DragonBox Algebra 12+ Critique

My critique will be about a game called DragonBox Algebra 12+, a game that is all about learning algebra. This game was developed by the WeWantToKnow team in Norway (although the game is published on Google Play under the Kahoots DragonBox brand), a company founded by former math teacher Jean-Baptiste Huynh and cognitive scientist Patrick Marchal. Together, they began prototyping an algebra game in 2011, which later became DragonBox 5+, the first game in the DragonBox franchise.

DragonBox 5+ was a huge success, and was followed up in 2013 with DragonBox 12+. Both games attempt to “secretly teach algebra”, as Patrick Marchal puts it, with DragonBox 12+ targeting learners ages 12 and over with more advanced algebraic concepts. The game is available on iOS and Android devices as well as on Amazon App Store for $7.99 USD.

Learning Objectives

At its core, DragonBox is a “series of learning tools for algebra that can teach anyone to solve equations by turning algebra into an intuitive and motivating game” [1]. DragonBox 12+, in particular, aims to move build upon the fundamentals of algebra that its predecessor, DragonBox Algebra 5+ was concerned with. In 12+, the algebraic concepts are more advanced and akin to the algebraic content found in the mathematics curriculum of grades 6–8.

The prior knowledge required to play DragonBox 12+ includes the following:

1. Understanding of mathematical operations, namely addition, subtraction, multiplication and division.
2. Basic understanding of algebraic notation, including alphabetic variables (e.g. x or y).

By focusing on building a greater understanding of algebra, the game aims to improve fluency in the following areas:

1. Variable isolation and solving
2. The rules of modifying both sides of an algebraic equation (e.g. adding a value to one side means you must add it to another)
3. Factorization
4. Cancelling out inverse terms
5. Collecting like terms
6. Simplifying fractions

By playing DragonBox 12+, learners will get exposed to solving algebraic equations and “isolating x” to solve for its value, but also gain fluency in the approaches towards solving an algebraic equation in the most efficient way.

Side note: Even though the DragonBox series is quite popular, there are multiple studies that were recently published with conflicting results about how successful the game is in achieving the above learning goals. According to Siew et. al, DragonBox 12 + did help enhance algebraic thinking and attitudes towards algebra compared to the control group. Participants also showed more confidence towards algebra [3]. However, according to Gibbs et. al, DragonBox did not enhance algebra performance, and attitudes towards math was not related to the amount of time spent playing the game [2]. Furthermore, students thought DragonBox was fun, but repetitive in its execution.

Game Elements

The goal of DragonBox Algebra 12+ is to isolate the red box on one side

In DragonBox, the goal is to isolate the unknown value, represented by a box, using algebraic operations. Narratively, the goal is to get the box on its own on one side because it contains a dragon that wants to be alone. The game consists of 10 “Worlds”, and each “World” consists of 20 levels. As the problems are completed, the dragon in the box grows; it is being “nurtured” by the player when they complete a level. Each world grows a different type of dragon and as the world is completed when the dragon is fully grown at level 20.

One of the unique properties of DragonBox is how it uses design metaphors in its scaffolding approach. At the start of the game, no variables or numbers are found in the levels. Instead, there is a red box representing the “x” variable that is being solved, and a number of creatures that represent other numeric values. Inverse coloring is used to represent the positive and negative representation of these creatures. The algebraic operations are introduced one at a time (usually 1–2 per world) in the form of “powers” that help the player get the red box isolated. In each world, the final 4–5 levels begin introducing algebraic symbols such as X in place of the red box, to reinforce the concepts and transfer them to the non-game context. By world 10, the levels are essentially algebraic exercises with no design metaphors and incorporating concepts such as factoring, cancelling of like terms, and inverse operations.

Using Zubeck’s updated MDA framework, the game elements can be broken down as follows:

The reward system of the game. If the box is alone, the equation is solved with the right number of moves, and all values are simplified, the player gets a 3 star rating

Mechanics — The game is a 2D world and has a top down view. The entire level is visible on screen at one time. There are ten worlds with twenty levels each, and in each level, there is a red box (or X variable in later levels), and a series of “powers” available to isolate the variable on one side. Aside from the first two tutorial levels, the layout is a “split screen” with two separate sides. The game is touch-based, and each touch gesture corresponds to one of the powers. For example, swiping to the right on a value attaches the value of 1 to it, representing the multiplication of a value by 1. While the powers serve as additional algebraic operations for the player to use, they also carry with them constraints and rules that cannot be broken. For example, if a value is dragged from the bottom-center of the screen to one side, the game will not allow the player to do another action until the full operation is complete; the player must also drag that value to the other side in order to satisfy the algebraic rules. If the red box (or X variable) is on one side of the split screen with no other values, then the level is completed. The game also supports restarting the level and undoing the last move (which Angle Jungle did not have, and was one of my criticisms for it). Visually, the game employs a fantasy/medieval art style.

Systems — There are a few systems at play in DragonBox. The powers available in each level link up to form an algebraic problem solving system, which is the core of the game. There is a robust reward system based on level completion ratings of up to three stars. If the player completes the level with all values simplified and within a certain amount of moves, they get three stars. This system helps motivate players to achieve mastery and better fluency, and also translates to better learning outcomes since the rewarding system is based on good algebraic practice. A group of twenty levels forms a world, which is its own form of system that includes a set of powers and a unique dragon to be nurtured. There is also a character creation system at the start of the level that adds some minor customization to the game.

Dynamics — The powers and associated rules offer immediate feedback to the player when an error is made, which, combined with the undo mechanic, encourages experimentation and different approaches. Unlike Angle Jungle, this game does a better job with presenting what can and cannot be tapped through the use of particle effects and visual cues. However, the vast amount of gestures available can result in mistakes and accidental presses. The rewards system encourages the player to find the most efficient solution. This often means that, rather than only paying attention to the one side where the red box is, the player shifts their attention to the other side of the equation to simplify any values.

Aesthetics — The use of the character creator, art style, and narrative adds to the player experience by helping with motivation. These elements, along with the design metaphors, help contribute to the feeling that these levels are “algebra in disguise”. The introduction of a reward system also adds motivation and a feeling of accomplishment for players when they receive a three star rating. This feeling of accomplishment is reinforced upon completing a level by seeing the dragon grow, and the effect is even more pronounced at the end of a world where the dragon is fully grown. In my opinion, even though the art style and visuals contribute to the aesthetic experience, I feel that the narrative is not well integrated and can be confusing. There is a brief “cutscene” at the start of the game (it’s the only cutscene in the entire game) that only tells the player “When the dragon is alone, he will come out to play”. This is a very confusing introduction, and contributes to the game’s shortcoming in narrative integration. As a result, the motivation to “nurture the dragon” falls a little flat, and feels like a missed opportunity to help motivate players.

Example of a level from world 10

Learning Principles

Example of the scaffolding using the implemented design metaphors

One of my favorite aspects of DragonBox is how well it uses scaffolding as a tool to reveal the “real algebra” as the game progresses. I believe the game does an excellent job of using in-game feedback and visual cues to move from the design metaphor to the real algebra. The levels are also well segmented and are relatively self-contained, helping learners with self-paced learning.

Another principle that this game employs well is immediate feedback. This game makes it abundantly clear when a move is not possible or if an algebraic rule is being broken, and it does so in real-time and not at the end of a level. It also supports Gee’s principle of allowing learners to get lots of opportunities to practice their skills in the game. Additionally, the 200 levels in the game provide lots of variability that can help learners with the different situations that can appear when solving algebraic equations. For example, some levels are designed to showcase that it is better to simplify all addition or subtraction terms first before using multiplication or division to isolate the red box. That way, the simplifying operations on one side can be done more easily.

Overall Critique

In many ways, I really do love this game. The use of design metaphors to make algebra more digestible is extremely well executed, and will inspire me in my own educational game design journey. I do not, however, believe the narrative elements are well integrated or help serve the motivation of players. Furthermore, I am not entirely convinced of how effective this game is in teaching algebra to those who struggle with the topic; DragonBox feels like an experience that those who are relatively proficient in algebra will enjoy, and not as a game that can help those who are struggling learn in alternative ways.

References

[1] https://www.tutorfair.com/resource/209/maths-algebra

[2] Gibbs, Pamela. “Game Based Learning: The Effects of DragonBox 12+ on Algebraic Performance of Middle School Students.” (2020).

[3] Siew, Nyet Moi, Jolly Geofrey, and Bih Ni Lee. “Students’ algebraic thinking and attitudes towards algebra: the effects of game-based learning using Dragonbox 12+ App.” The Research Journal of Mathematics and Technology 5.1 (2016): 66–79.