How Multilinear Math Problems Can Help Struggling Students
How Multilinear Math Problems Can Help Struggling Students
May 20, 2020
One irritant when writing math problems in a traditional format, is deciding how much information and support to provide at any given point. Should this section on fractions be 10 words, or 10,000 words? For the more adept, more instructional text is annoying and slows their progress, but the beginners can be completely stuck without it.
Video games (be they visual novels or interactive fiction) elegantly handle this entire issue by not making math problems one-size-fits-all, and instead dynamically displaying content when it is needed. When the conditions are met, interactive media can change the virtual world, the difficulty and even the players location in the puzzle.
So an experienced player may make short work of a problem, not triggering any additional support dialogues because they evidently aren’t necessary. Whereas a beginner might have a longer experience, where more fundamental concepts are explored or where they can have additional attempts at failed challenges.
What conditions trigger these mistake dialogues?
It could technically be anything, but to maximize learning potential, it would have to be when the player either wants more support, or makes a mistake. It would also be possible to trigger dialogues based on the amount of time players spend answering a question. This approach has issues as it targets slow readers or people who’ve been distracted from the game, too.
Lets look at my preferred triggers more closely, as they do effect game-flow.
Condition 1: When the player makes a mistake, trigger a support dialogue
This was my initial strategy when designing math problems. While it is effective at providing more information when it’s needed, it has the problem of correcting a mistake and ensuring there is only 1 valid answer, rather than allowing the error to carry forwards. Why would you want an error to carry forwards?
One major advantage game based math problems have over traditional counterparts, is that games have a CPU. Games can perform the calculations live, dynamically, in response to players actions. This gives use two ways to help the player see the error of their ways. They get the instant feedback for their answer and, if the error can carry forward, they can see the results of subsequent calculations performed with this mistake.
Here’s an example:
Through a series of multiple choice questions, the player is asked about the number of seconds in a minute, the number of minutes in an hour and whether to divide or multiply seconds to get minutes. If the player gives the wrong answers, for instance 120 seconds in a minute, 80 minutes in an hour, and then converts to hours by multiply the seconds by 120 and 80, they can get some joyfully bizarre answers. Even the most math shy player can get a gut feeling that something is a little off when 1000 seconds converts to 1,000,000 hours, or some random variation there of.
Of course players still get instant feedback on their answer to any individual multiple choice question, but one wrong answer in a sequence of questions can throw a calculation off course. This is reminiscent of teachers giving you marks for your working, but docking you for the wrong answer.
Since I really enjoy having a computer calculate these ridiculous answers for me (I’m a little lazy to do it myself), I prefer to let the game proceed and use my mistakes, showing me the results of using the wrong equation or value at the wrong time.
Condition 1 variation: Trigger on detection of a sequence of player actions
A variation of conditioning a dialogue to a player mistake, is analyzing and triggering based on specific sequences of choices that indicate a problem. An example of this is found in my lovecraftian math problem (currently under development), where the player solves the problem by conducting experiments on their environment. If the player changes multiple variables at a time, the game will trigger a dialogue explaining the scientific importance of changing one variable at a time in an experiment.
I like this method as it targets errors that simple multiple choice questions can’t detect. It’d be less effective to ask a player ‘how many variables should you change at a time, in an experiment trial? -1, 0, 1 or 2?’.
The downside is, it’s not a rapid response. The player may be confused for sometime, before the game detects the pattern and pops in with additional support. As there are some educational theories that conclude struggle is important for learning, this technique may be beneficial. The data on player performance and drop off rates relative to other intervention methods, will provide insight in the future.
Condition 2: Give players the option to view support dialogues
I give players this option with choices like ‘think the problem through...’. When clicked, this triggers the support dialogue so the player can explore the current question more deeply.
Giving the player the choice to access support may be the best option, as they now know there is additional content if they want it, and their mistakes can carry forward through the dialogue tree.
It is unclear if providing this extra option will make players more cautious, more likely to click it and review, or if they’ll be more experimental, knowing there is support if they happen to need it.
Diagnosing Math Errors
If games are to conditionally supply additional support to some players, it becomes important to carefully design these diagnostic questions that expose subtle misunderstandings in the players mind. Breaking thought processes down to series of questions is a subject I won’t delve into here, but suffice it say, if the questions are too large or poorly place, a lot of important mistakes can be missed.
How Much Branching Is Too Much Branching?
Now that games have granted us the impossible ability to stuff a game with more dialogue than meets the eye, a writer begins to ask exactly which mistakes they should correct, and which they should pass off to other content. If a game is about fractions, then it seems reasonable to explore topics relating to the addition, multiplication and division of fractions, but should it also teach players how to read fractions?
It’s just a line in the sand, but a line that must be determined and drawn in advanced, so one doesn’t find themselves writing dialogues on how to read ½, or what the numbers 1 and 2 mean. If my game detects a player that crosses that line in the sand, I then send them on to other content that might be better suited to their needs, like the wonderful khan academy or math antics videos on youtube.
Data and Analytics
Outfitting these dialogues with analytics take them from useful, to potentially insightful. With a large enough player base (which my games currently do not have), it may be possible to correlate different mistakes together, showing different thought strategies strengths and weaknesses. Specific combinations of answers could be used to guess at the likelihood a player doesn’t understand fractions, before exposing them to any questions. This might enable more advanced strategies in story content and priming, to make a Eureka moment more likely. This is all hypothetical and far off at the moment, but new data does have the potential to uncover new potential.
We’ve only caught a whiff of video games, be they visual novels or interactive fiction or some other variant’s, potential for education. Being able to seamlessly adapt to a players interactions with the simulation, while providing instant feedback and support when conditions are met, give them several novel abilities.
I’ll continue documenting my R&D into text games as educational tools here. Please say hello on twitter if you’re also interested in ways games could enhance education.