In teaching 10th grade algebra and geometry students, I am always looking for creative math games and activities that are not seemingly designed for the middle school ages (and younger). I finally came across an app called Euclidea, which is essentially a “game” to practice Euclidean geometric constructions. The game is multi-level, starting with the most basic constructions (like creating an equilateral triangle) and building towards more and more complicated constructions (like inscribing a circle in a square).
The game is a bit short on instructions, so the learning curve on each new level can be challenging as the constructions become more complicated. But once you learn how the game is manipulated using the different types of drawing tools, it is simple enough to play. The objective of each level is to create a geometric figure in the least number of moves possible. There are two types of moves that are independently counted (E and L-type) and each type of move has its own goal. Complex moves (like using a segment bisector) count as a single “L-type” move (you used it once), but, in recognition that it takes three “sub-moves” to actually produce that segment bisector using a compass and straightedge, it counts as 3 “E-type” moves. A level is completed by actually making the construction, but a goal is to make the construction in a set number of L-type or E-type moves.
I have spent an hour or so in the game. It was quick to figure out how to manipulate the tools, but I lost interest pretty quickly – largely because I struggled to figure out some of the constructions and there were no helpful hints available – (actually the hints were pretty obscure). I think it would be a tough game to play for any extended period of time, but definitely a fun mental challenge to tackle from time to time. If I had a reason to tackle a particular construction (for example, in relation to a lesson), my interest would be piqued further.
For this reason, I think the game would work well as part of a geometry curriculum – particularly one that emphasizes Euclid’s constructions. I don’t think a student would pick the game up on their own (unless they were strongly interested in Euclid’s methods). It requires a fair amount of intentional thought to play the game “successfully” but the reward is in seeing the sophisticated geometric figures that can be built using nothing more than lines and circles in a logical and strategic order. If a player is not intrinsically or extrinsically motivated to hit the goals and achieve the construction in a minimal number of moves, she may miss some of the benefits of the game by throwing in more and more moves hoping to hit on the solution eventually.
I wish there were more opportunities to guide the player (with hints, etc.) since some of the levels can be quite challenging. It is not easy to skip over levels that can’t be completed – unless, like me, you pay the $.99 to unlock everything. The game can be quite frustrating if you cannot figure out how to make the construction. It is not a drill and practice game, but it is not a sandbox game or a choose your own adventure game. There is a defined construction to make in each level and no real benefit in trying to be creative outside of that goal. Honestly, there are other programs (like Geogebra) that better facilitate being “creative” using geometric shapes.
I could envision the game being used as a challenge activity within the classroom. If a version having all of the levels open is accessible, then students can be given a specific construction to work on (in connection with the class topic) and challenged to compete for the most efficient construction. It could also be used as a demonstration tool by the teacher.
The game will not replace x-box anytime soon, but as a tool in the classroom – I’d consider it.
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I find it very interesting how you said you lost interest pretty quickly, I wonder if the students would feel the same way. It seems as though this would be a supplement to a lesson every now and then rather than having it play a large role within a lesson plan.
I think it is great that it is mentally challenging and would push students into that zone of proximal development. It also appears that teacher driven instruction would be necessary, in order to keep the students moving in a positive learning space.
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Thanks for the comment. I wouldn’t be inclined to make students play through more than a few levels at a time – and likely only those relating to the work we are doing in class. The risk of students falling out of the ZPD in relation to the game levels is pretty high. They can quickly reach levels for which there is no real scaffolding in the curriculum.
The game is way more like chess than any of the interactive war games – in fact, I think it is not interactive (i.e., social) at all, which is another potential downside of using it widely. The game doesn’t include the kinds of tools that facilitate teacher engagement.
I’m going to go look for other games that practice euclidean constructions (maybe for younger kids.) I would guess there are some geogebra.com class activities that would be more “social” in a classroom setting.
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You said at one point that the game can be frustrating if a player cannot figure out how to make the construction. I wonder what other hints they could provide? As someone who is not really confident in my math skills, it sounds like this game would be the opposite of “fun” for me. The information in the game definitely seems beneficial to know, and for that reason it probably would work well in a geometry class. Maybe if you had the chance, you could use your students as guinea pigs to test out how they like it or dislike it!
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I’ve been trying to think about analogous games in other contexts. Perhaps this game is something like crossword puzzles using French vocabulary words (where you aren’t given the words, just the clues… in French). That would not be fun for me; though for someone interested in the language, it could be a fun challenge. This game reminds me a bit of chess. One can understand how the pieces move about the board, how one loses pieces, and the overall objective of the game, but struggle mightily to “see” the strategy that is needed to be successful. With Euclidea, one can understand how to use the built in tools and the objective, but struggle to see the order of steps needed to achieve the end construction. In one sense, that struggle is the nature of mathematical “learning” (IMHO), but it doesn’t come easy and it often isn’t perceived as fun or applicable to real life. Alas, one of the great challenges of mathematics.
If I were designing hints for the game, I think I’d let students struggle a couple of times, and then, perhaps after the second or third effort, give students a chance to have the game give the first move of the construction – or even a suggestion about the first move. As noted above, the issue isn’t so much “how” the game works as it is “what” to do.
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