Week 6 Say, say, oh playmate... ( February 20-26)

This week, the focus is on play and games in modern mathematics education. You will be happy to hear that people hardly argue anymore against the use of games in mathematics education, overall. There is a current hot issue related to games, however!

There are two types of play. One type is based on so-called "intrinsically mathematical game mechanics."

For example, in the game of "Set" players need to spot a full set of similar or dissimilar attributes: http://www.setgame.com/set/puzzle_frame.htm You can see several discussions of the mathematics in the game here: http://www.setgame.com/set/puzzle_frame.htm You can play set about other objects with attributes, but you can't make the game be about multiplication or probability without major redesign. The rules of "Set" are intrinsic to mathematics in it.

Another type of play is based on generic rules that can "wrap" any content. For example, questions from any mathematical area can come up on "Jeopardy" or "Bingo" without changing the rules of the game. In some computer games, solving a math problem explodes a spaceship or disables a monster carrying it. Again, any problem can be there - play elements are extrinsic to the content of the problem. If play is based on points, achievements and leveling a character, it is called "gamification."

Some educators say gamification and generic games are manipulative and boring - the game dev term is "chocolate covered broccoli." Mathematics should be interesting by itself, and math gameplay should be math-based in nature, these people claim. What do you think?


  1. Find an intrinsic math game you would use with elementary students. Briefly describe why you like it.
  2. Find a generic/extrinsic game you would use, and describe why you like it.
  3. Find a blog post, a forum discussion, a video or an article about intrinsic games or gamification in education. Leave a comment there if you can, and link what you found and your comment here.

Task Discussion

  • Carolyn Lesser   26 februari 2012 23:33


    Intrinsic Game:

    Pig Math Game- http://www.learn-with-math-games.com/probability-math-games.html

    This is a probability game where players take turns rolling two dice. Whoever reaches the goal number first, for example 100, wins the game. The person rolling the dice can roll as many times as they want adding up their score each round until they roll a 1. If they roll 1 they lose all the points from that round and if they roll two 1’s they lose all their accumulated points. It is a great way to learn probability and talk about strategies when dealing with probability. I always found probability to be tricky to grasp so I think learning strategies of probability through games is a good way to do this. Students are also able to compare strategies while they converse during the game.

    Extrinsic Game:

    Around the World

    This is a math game I grew up playing in the classroom. I always enjoyed playing it and love the competitiveness of it. We always wanted to be the last student standing so we always tried our best. Students sit in a circle except for one student who stands behind another classmate. The teacher flashes a math fact and the student who guesses first gets to move on. If the student standing gets the correct answer this person moves on to the next person in line. If the person sitting down answers first they switch spots and the person sitting gets to stand up. This game could easily be used in other ways. You could ask any question and follow the same rules.

    Blog: The Dangers of “Gamification” In Education


    This blog post is from a high school teacher in California. He introduces an article that talks gamification and the issues that go along with it. It was very interesting!

    Comment: I am not very up-to-date with gamification either but found this to be interesting. There is a fine line between gamification working and not working. If used in the right way it can be very useful. There have to be short and long term goals or awards. If there is just one goal students might lose interest if they have no hope to reach it. If they can reach smaller, attainable goals along the way they can stay motivated to keep going and try hard. I personally believe that in our capitalist society we are brought up learning competition and why not build off of this?

  • Keisha   26 februari 2012 21:34

    I'm not sure if I fully understand the difference between intrinsic and extrinsic math games but here's my try at it.

    Find an intrinsic math game you would use with elementary students. Briefly describe why you like it.

    An intrinsic math game I think that will be good with Elementary students is Tetris. This game is all about shapes and spatial awareness. You are given different geometric shaped blocks that you have to "manipulate by moving each one sideways and rotating it by 90 degree units, with the aim of creating a horizontal line of ten blocks without gaps." This game is usually played on phones or computers. I'm not sure if they have actual blocks that kids can play with but it's pretty easy to make with sheets of papers. I noticed that a lot of schools are starting to use Ipads and Mac computers in their classrooms which Tetris is easily accessible on.

    Find a generic/extrinsic game you would use, and describe why you like it.

    An extrinsic math game, that I think is extrinsic, is Solitaire. In Solitaire the goal is to arrange the cards into decending order by suit. You should have four rows: hearts, clubs, diamonds, and spades. This game is very good for younger students learning how to count forward and backwards. It might be hard for them to understand that King, Queen, and Jack has a number too so they can be taken out until they are ready to add them in.

    Find a blog post, a forum discussion, a video or an article about intrinsic games or gamification in education. Leave a comment there if you can, and link what you found and your comment here.

    I'm also having a hard time finding an article, blog, or video about intrinsic/extrinsic math games. What are you guys typing in the search engine?

  • Amanda Graf   26 februari 2012 17:03

    One intrinsic math game that I remember playing as a kid is a level on a computer game called The Logical Journey of the Zoombinis. When I was young, I didn't even realize that this game was mathematical or educational but, analyzing it now, I understand it's educational value and its methods for teaching patterns. Here is a description of one level of the game called "Mudbrick Wall:"

    "A large stone wall inconveniently blocks the path of the Zoombinis. A nearby machine creates mud balls that can be colored and stamped with a shape. If the mud balls hit a certain target on the wall, either one, two or three Zoombinis get catapulted over the wall to safety. Eventually, the mud in the machine will run out, stranding those who did not make it over the wall. As the difficulty increases, additional squares will be added that require the player to pick the correct shape, mud colour and the colour inside the shape, and the color pattern will shift diagonally."

    This youtube.com clip is of the Mudbrick Wall level of Zoombinis on the highest level...so if it doesn't really make sense, don't worry, there are much easier patterns for younger kids. http://www.youtube.com/watch?v=Dmloy9B7CLo

    This youtube.com clip shows a level of Zoombinis where the player practices combinations and the process of elimination to pass the level.                                          http://www.youtube.com/watch?v=pTKR6TIvO9o

    All of the levels of the Logical Journey of the Zoombinis are simply that - a logical journey - and each deals with a different math/pattern related problem.


    I found this blog about intrinsic math and the importance of intrinsic math games:


    I found this blog interesting because it drew an interesting parallel between games and math. The author of this blog expresses her belief that "intrinsic mechanics are in-game actions that are metaphors for math actions. The author and those who have commented on the blog also discuss ways to define a "good" intrinsic math game. Some of the guidelines they feel to be important are intrinsically relating the game mechanics to the target mathematical concepts, in in-game consequences rather than the player being told that they answered a question wrong, and by the end of the game, the players understand something bigger, better and on a whole new conceptual level about the target concepts from the STRATEGY of the game, rather than the individual steps of the game.

  • Susan Weiss   26 februari 2012 18:05
    Reageer op:   Amanda Graf   26 februari 2012 17:03

    You played one of my favorite games Zoombinis.   I even have a mini zoombini among my stuffed animals (grandsons).   The game allowed children to think and rethink if they made a mistake.  There was no quick answers.    On the older PC, I have had my students play the game.   I have not tried with Windows 7 and  I know there no longer is a  mac version.  This is one game I always wanted to reproduce either with Microworld (logo)  or perhaps some other java script.    Zoombinis characters were also part of another sorting -graphing program which was part of a math program.     Hopefully someone with computer skills will take the time to make a modern Zoombinis.

  • Maria Droujkova   27 februari 2012 07:06
    Reageer op:   Susan Weiss   26 februari 2012 18:05

    I would love Zoombinis as a browser-based game and/or mobile game. I think touch screen will work well with many puzzles there, and may add to it. The game is copyrighted and researchers who developed it are our contemporaries, but they moved on to other projects. 

    I also think the underlying mechanic of Zoombinis (combinatorics and logic, using creature attributes) will make an excellent level creator environment!

  • Denise   23 februari 2012 22:47

    Find an intrinsic math game you would use with elementary students. Briefly describe why you like it.

    I've written up several of the games I like on my blog. A game with intrinsic math would be Euclid's Game. I like it because it's easy to explain and quick to play with elementary students for basic subtraction practice, but it also lends itself to investigation and deeper reasoning about factors and multiples with middle school students.

    Find a generic/extrinsic game you would use, and describe why you like it.

    Tens Concentration is an adaptation of the generic memory game, matching number bonds (partners that make 10) instead of matching numbers that are exactly the same. It's a fun icebreaker for math club meetings, because people of all ages enjoy playing.

    Find a blog post, a forum discussion, a video or an article about intrinsic games or gamification in education. Leave a comment there if you can, and link what you found and your comment here.

    One of my favorite bloggers-about-math-games is Math Hombre. He wrote several posts about game design a few months back:

    Ten Rules for Game Design

    Game Design: 6-10

    Game Evaluation via NCTM

    Since then, whenever he shares a game, he evaluates it according to those ten characteristics. For instance:

    Fraction Catch


  • Carolyn   23 februari 2012 17:50

    While searching for different games for this weeks task I came across First in Math. I believe this is the game that the students in the fourth grade classroom that I worked in last semester played. It is a game that studenst from all over the country play in competition witheah other. There are prizes for the school that wins. I see this game as both intrinisc and generic. The First in Math 24 game has 4 numbers and the purpose is to some how get 24 through addition, subtraction, multiplication, or division. The game works on adding, subtracting, multiplication, and division and in that sense is generic becasue it works on many different skills and can be altered to different grade levels using positive, negatives and fractions. However I also view the game as instrinsic becasue only those skills are being worked on. I do believe that  adding, subtracting, multiplication, and division are the basis for mathematics but there are many other areas of focus. 

    Here is an article on the First in Math game and how it is really helping children:


    Comment: Although I love the idea of First in Math and see that it is helping many students get excited about math, the first pararaph struck me a bit, "colorful wristbands set apart the students that do well in math." I understand that this is reinforcing positive behavior and achievement but I cannot help but wonder how the other students feel, especially thos ehwo strugg;e in math but may do well in other subjects. Do other subjects have such rewards? However despite that small surprise, the rest of the article is a big promotoer of games in the classroom, which I love.  think play is a great way to learn and it looks like some studies have proved that success.

    Another intrinsic game I found was to do tanagrams for practice in geometry. You create a shape and then have different smaller shapes that fit into the big shape like a puzzle. Obviously this could be altered tfor younger and older kids depending on the size of the shapes.


  • Kathy Cianciola   23 februari 2012 12:27

    Almost everyone is familiar with the game, "Go Fish."  This game is called "Go-Fish Addition" and it's played with cards numbered from 0-10 (3 sets of each number.)  At first I was thinking that this game would be a no-go for the classroom, however I feel that it could be easily be adapted for the classroom by pairing or grouping students.  It's played like "Go-Fish," but instead of putting down pairs that match you put down pairs that equal 10.  For example if you have a 7 you would ask the other player for a 3 in order to make 10. Who ever runs out of cards first wins.  Most people enjoy "Go-Fish" because of its fun-factor, and competitiveness. In this game the math is intrinsic.

    Jennifer Gold, Hosted by Host Gator, www.mrsgoldsclass.com


    Back when my daughter was around 5 (She's 17 now) I ordered a set of little plastic transformer-like figures called Number-bots.  There was one to represent each number, 0-9.  They were hinged so they could easily be changed from numbers into robots by manipulation.  These would be an example of extrinsic/ generic math.  She had lots of fun with those, and I wish I could find them now,. Unfortunately they don't make them anymore.


  • Laura Haeberle   21 februari 2012 19:07

    One intrinsic math game that I remember loving as a child is Dominoes. Growing up, my mom and I would spend Sunday afternoons playing for hours. I believe the game could easily be integrated into the classroom setting, and children can pick up on the rules very quickly. Essentially, I think Dominoes could be beneficial, especially for younger students, because it reinforces number values. They're matching the six circles with the other six circles. They're thinking of the numbers and associating values with the amount they see on each domino. 

    A generic game could be a memory game. For example, there might be a pile of 20 cards, each with a number on it (1-10). There is a pair for each number, and the children spread the cards on the floor or table. Children go one at a time picking up two cards, hoping they can remember the location of the pairs based on which cards are flipped. This game could be done with numbers, a regular deck of cards, pictures, words/sounds, etc. I know that children have a lot of fun with these games, and often, their memories are better than mine! Again, this game would get children familiar with numbers and understanding similarities (while practicing memorization). 

    I read this article on gamification in the classroom:


    The article discussed the efforts of one teacher, Mr. Pai. He noticed that his students' math skills were low, and wanted to find a way to engage them. He recognized that the students became passionate about video games, and started using Nintendo Ds' in the classroom, programmed with math games. He has had great success, and urges gamification.

    Comment: I think it's so important for students to be able to connect to what they're learning. I imagine that using games gave a sense of competition in the classroom, and introduced the concept of virtual incentives. The students are trying hard to be the best, and Mr. Pai was bringing his content to their preferred media. This is proof that video games can be an excellent education tool!

  • Denise   23 februari 2012 21:33
    Reageer op:   Laura Haeberle   21 februari 2012 19:07

    Laura, you can modify both dominoes and Go Fish for older children by changing the matching rules. Instead of matching the same numbers, match number bonds (for instance, partners that add up to 10). For dominoes, you would need a double-9 set with the blanks removed, and for Go Fish a deck of cards with the face cards removed (10s count as a "match" all by themselves).

  • SandyG   20 februari 2012 09:22

    I found an online example of an intrinsic math game at http://www.oswego.org/ocsd-web/games/SpeedGrid/Subtraction/urikasub1res.html  I like this subtraction grid because it clearly combines gaming and learning.  Even my 12-year-old son played it a couple of times when he saw me looking at it!  A race against the clock is fun, and I like that it requires the student to work from memory, rather than finger counting, in order to increase the difficulty of the challenge. 

    An example of an extrensic game would be basketball (a.k.a trashetball as we usually use our trashcans to play it).  Though you could play this with any subject matter (even converting it to a Horse-like format for spelling), the rules are the same: put up the ball and get it through the net to win.  For a math class, the teacher could give the student a problem, and if they get it right, they get to shoot for points.  There are ways to vary the game, too. It could be played in smaller groups, or teams could be given points for right answers w/ the baskets as bonus points.  It could be teacher vs. the class, too, to direct the competetion from student vs. student to teacher vs. class.  I like doing this as a bell ringer activity, too, asking for volunteers (though being certain everyone gets a chance if they want one).  Students, as a single team, must make ___ baskets to leave or avoide homework, for example.

    A video of an extrensic game would be here: http://youtu.be/FtD-6mUShdA.  The basic premise of paper could cross curriculum areas, and it could also be modified for many different math functions. 

    A video showing an intrinsic game can be found at http://youtu.be/GrcOjAyOeg4.  Though this is just a demonstration of the game, it is clearly designed to work with shapes.  To change the program would take an incredible amount of work.

  • Denise   23 februari 2012 21:41
    Reageer op:   SandyG   20 februari 2012 09:22

    I think it's interesting that you see a race against the clock as fun, Sandy. My kids (and I) have always hated race-against-the-clock situations, whether in games, drill worksheets, or timed tests. The moment a timer goes on, our stress levels go up, and our performance plummets. People are so different!