Artifact 5 : Escape from the Divisor


Primary Alignments:

Standard 2: This is a gamified formative assessment that can serve as an platform for instruction. The final reflection represents an evolution in my views on the role of assessment in learning.

Standard 3: In creating and discussing this assessment I studied theories related to gamified learning and internal and external grammer of a game experience. I applied these theories to the creation of a formative assessment that I would use in my practice which address a particular problem of practice: teaching dividing fractions for understanding. The assessment was compared to the assessment design check list that I created for the same course. The final reflection goes into this process as related to my time in CEP 813 in detail.

Standard 5: In addition to creating a unique game experience through programming in HTML and CSS, I wrote extensively on the theories which informed the creation of the assessment.

Secondary Alignments:

Goal 2: Desiging this assessment required me to reflect and refine the way I was teaching this concept.

You are a prisoner in the dungeon of an evil genius.

Do you have the intelligence, the strength, and the perseverance to escape?

The challenge has been issued, will you meet the call?

Yes… Yes, I will

A Gamified Assessment

For our next assessment we have been asked to create an assessment using Twine.

I am excited about this for a few reasons.

First, I love the idea of gamified assessment. In fact, just last night I was having a conversation with my school-aged kids, and they told me school would be much better if “our tests and homework was more like Assassin’s Creed”. It has been my experience, that the same kids who appear to have little grit when it comes to learning a math concept can also be the ones who will stay up all night trying to get slay a boss in their favorite game. It all reminded me of this video with Paul Gee.

Second, I am very interested in working with Twine. The interface for the teacher seems very logical, and I like that you can use HTML to customize it. While Twine will demand a fairly linear narrative and it appears that the questions always break-down to some sort of objective choice, I still think that I can find some interesting ways to lead a student through a learning/assessment experience.

My semiotic domain

For my assessment, I am focusing on middle-school math. Specifically, I am focusing on the skill of dividing fractions. One reason I find this an interesting study is because of the interaction between the internal and external grammar of the topic. On a conceptual level, dividing by fractions can be a bit opaque. While it is easy to teach students to conceive of dividing with whole numbers by drawing circles and counting up tally marks (one for you, one for me, when you divide by two) what does it mean to divide something by less than one? Why is the quotient bigger than the dividend?

Often, students are taught workarounds. For example, the ever popular KCF (sometimes also taught as KFC-like the yummy chicken place). This method has become so popular there are even songs dedicated to it like the one below:

While it is an effective algorithm, there is something that has always bothered me about KCF (KFC), and that is that kids apply it without really understanding why. It seems to me to reinforce the idea that math (especially math after 3rd grade) is a collection of secret handshakes and complex procedures that don’t relate to reality. So while KCF satisfies the internal grammar of mathematics (it gives you the right answers) it doesn’t help kids actually learn how to do mathematics (external grammar). Likewise, it reinforces a common attitude amongst the peer group that views math as esoteric and unrelatable.

The Escape Room

My plan is to make an escape room:

The Grand Divisor has locked you in his study.

In order to escape, you must decipher his devious puzzles and enter the 8-digit code that unlocks the room.

You will explore the room and are given questions along the way, the answers to these questions make up the numbers of the code.

When you successfully enter the 8-digit code, you will escape.

Assessment As Learning

The Grand Divisor did not realize that your super-intelligent rat,

Denny, is with you. If you get stuck or make a mistake, he will use his magical-mathematical telepathy to teach you what you need to know.

While Denny has incredible mathematical skill, he will not give you answers.

Your problems are yours alone; only you can solve them.

This feature of the game will allow me to cycle students through mini-lessons if there is an idea that they do not understand. If a student misses a question, Twine can be used to branch them into an instructional track before looping them back to the problem to allow them to try it again.

While Denny will teach KCF to help students solve a problem, some of the questions and mini-lessons will focus on the underlying principles of fractions and dividing them, so that students will have a deeper understanding of why we KCF.

Check It with the List

This assessment aligns well with my assessment design checklist, but there are a couple of areas that I am concerned with. The assessment is fairly cut-and-dry in terms of the content. The answers always end up being the selection of one “right” answer. While this is ok, I would prefer something that is a little more flexible. I read that variables can be used in Twine, but I need to explore more how they could be used to create a more personalized experience. Also, I do not know what sort of accessibility features Twine has so this could create some problems.

I am really looking forward to building this assessment and getting to know Twine!

As discussed in my last 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.

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

Final Reflection on Assessment

Image from Wikipedia Commons source linked with image

It is hard to believe that our time has come to an end, but it has. My course on assessment is closing, and I have been asked to reflect on the experience and the evolution of my thoughts on assessment.

To begin, I reviewed the three things I wrote  I believed about assessment at the beginning of the semester.

  • Assessment allows for teachers to evaluate and adjust their practice.
  • Assessment gives students a goal to strive for.
  • Quality assessment should test understanding of underlying concepts through creative problem-solving.

Looking back on these, I still largely agree with the premise of the three although a number of details have been filled in. Additionally, this course has given me a number of new tools and pathways for inquiry into my use of assessment.

Where I stand now

Assessment is essential to learning.

If we define the desired outcome of education to be the acquisition of a certain understanding or skill it is only through assessment that we can know that it has been learned. As a jazz student at the University of New Orleans, I was fortunate enough to study with the great Ellis Marsalis. Prof. Marsalis and the other faculty at the school had a mantra that was a question, “but can he play?” Sure, the student is doing the work and coming to class, but when they get up on the bandstand can they actually do what we think they can.

This is an essential function of assessment, can you do what you think you can do? The problem is that this sort of outcome-based summative assessment is often seen as the only type of assessment there is. Additionally, the pressure to perform on these high stakes assessments has led many student and teachers for that matter to view assessment as the measure of a fixed ability that either reflects success or failure. Throughout the course we have been presented with a variety of assessment types: formative assessment, summative assessment, assessment of learning, assessment for learning, assessment as learning.

In a way, all learning is a form of assessment. You gain information, you see if you can apply it, then you try again. It is this loop of learning, testing, feedback, reevaluation that allows all creatures to learn in their environments. Sadly, we have learned to have contempt for the testing and feedback portion of this loop, and as a result, we have created schools and students that are afraid to take chances and afraid to get things wrong. In a way, we are creating people who are afraid to learn. Assessment is not to be feared or tolerated, it is to be appreciated as an essential (arguably the central) component in learning.

Assessment provides clear pathways for going forward.

One of my favorite passages in Alice and Wonderland goes as follows:

Would you tell me, please, which way I ought to go from here?’

‘That depends a good deal on where you want to get to,’ said the Cat

‘I don’t much care where—’ said Alice.

‘Then it doesn’t matter which way you go,’ said the Cat. (Carroll, 2008)

This quote says so much about the value of assessment. Assessment should point to where we are going and test where we have been. In the diverse classrooms in which we teach today, students are diverse in terms of experience, ability, and background. This creates unique challenges and opportunities. We have so many tools to identify the specific areas in which a student is lacking understanding, and there is no dearth of resources available for helping students learn. The difficulty is putting it all together. Teachers need quality data about student performance and a clear idea of how to get their students the help that they need.

A particular challenge that goes along with this view of assessment is student motivation. In the words of Dr. Lorrie Shepard (2000) “teachers need help in fending off the distorting and de-motivating effects of external assessments” (p.7). But here assessment can serve as an affordance rather than a constraint. When students are invested in their learning and have a clear sense of where they are and where they are going, they can be more autonomous learners. For example, it has been found that digital portfolios, when teachers are comfortable with the technology being used and they employ assessment for learning strategies, are a very effective means of gauging student progress (Barrett, 2007).

Feedback is an essential element in knowing that you are on the right track. We have all had the experience of trying to give directions to someone and saying something like, “if you get to the red barn with the dog barking in front of it, you went too far.” It is feedback to that tells us how we are doing on the path, and having quick actionable feedback is essential to a quality learning experience. As we read in  Van den Bergh, Ros, & Beijaard (2013), feedback given during active learning is most effective.

The Creative Application of Differentiated Formative Assessments AS Learning is the key to 21st-century education.

As teachers in the 21st century, we have tools that most generations could never have dreamed of. Additionally, the requirements for our students–their abilities to confidently navigate various technological and social settings, their ability to creatively solve problems, and their need to be self-motivated and independent–is unique to our age as well. Here technology offers wonderful opportunities to meet these needs, but it will require a fundamental reexamination of learning and teaching.

We are all familiar with the importance of differentiated learning. Technology can greatly facilitate this. Whether it is using technology to create a comprehensive reading assessment that lets teachers know both their student’s reading skills and habits, as I tried to do in or the very rich data that can be collected from standardized tests, teachers can gather an incredible amount of data and link it to useful resources that are more tailored to the students needs. Not only does this help students learn better, having students work on material that is appropriate and relevant to them can help in classroom management and recruitment of students’ intrinsic motivations.

But in order to do this, it has to feel authentic to the learner., it has to feel like it is theirs and it has to engage them creatively. If we want students to not feel learning is a stick they are being measured against, we need to craft learning and assessment scenarios that feel more like games than physical exams. Games offer a unique opportunity to explore this. I was recently invited to play the card game Smash Up with my two sons. The volume of complex information that they were processing at lightning quick speed was astonishing. Now how do we get that type of learning and mastery of the concepts we are teaching in school? Games provide players the opportunity to in active learning that has them: “experiencing the world in new ways, forming new affiliations, and preparing for future learning” (Gee, 2003, p. 24). And they will do all of this, even when it requires great effort. I would like to be able to blend this sort of learning with assessment.

When making the game Escape from the Divisor, I tried to combine these two elements. Using Twine, I took the user through the concept of dividing fractions, checking to see that they had a working understanding of how to divide fractions. As we saw in the work of Randy Bennett (2011) in Module 2, there is an interplay between formative and summative assessment. Throughout the game, I tried to incorporate mini-lessons throughout the game for students that either missed questions or did not feel confident answering them. To get the key and escape from the divisor, a student needed to pass all of the modules, but they had opportunities to learn and get feedback throughout the game.

Another interesting tool for differentiation available in this setting is crafting distractors with common misconceptions that can be used as teachable moments for students. In this way, the assessment becomes an assessment that is also teaching the student as they take it. While this idea of assessment as learning may sound a little heady. It is, in fact, how we learn to do just about everything. When you try to cook an omelet, you are taking an assessment. You take what you think you know, apply it, get feedback (taste, texture, etc) and then reevaluate your knowledge. The more precisely you can identify the specific knowledge that you are lacking (the flavor is not good, I can’t flip it over in time) the better chance you will have to master the skill next time.

It is through this process that the student develops a sense of mastery and autonomy. They begin to understand the essential principles that underlie a particular skill or concept. In the omelet example, you need to learn about cooking temperature, different cooking surfaces, how heat affects egg texture, ratios for salt and other seasonings. Once you know how to make a good omelet these same principles can be applied in a new scenario, making scrambled eggs. While all of the parameters are similar the values of those parameters (especially heat) are very different in this new scenario.

While trends come and go in education, there is an underlying theme to so much of 21st-century learning “active learning works best. Telling doesn’t work very well. Doing is the secret. Active student engagement is necessary, and one of the best ways to get it is to use stories that catch students’ interest and emotion” Herreid & Schiller (2013 p. 65). Technology affords us the opportunity to invent these types of learning scenarios. But it takes a great deal of work, creativity, and most importantly, the willingness to let go of some preconceived ideas of what “good” education is. For example, it is good to get a question wrong, that is how you learn. It is good for students to be working at their own pace, guided by their own interest. It is good for the teacher to not know all the answers, but rather be a facilitator in the student’s own construction of knowledge.

Means to a Better End

One way to begin this process was to create the assessment design checklist, which I have referred to frequently throughout the course. The checklist provides me with clear benchmarks for creating the types of assessment that I want to create. I find that whenever I work with the checklist I find oversights to address and new things to add. For example, in the reading assessment, my assessment design checklist suggested that I need to focus “on the most relevant skills and big ideas in the topic”. This prompted me to make a whole new section to my reading assessment focused on decoding and comprehension. And while working on this my design checklist encouraged me to promote student autonomy which led to the addition of the username and avatar to the application.

My ideas about assessment have changed greatly through this course. Not only do I now see assessment as a central element in the learning process, rather than a snapshot taken from outside of that process, I now see assessment as needing to be creative and constructive. Not just constructive in the typical constructive criticism way, but more importantly, constructive meaning that it facilitates the students’ construction of meaning by drawing on the students’ backgrounds and interests and gives them space to explore, get feedback, and adjust. Assessment is essential in this process. “From a sociocultural perspective, formative assessment — like scaffolding — is a collaborative process and involves negotiation of meaning between teacher and learner about expectations and how best to improve performance” (Shepard 2005). While the outcomes of my three things I believe about assessment seem to be similar, when comparing this list with my initial list I am struck by the fact that my first list is about what assessment should be. It sees assessment as a narrow component of instruction that can be perfected. My new ideas about assessment center on what assessment can do, and the essential role it plays in creating rich learning experiences for students. Before I was trying to find a better assessment, now I am thinking how assessment can better learning. This is a very different view of assessment, I look forward to exploring and expanding throughout my life as a teacher and scholar.


Barrett, H. (2007). Researching Electronic Portfolios and Learner Engagement: The Reflect Initiative. Journal of Adolescent & Adult Literacy, 50(6), 436-449. Retrieved from http://www.jstor.org.proxy1.cl.msu.edu/stable/40015496

Bennett, R. E. (2011). Formative assessment: A critical review. Assessment in Education: Principles, Policy & Practice, 18(1), 5-25. doi: 10.1080/0969594X.2010.513678

Carroll, Lewis (2008) Project Gutenberg’s Alice’s Adventures in Wonderland, retrieved from http://www.gutenberg.org/files/11/11-h/11-h.htm

DMLResearchHub. (2011, August 4). Games and Education Scholar James Paul Gee on Video Games, Learning, and Literacy. [Youtube video]. Retrieved from https://www.youtube.com/watch?v=LNfPdaKYOPI&t=2s

Gee, J. P. (2003). What video games have to teach us about learning and literacy. New York, NY: Palgrave Macmillan.

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

Herreid, C. F., & Schiller, N. A. (2013). Case studies and the flipped classroom. Journal of College Science Teaching, 42(5), 62-66. [PDF]

Mobile Learning Center. (2015, November 25). Watch Me Flip Dividing Fractions Song.[Youtube video]. Retrieved from https://www.youtube.com/watch?v=8Tv7WunDsLg

Shepard, L. (2000). The role of assessment in a learning culture. Educational Researcher, 29(7), 4-14

Shepard, L. (2005). Linking formative assessment to scaffolding. Educational Leadership, 63(3), 66-70..

van den Berghe, L., Ros, A., & Beijaard, D. (2013). Teacher feedback during active learning: Current practices in primary schools. British Journal of Educational Psychology, 83, 341-362. doi:10.1111/j.2044-8279.2012.02073.x [PDF]

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