Fun learning math while conquering a foreign village

For several months now, my 10 year old son and I have been having LOTS of fun playing the online real-time war game Travian. We recorded podcasts in December 2007 and March 2008 to discuss what we have learned so far playing the game. This week, we have been focusing on “chiefing” other villages. There are two basic ways to expand your personal “empire” in Travian and build/obtain more villages. The first way is to build up your palace or residence (one of the buildings in each of your villages) to level 10, 15, or 20, and earn enough “culture points” to found a new village. You can found a new village either by training “settlers” who can be sent with basic resources to an unoccupied area on the virtual Travian map grid, or you can train a “chief” (in my case he is called a Senator, because I am in the Roman tribe) who can be sent repeatedly to another existing village. It is necessary to destroy the residence in the village you want to take over with your chief first, before sending the chief, and afterwards each time your chief arrives in the village he lowers the “loyalty” of that village by a percentage. When the village’s loyalty is lowered to zero, the entire village becomes yours. This entire process (which is admittedly and delightfully complex) is explained well in this official Travian tutorial, “Preventing Conquerings.” This is the screen I saw yesterday after having destroyed the residence of a nearby village and repeatedly sending my Senator to it with an armed escort:

I chose to “chief” a smaller village than Alexander did, and the player who owned the village I successfully “chiefed” wasn’t active in trying to fight off or resist my attacks. The situation with the village Alexander is trying to take over has been quite different, however. The population of the village is larger, and the player is very active. This situation has provided a great context for us to discuss math skills and learn some new ways to use mathematical tools as well as strategies to solve problems.

I have written previously about the value of playing Travian in terms of learning Internet safety. I have not posted about the mathematics learning value of Travian previously, but this has been one of the main reasons Travian caught my attention in the first place and I considered playing this game with my son. One evening a few months ago, Alexander was working out double digit multiplication problems on paper at the dining room table. He was not doing any homework, so I asked him what he was doing, and he explained that he was calculating how many resources he needed to trade or send to his village to build some type of new building. I was quite impressed that he was voluntarily doing some arithmetic “for fun,” and the more I learned about Travian, the more I learned about the value it can provide as a meaningful context for problem solving, math skills, communication skills, team leadership, and other important things.

I will post later about what Alexander has learned about coordinate plane geometry and two-dimensional graphing, because I am not able to locate a copy of one of the early graphs he created for our alliance using an online graphing program. This evening, I’d like to relate and document some of the learning I’ve seen him experience related to “chiefing” a new village.”

The following image shows a troop report from Alexander’s “rally point” in Travian, from his main village which he is using to “chief” or take over a neighboring village.

In this report, you can see that Alexander had sent two attacks to the target village. The first attack includes two different types of soldiers, battering rams, and trebuchets. (Trebuchets are the catapults or “cats” for Gauls in Travian.) This first attack is sent to destroy the “residence” building of the opponent. Alexander timed his second attack, which included soldiers that could move much faster because they weren’t traveling with battering rams at cats, to “land” (arrive) 1 minute and 34 seconds after the first attack landed. This was somewhat challenging to do, because of the different speeds of the attack forces. He did it, however, and the result was that his opponent did not have time to reconstruct (or start construction) on a new residence building after the first attack destroyed that building via the trebuchets.

Since I have a larger set of villages on our Travian server and want to help out my son, I offered (and he accepted) to send my own troops and catpults (called “Fire Catapults” since I am a Roman) to destroy the residence building in the village Alexander is trying to “chief.” I am much farther away, geographically, from the targeted village than Alexander’s main village is, however. One result of this difference is that my troops take MUCH longer to travel to that village and attack it. Travian is a realtime war and strategy came, which means events take place according to real time in the face-to-face world. Alexander’s cats can depart and land in the target village in a just under two hours, but it takes over ten hours for my troops and cats to land. Because of this challenge, last night we created a basic Excel spreadsheet together to make some calculations, based on the inputs we knew. We used the Travian website to calculate when I should send my troops and cats, so they could hopefully arrive just before Alexander’s. We were basing his options on when he would get up in the morning, since he couldn’t send the attacks in the middle of the night. This is what our spreadsheet looked like:

This morning Alexander launched his attack, but it turned out the defending player had enough time (about 30 minutes) to start reconstruction on his residence after my attacks had landed. The result was that Alexander’s “chief” attack failed. The message he received said the residence had not yet been destroyed:

In considering these events, keep in mind that Alexander is attending 4th grade at our local, public elementary school during the day, so is having to make these decisions and send out these attacks before and after school. (He doesn’t have web access to Travian during the day, since he doesn’t use his personal laptop at school at all or have an iPhone.) Since our attempted coordinated attack had failed this morning when he was at school, we discussed a new battle strategy late this afternoon. We realized that instead of sending ALL his cats in an initial “cleaning wave” attack, and then having to carefully time his second attack with his “chief” to arrive closely after the first one, he could hold back one cat (trebuchet) and send it with the chief’s attack. That way, the two attacking parties would have the same speed and “land” immediately after one another. The result? The first “cleaning attack” successfully destroyed the opponent village’s residence and village wall:

The second attack (including the “chief” who would persuade the inhabitants of the receiving village to have lessened “loyalty” to the current owner/ruler/player of that village) landed exactly 1 minute and 34 seconds later. The defending player didn’t have sufficient time to rebuild his/her residence, so the village’s loyalty was reduced by almost 25 percent:

This entire sequence of conversations, decisions, and actions by Alexander was a great opportunity to see him practice problem solving and mathematical calculations in a relevant, meaningful context. Too often in school, we are teaching skills “just in case” instead of “just in time.” Alexander is using his math skills and learning new ones in Travian, as well as further developing his problem solving skills, to accomplish tangible objectives he really cares about.

It is exciting to be learning and playing together in Travian, and to witness how online games like Travian can help young students develop a rich repertoire of skills– including mathematical abilities! 🙂

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