instruction more engaging and motivating, too.  Now, if you’ll excuse me, I have proportional structures to build, snow leopards to feed, and pets to rescue from labyrinth monsters…

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