Insights gained after glancing through some books on game design

I have been glancing through the following two books: “The Art of Game Design: A Book of Lenses”, by Jesse Schell, and “Game Mechanics: Advanced Game Design” by Adams and Dormans.

Here are some insights that I have gained after reading a little (not thorougly). I am mostly finished glancing through Adams and Dormans. I have quite a bit reading left to do in Schell.

Insight 1: A simple model of game design

I started out reading in the book to the left: “The Art of Game Design”. When compared to the other book, I find that it provides the gentler introduction for a complete beginner such as myself. It discusses various definitions of the term “game” in an entertaining fashion, and it provides a useful simple model of game design.

I took the model from Schell and adapted it for use in education (click to enlarge):


A model with some similarities can be found in Adams and Dormans (p. 276). Of particular interest to me is the notion that the game generates an experience in the player’s mind.

Insight 2: A working definition for the terms “game” and “gameplay”.

Since there appears to be little consensus within the field regarding definitions, I take the opportunity to state my own working definitions of the terms “game” and “gameplay”. I have been inspired by what I have read in the aforementioned books.

In my opinion, a “game” is a machine that produces gameplay. Then, what is gameplay?

In my opinion, “gameplay” is a process in which the attention of a player is converted into choices for action in a way that generates an experience in the player’s mind.

Insight 3: The distinction between “emergent” and “progressive” games appears to be important

At some point, I switched over from Schell to Adams and Dormans. There I found an interesting discussion about two classes of games, named “emergent” and “progressive”, respectively.

The class “emergent games” appears to include games such as Civilization and chess, where the playing pieces and their interactions are what makes the gameplay “emerge”. This can produce a wide range of complex game states out of a surprisingly simple setup. Such games tend to have great replayability. Adams and Dormans include examples of an analysis tool called “Machinations”, which seems great for abstracting the mechanics of emergent games and improving them by simulating their gameplay on a computer. Anyone who would like to design their own version of a “Puerto Rico”-style game would in my opinion benefit greatly from mastering Machinations.

The other class, called “progressive games”, appears to include games such as “Zelda” and “Monkey Island”. These are games in which the designer appearently makes the player complete certain tasks in succession or semi-succession. Such games appear well suited for controlling the player’s experience, which could be useful for telling stories.

There are hybrid games that utilise elements from both classes.

Insight 4: When viewing education as comprising of game-like activities, the progressive ones appear to have the upper hand

After some reflection on past experiences as a student and my current occupation as a teacher, it appears to me that the activities of education include both emergent and progressive elements.

Take for instance the following game in mathematics, called The Fraction Machine

In this game, the student must solve 10 problems about fractions. When the 10th problem is solved, the student receives an automatically generated report displaying whether he or she answered correctly. Then the student can try again, optionally choosing another difficulty setting.

This appears to be a progressive game. The student is must complete one task before proceding to the next in order to reach the final goal. There is no emergent gameplay from an initial set of pieces and their interactions.

Then one can ask: How is this game different from a typical classroom activity where an instructor tells the students: “Now please complete every problem on page X” or “Please read pages X-Y, then answer every question on page Z”?

Typical classroom activities are progressive. If the activities themselves are not of particular interest to the students, things tend to get boring quickly.

One can find activities in education with similarities to emergent games. In mathematics instruction, one can ask the students to explore various matematical structures, i.e. “Find as many mathematical patterns as you can within a 10 x 10 table containing the numbers from 1 through 100.” Any activity in which you give the students a few mathematical “playing pieces” along with small set of rules describing what they are allowed to do with those pieces has the potential for being an emergent game.

In my experience, when viewing education as comprising of game-like activities, the progressive ones appear to have the upper hand. The question then becomes: Does it have to be that way?

Could student motivation be increased by replacing some of the “progressive game-like” activities with “emergent game-like” activities?

Could we improve the students’ motivations for engaging in “progressive game-like” exercies that we know to be necessary, by adding game mechanics from popular progressive games that generate experiences in the students’ minds? If so, how and where to start?

These are questions that I will pay attention to in my further reading.

Prototype of skill overview sheets for use in skill-based gamification of precalculus/calculus instruction

Skill overview sheets for gamification

I have produced several so-called “skill overview sheets” that I intend to use as a teacher in the upcoming semester in my precalculus/calculus instruction. The target audience are students at ages 16-17.

I have provided links to PDFs of the sheets below. The sheets describe most of the learning goals for the semester in a carefully designed way, which you will see. The sheets are worded in Norwegian, however I believe you can get the picture of what I am trying to do.

2013_06_30_ferdigheter_tall_og_algebra – Google Drive

2013_06_30_ferdigheter_sannsynlighetsregning – Google Drive

2013_06_30_ferdigheter_trigonometri_og_geometri – Google Drive

2013_06_30_ferdigheter_derivasjon_og_funksjonsdrøfting – Google Drive

Why I chose Google Docs as a medium for skill overview sheets

I chose Google Docs as a medium because I needed several features:

  • Collaboration (in the future)
  • Visual structuring of learning goals (“skills”) using tables
  • Support for mathematical notation
  • Hyperlink support
  • Support for “publishing to the web”, which enables easy Fronter (LMS) integration

Possible applications for gamification

I haven’t thought much yet about how these skill overview sheets could be used in gamification of instruction and assessment. Here are some properties of the sheets at first glance that could possibly prove useful for gamification:

  • Each learning goal is neatly presented in a visual way. By limiting the number of skills/learning goals, I communicate to the students: “This is what I expect you to learn, no more, no less. If you can master all of this, you will earn the highest grade.”
  • Each sheet has two sections. “Advanced” skills (upper section), and “Basic” skills (lower section), separated by a line. The idea is that assessment will focus on the relatively small number of advanced skills. By design however, mastery of any advanced skill also requires the mastery of a large number of basic skills. This gives the student the motivation for mastering every skill on the sheet, even though only a few of the skills will actually be assessed.
  • There are some very crude elements of a hiearchy and they are restricted exlusively for advanced skills. Some advanced skills lead to others, as indicated by small arrows. This may increase motivation with students (“I need that skill in order to master the other”).
  • Skill descriptions are very brief and are presented on a coloured rectangular shape. Each learning goal is in effect a tiny “skill card”, which opens up possibilities for game mechanics which involve the use of cards. In order to stimulate memorisation, individual skill cards could be attached to surfaces in the homes where the students would frequently look at them.
  • If every student printed out their own copy of the skill overview sheets, they could easily keep track of which skills that are “in progress” and which skills that they have already mastered. This property could potentially activate student desire for “hoarding” of mastered skills. It is easy to imagine some kind of gamification scheme that would reward the student with development points for a fictional character, or grant some kind of story-based reward, in return for the student’s hoarding of mastered skills.

Limitations by non-interactivity

At its current state, my skill overview sheet is quite limited with regard to interactivity. There is the possibility for hyperlinks that could lead to a web page offering further descriptions of each skill as well as instructional videos, but that’s about it.

In the future I could envision developing an interactive version of the skill overview sheet. By using web programming and touch screen devices, a student’s progress with each skill could be easily registered by touch input, and the skill overview sheet could change accordingly in order to display a status for each skill.

In the meantime however, I will focus on executing a full semester of math instruction using these sheets in their current non-interactive state and establish a proof-of-concept on the gamification that they hopefully will enable.


If you would like to know how to make skill overview sheets like these yourself using tables in Google Docs, feel free to contact me. I could even make a blog post about it if someone asked me.

As always, feel free to leave a comment. Thanks for reading.




Skill-based gamification of precalculus/calculus instruction and assessment, Part 1: Skills

As alluded to in a previous post, I shall now examine the “games” of precalculus/calculus instruction and assessment more closely. As mentioned, the intent will be to try and identify new ways of introducing and assessing mathematical skills that could utilise game mechanics.

The following applies to subjects “Matematikk 1T”, “Matematikk R1”, and “Matematikk R2” at ages 16-19, as those are the main subjects that I expect to be teaching in the coming years.

The big idea: Skills

I propose introducing the notion of mathematical “skills” as the “central unit”, so to speak, of precalculus/calculus instruction and assessment. Without further delay, here is the definition that I propose as of 20.05.2013.

A skill in the gamification of mathematics instruction and assessment is a trainable and uniquely named ability to perform a specific set of operations required during the solution of a given mathematical problem.

Example: Differentation (the process of finding a derivative) would be regarded as a trainable and uniquely named “skill” in this system of gamification.

Mathematical problems and the hierarchy of skills

Depending of how the skills are defined, the solution of a given mathematical exercise could require the application of several skills in some order.  In addition, for some higher-level skills it could be true that whenever the high-level skill is invoked, certain lower-level skills would almost certainly be invoked too as part of the resolution of the higher-level skill. This gives the following picture (see Figure, click to amplify):

Figure_ Skill-based gamification_ Hierarchy of skills

The mathematical problem in Figure invokes Skills 1 and 2, which in turn invoke Skills A, B and C upon resolution. Skills 1 and 2 are higher-level skills while Skills A, B and C are lower-level.

Example: Differentation of a quotient u(x)/v(x). This problem invokes the “quotient rule” skill:

d/dx u(x)/v(x) = (u(x)’v(x)-v(x)’u(x)) * v(x)^-2.

However, upon resolving this skill, a student is usually also expected to simplify the numerator and check for a possible factorization with the aim of cancelling out a common factor with v(x). Thus, the lower-level “factorization” and “cancelling” skills are invoked as part of resolving the higher-level skill “quotient rule”.

Note: Drawing inspiration from computer role-playing games (RPGs), higher-level skills and lower-level skills could instead be denoted as “active” and “passive” skills. In this context, an “active” skill would be a higher-level skill that is invoked only when called for by a specific type of problems which require it.  Otherwise, the skill is stored for later use. “Passive” skills on the other hand would be a more general “toolbox” consisting of essential lower-level skills which are constantly probed for upon the resolution of varous active skills. Hence, passive skills need to be extremely well memorised in order to enable efficient probing.

I’m still undecided about the usefulness of the active/passive naming convention. It could resonate with students familiar to computer RPGs, yet alienate others.

The teacher should maintain a complete list of all higher-level and lower-level skills in a curriculum

In order to utilise the notion of skills in instruction and assessment, for a given curriculum the teacher should maintain a complete list of all the higher-level and lower-level skills that the students need in order to master that curriculum. This enables the teacher to tell the students: “Look! This is all there is to learn. If you can master all of these skills, you will master the subject.”

Given a suitable technical implementation on touch devices (e.g. a finger-browsable list of skills icons that can be tapped for further description of the skill), I can imagine all sorts of motivational advantages for the students as a result of this kind of superior overview.

The teacher should not necessarily reveal all parts of the list of skills to the students upon starting instruction of a new subject

If I was to use the concept of skills in the instruction of “Matematikk 1T” (age 16-17), “Matematikk R1” (age 17-18) and “matematikk R2” (age 18-19), I would not necessarily reveal all parts of the list of skills to the students upon starting instruction of a new subject.

For the younger tier (age 16-17) I would probably reveal the entire list to get them kick-started and train the required skills as efficiently as possible. However, as the students progressed through tiers 17-18 and 18-19, I would gradually enourage them to analyse the subject material themselves: “What do you think that the skills are? Which skills do you think are required to master the mathematical problems of this subject?” Afterwards, when the students had made their candidate lists of skills, they could compare the lists with oneanother. Ultimately, they could compare with the teacher’s list.

The reason for this is that when the students leave Matematikk R2 for advanced mathematical education at universities, they will not have the teacher or anyone else to make a list of skils for them. By then they should have learned how to analyse a curriculum and make such a list themselves. That’s why I would start out revealing the entire list at lower tiers and then gradually start holding it back, making them do the analysis themselves.

There is much more to say. I haven’t even started going into the details of skill-based instruction, much less skill-based assessment. I can think of a number of ideas that I will share with you in subsequent posts. Until then, thanks for reading, and be sure to leave your comments below.





Gamification and the game of education

In this post I start by asserting that education itself is a game that has certain rules. I then state that gamification in education is the process of altering the rules of that game in new and creative ways that enhance learning.

Education is a game

Education is a game that has certain rules. The grown-ups say to the students: “This is what we make you do in order to develop your skills so that you can enter our world of economic opportunity.”

Some students handle the game fairly well and enter the world of economic opportunity without facing major obstacles on the way. Other students struggle with the game, for various reasons.

Improved awareness and understanding of the game could remedy feelings of helplessness

Every student has at least a basic awareness of the game of education. They know that there are certain rules. For various actions, they know at least subconsciously that “If I do X, then Y will probably happen.” However, I do believe that there are many students who do not reflect conciously about the fact that education is a game. They just do what they are told.

When the students get the results they want, they feel fine. (“I guess I made it.”) When they don’t, they become unhappy. If they are unhappy about their situation and can’t identify a way of changing it, they could develop feelings of helplessness.

If we could train the students into thinking consciously about how the game works, i.e., “I know everything about this game. I know exactly how I can manipulate it in order to get outcome I want”, then I believe we could remedy some of those feelings.

Rules of the game of education that are not easily changed

Since I am a precalculus/calculus teacher for students at ages 16-19 in the Norwegian education system, I will focus on the rules of that particular system. Rules that appear as rather unchangeable include the following:

The curriculum

There is a national Norwegian curriculum of precalculus/calculus education at ages 16-19. The curriculum for age 16-17 can be found in this document on page 9-10 in the section named “Competence aims after 1T”.  The curricula for ages 17-18 and 18-19 can be found in this document on pages 3-5 in the section named “Competence aims”, subsections “Mathematics R1” and “Mathematics R2”, respectively.


For most students, attending class represents their best chance of learning something. The students know this and show up for the most part. In any case, they know that someone is keeping track of their attendance and that there will be a consequence if their attendace drops low without good reason.

General principles for formative and summative assessment

At the end of the semester, students receive a total score called “summative assessment”. At various times throughout the semester, students are required to play certain minigames known as “formative assessment”. In precalculus/calculus, these minigames often consist of solving logical exercises. There are various rules that define the outcome of each minigame. Under Norwegian law, students are entitled to having their total score assessed based solely on their “competence at the end of the semester”.

Written exam

There is a chance each year during ages 16-19 that some of the students are drafted to a written exam in mathematics. The exam follows the national curriculum. The texts of previous exam exercises and their solutions are available online.

Oral exam

There is a chance each year during ages 16-19 that some of the students are drafted to an oral exam in mathematics. The exam follows the national curriculum and there are national guidelines for the procedure of the exam.

Rules of the game of education that are easily changed

Again I will focus on my own teaching situation. The following rules apparently can be quite easily changed:


The interaction between the teacher and the students during instruction is a game in its own right. At age 16 when I first meet them, my students have already experienced playing that game for 10 years. The rules of the game of instruction are deeply rooted in tradition. However, we could bend the rules, break them, or even make up our own rules, if doing so would enhance learning.


Assessment, and the practicing of skills prior to assessment, is a game in its own right. Similarly to instruction, the rules of assessment could be bent, broken, or even entirely remade, if doing so would enhance learning.

Gamification in education is the process of altering the rules of the game of education in new and creative ways that enhance learning

If we accept the notion that education itself is a game, then gamification can be viewed as the process of altering the rules of that game in new and creative ways that enhance learning. An educator who is skilled at gamification is someone who knows a lot about games, their mechanics, and what makes them fun, and knows how to incorporate such mechanics into the game of education.

In subsequent posts I shall examine the games of instruction and assessment more closely. The intent will be to try and identify new ways of introducing and assessing mathematical skills that could utilise game mechanics.

Feel free to leave your comment below. Thanks for reading.











Gamification of precalculus/calculus instruction in the Norwegian education system

As a part of my work as a math teacher in Videregående skole in the Norwegian education system I intend to develop a method of instruction in precalculus/calculus which utilises gamification. Whenever I teach precalculus or calculus in any of the following courses: Matematikk 1T, Matematikk R1, Matematikk R2 (See Figure), I will offer each student the choice of applying gamification principles to enhance their learning.


I sincerely believe that gamification in education could:

  • make learning more fun
  • motivate students to practice their skills more
  • stimulate metacognition and help students develop their own schemes for structuring their work which could be useful once they reach higher levels of education

However, I will not force gamification on anyone. If the students desire it, they can have the curriculum without gamification.

This will be a work from scratch as I have no previous training in the subject. I have a couple of ideas that I will be working on and will post the results on this blog in English once I get started.

If you have ideas for how one can implement gamification principles in precalculus/calculus instruction, or in any other subject at any level of education, feel free to leave your comment below!