With the holiday season upon us, many of you out there are probably giving or getting new tech gadgets as gifts. Once you unwrap your fancy new iPad, iPhone, or Android tablet, you’re probably asking yourself, “Now what do I do with this?” While you will probably be downloading lots of fun games and apps, you will somehow need to justify all the hours you spend in front of the screen to your family. One of the best ways to do this is to install a few math-related games, and provide some educational value for your children. But there is a bewildering array of supposedly educational games available for these systems. How do you know which ones to get? Today I will share some suggestions based on my experiences.

The first thing I should point out is that there are hundreds of games out there that are basically glamorized flashcards, presenting math problems directly and giving some kind of in-game reward for correct solutions. For example, they will put up a math problem, like “What is 5 x 5?”, and if the answer is correct, the player gets a few points. These points can then be traded in for virtual stickers, virtual ammunition against alien robots, or similar rewards. While there is nothing wrong with this type of game, and they have the advantage of being able to easily draw on large libraries of problems for different skill levels, I don’t find them very exciting. My daughter will play them if I tell her she needs to practice her math, but doesn’t usually come to me asking to play them. What I really want are original games that both teach math and can stand on their own as fun games. Fortunately, I have found two games that fit these requirements.

The first game I want to highlight is called “DragonBox Elements”. This game is designed to teach the basics of geometric proofs, a seemingly advanced topic, but they present it in a very accessible and intuitive way. Each basic shape, triangles and quadrilaterals, can summon a basic type of monster related to that shape. So if you can identify a quadrilateral among the shapes on the screen, you trace it out and summon a quadrilateral-monster. Line segments and angles are also marked with colors, such that any two objects with the same color have equal length, and you can upgrade the monsters to “special” ones using these. So, for example, if you notice a triangle-monster has two equal sides, you can click on them to upgrade to the slightly more powerful isoceles-monster. The monsters also have powers, which essentially invert this process: so if you have been given an isosceles-monster and its two equal sides are not yet colored, you can click on the monster and the two sides to mark them as equal. They also introduce other powers related to ideas like opposite angles, radii of circles, and parallel lines. So the basic Euclidean concepts of definitions, axioms, and theorems have been transformed into monsters and powers. I’m not totally sure how this will translate to actual proof skills when my daughter reaches that level of math class, but laying the foundations at such a young age can’t hurt. And more importantly, she loves this game, even asking to replay all the levels at “hard” difficulty after beating it once.

The second truly engaging iPad math game I have discovered is called “Calculords”. This is a card game, where each turn you have a bunch of cards in hand that you can use to summon creatures for battle. There are two types of cards, number cards and creature cards. It’s not a simple energy system like in most popular collectible card games though: in order to summon a creature for battle, you need to add, subtract, and multiply number cards to reach the creature’s number. The creatures are then placed on a lane-based battlefield, where they fight the evil monsters summoned by an alien enemy. For example, suppose you have a Hungry Blob card, a monster with a summoning cost of 15, and your number cards are 3, 3, 4, and 1. You can form a 15 using 3 x 4 + 3, so you can play those cards to summon your blob. But an additional wrinkle, adding to the mathematical challenge, is that you also gain extra bonuses if you precisely use up all your number or creature cards. So a better move would be to play 3 x 4 x 1 + 3, which still reaches your 15, but uses up your numbers. Since you have 9 creature cards and 9 number cards on each turn, the number of potential choices and calculations is quite large, and the strategy to summon the best set of monsters while trying to use up cards to get the bonus can get very involved. But the game offers many enemies at a variety of difficulty levels; my daughter has been playing at the easier levels since she was in 2nd grade. This is another game that she and I have found quite addictive, and an amazing way to get her to eagerly practice her basic arithmetic. And at the top difficulty levels, even I find it challenging, when I sneak in a chance to play on my own.

So, in short, these are the two truly original smartphone/tablet math games I currently recommend for elementary-age students: DragonBox Elements and Calculords. Naturally, these are heavily influenced by my 4th-grade daughter’s tastes, and their effectiveness probably varies a lot at older and younger ages. DragonBox elements provides the amusing and engaging transformation of Euclidean definitions, axioms, and theorems into monsters and powers. And Calculords provides a strategic challenge involving arithmetic calculations that is accessible to young children at lower levels, and fun even for adult math geeks at the hardest settings. If you have kids at the upper elementary level who could use some extra math practice, be sure to take a look at these excellent games. Also be sure to post reviews on iTunes or similar sites if you like them, as this will increase the chance of further games appearing from these talented authors.. And as always, I’ll be interested to hear from you on this topic: with such an overwhelming number of smartphone and tablet games out there, I’m sure there are a few great ones that I haven’t discovered yet.

And this has been your math mutation for today.

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