Grammars, Gamers, and the Great Divisor

As discussed in a previous post, I am creating a gamified assessment in Twine. The semiotic domain I focused on division of fractions. I chose this domain because it is a challenging topic to teach. What is particularly interesting is the interplay between the internal and external grammar of the domain. While math educators are pushing to include more understanding in the instruction of mathematics, dividing by fractions is a particularly difficult topic to understand. In my experience, most teachers abandon trying to really explain why the students should do a particular algorithm of multiplying by the inverse to find the sections within what is being divided and opt instead for a rote memorization of Keep, Change, Flip. This rote memorization works but it does not promote understanding. So the algorithm satisfies the internal grammar (the procedure used to get the right answer) but leaves them with little understanding of actual mathematics (the underlying reasoning of the procedure).

An Escape Room as a Formative Assessment AS Learning

I designed my Twine to be a formative assessment as learning. The premise of the game is that the player has been trapped in a locked room by the Great Divisor. There is only one door, and it is sealed with three locks. In order to escape, the player has to find three different colored keys. The three keys are inside of boxes that will only open if the player solves the problems that are on the boxes. The three keys represent the three foundational steps in learning to divide fractions:

  • Blue key – understanding of numerator, denominator, and how to find the inverse of a fraction
  • Red key – review of how to multiply fractions
  • Yellow key – Division of fractions

Each box has a minimum of four problems that get progressively harder. Fortunately, the player is not alone; they have their trusted mouse, Denny, who is very good and math and can communicate telepathically. Unfortunately, he cannot tell the player the answers, but if the player misses a problem, Denny can offer mini-lessons on how to solve that type of problem. The player will then be prompted to do a few practice problems before going on to try to solve the box problems again.

The player may try the door at any time, but if they do not have the keys, it will not open. Additionally, the player may go through the boxes in any order, but the blue lock must be unlocked first. I did this so that players could have a sense of freedom but still be lead down a linear path.

On most questions, players have the option of asking Denny to explain one or more concept. (At one point he even convinces the player to not eat potentially poisoned food!). And if the player misses a question, Denny is there to offer some advice. After a few practice problems, the player is back to trying to solve the box problems. This practice was inspired by something I read from James Paul Gee (2008) “The game encourages him to think of himself as an active problem solver, one who persists in trying to solve problems even after making mistakes, one who, in fact, does not see mistakes as errors but as opportunities for reflection and learning (p.36)”.

Balancing My Grammars

I tried to balance the internal and external grammar issue by first having the blue box section where students are tested on the key terms for the unit. This will ensure that they will be able to process later instruction at a deeper level. Additionally, the mini-lessons always begin with an explanation of the why (external grammar) before we get into the process of how to solve the problem. This is an important point as we want to teach for understanding (internal grammar). As an example, I have linked a video from the Twine where Denny explains how to deal with whole numbers when dividing fractions. While there is a temptation to say, “just put it over one” (procedure), for most students this seems totally arbitrary. In the video, Denny begins by demonstrating why 3 is the same as 3/1(the underlying reasoning) and then goes on to review the how to divide 3 by ⅖ (procedure).


Checking the List

Earlier this summer, I made an assessment design checklist. Here is how I think my gamified assessment measures up against the list.

Does this assessment explicitly address the most relevant skills and big ideas in the topic of the assessment and the discipline being taught in the course?

I do think that this assessment meets this standard. The big ideas in this topic are knowing the terms for parts of a fraction, understanding how to multiply fractions, and understanding that dividing fractions is the same as multiplying the dividend fraction by the inverse of the divisor. While much of this is expressed in terms of internal grammar–with the amorphous word “understanding” standing in for the external grammar–I do feel that the game makes a good attempt at teaching the underlying principles.

Does this assessment provide the teacher with actionable information about the student’s background and expectations for the topic?

On this count, I feel Twine falls a little short. The teacher can gather a lot of information from walking the room, but there does not appear to be any collection of data. There is not an easy way to build in recorded student feedback. I linked a survey at the end, in hopes of gathering some of this data, as well as collecting bugs.

There are a few features added to the story to allow the player a more customized experience, including the use of their name throughout the game as well as a reference to their favorite food.

Does this assessment prime the student for learning within the discipline and promote student autonomy and accountability?

I do think that it does prime students for learning. Not only does it cover the “must-have” concepts for dividing fractions, it has them work through some problems with a fair amount of guidance in a fun way.

Does this assessment provide the student with clear feedback that is informative and actionable?

This is what I really like about Twine. You can direct students through the experience based on their responses. There were a few times where one answer option was an un-simplified fraction. While technically right, the structure of Twine, allows me to refer them back to the question to simplify the answer. It also allows me to set up common mistakes as distractors and address them directly.

Does this assessment address the primary skills being assessed and take into account the various learning styles, abilities, and disabilities of the students being assessed?

This is another point where the game might be a little limited by Twine. Since it runs on internet browsers, we can assume that the users with disabilities will have some tools that they are used to using for web browsing at their disposal. But beyond this, accessibility is an issue with the presentation. Also, given the text-driven nature of this assignment means that it will present a challenge to ELL players.

Final Reflection

It has been a fun experience to build an assessment in Twine. There are a number of features that make it useful for creating unique learning experiences. A few things that I really liked were the ability to use CSS to style the presentation, although I feel like I could have done a lot more to make an eye-popping presentation. The ability to embed content with HTML, and the ability to use variables and conditional selection to create game situations allowed for an interesting game. In the case of my game, a variable is assigned to each key. When the player goes to the door, they are asked to try each key, if the color key variable is true, the door opens, if not they are told to keep searching the room. This feature allows the creator to make for more engaging user experiences. I am really intrigued by how to make it more personable, as well as finding other ways to track user performance throughout the game.

To try the game yourself and let me know what you think!

Screenshot 2018-08-05 22.59.01

Please note: the game is hosted on a different server than this post.


Gee, J. P. (2008). What video games have to teach us about learning and literacy. Basingstoke: Palgrave Macmillan.

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