Educational Math game

Educational Math game

Educational Math game

By Isabelle Kok

Finally, you can begin your chosen study program. The only downside is that if you discover you need math, let that be your least favorite subject. You’re looking for ways to improve your math skills. You wish there was a more enjoyable way.

My solution is to play a game to practice your math skills. But how do you ensure that you have fun while also learning something? This led to my research question:

“What goes into designing an educational puzzle game with a learning goal?”

After a lot of literature research I came across different frameworks. I compared them and eventually chose one. With this framework, I designed a game and created a paper prototype. As seen below:

You can read about my entire process down below.

1.     Background

1.1       Learning Subject

1.2       Target Audience

2.     Framework

2.1       The 8 Pillar Octalysis framework.

2.1.1        Epic Meaning and Calling

2.1.2        Development and Accomplishment

2.1.3        Empowerment of Creativity and Feedback

2.1.4        Ownership and possession

2.1.5        Social influence and relatedness

2.1.6        Scarcity and Impatience

2.1.7        Loss and Avoidance

2.2       DULVAFT model

2.3       Framework digital educational games by Aleven

2.3.1        Learning objectives

2.3.2        MDA

2.3.3        Instructional Design Principles

2.4       Analyze the frameworks.

3.    My Game Idea

3.1       Original Game

3.2       My twist

3.2.1        Explaining

3.2.2        Visuals

3.3       Framework Aleven

3.3.1        Learning Objectives

3.3.2        MDA

3.3.3        Instructional Design Principles

4.    Paper prototype

5.    Resources

1.     Background

1.1        Learning Subject

The base of mathematics, from which you can readily build on afterwards. At the time being, my primary focus is on HVA HBO-ICT modules. And I concentrate on module A, Calculation with Numbers and Letters. Because it is the most fundamental of all the other math you could learn. Module A contain the following learning goals.

Learning goals of Module A: (hva hbo ict Essential Skills Wiskunde)

After studying this module, you should be able to:

  • Identify terms and factors.
    • eliminate brackets and factorize with numbers.
    • Divide a number into prime factors.
    • Be able to perform calculations involving fractions, powers, and square roots.
    • Understand how to count with letters.

This module includes priority order. And I used this knowledge to create my game around.

Priority order

  • Addition and subtraction is performed in the order they are
  • Multiplication and division are performed in the order in which these operations occur, from left to right.
  • Multiplication and division take precedence over addition and subtraction.

1.2        Target Audience

Any HBO student who needs to improve his mathematical skills for school. With the emphasis on non-gamers being able to play this game while learning math.

2.     Framework

It can often be easy to use models or frameworks that offer guidelines when designing games. But are there also specific frameworks for educational games? Several models and frameworks have been investigated.

2.1        The 8 Pillar Octalysis framework.

 Unpredictability and Curiosity

“Gamification is the craft of deriving all the fun and addicting elements found in games and applying them to real-world or productive activities” (Chou, 2015)


Gamification guru Yu-kai Chou developed the 8 Pillar Octalysis framework. The 8 core drives of Gamification are: 1. Epic Meaning and calling, 2. Development and accomplishment, 3. Empowerment of creativity and feedback, 4. Ownership and possession, 5. Social influence and relatedness, 6. Scarcity and impatience, 7. Unpredictability and curiosity and 8.  Loss and avoidance.

2.1.1      Epic Meaning and Calling

Epic Meaning & Calling is the core drive where a player believes that he is doing something greater than himself, or he was “chosen” to do something. (Bilham, 2021)

Duolingo is notorious for its constant (and almost over the top) notification bombardment. To some, these notifications might be a total hindrance, but to others, it’s that daily piece of encouragement / a friendly nudge to get back amongst their language learning.

It aims to make the user feel valued and wanted on the platform, igniting a sense of ‘calling’ to the user. It can make you feel like you are not only contributing to your own language learning goals but contributing to the Duolingo community.

2.1.2       Development and Accomplishment

The sense of getting closer to your goal and achieving it, can be provided by breaking the challenge into stages and displaying your progress (points, gems, levels and more.)

Achieving it can be provided by breaking your challenge into stages and showing your progress (points, gems, levels and more). Duolingo does not skip this vital step in the gamification process, celebrating every little win with its users.

Duolingo’s iconic are bright colours and playful illustrations are used in a positive manner to emphasise that something has been accomplished.

The enthusiastic and positive tone of voice is very prominent amongst these examples as well, with plenty of exclamation marks sprinkled in, ensuring the user feels as accomplished as possible after their action.

2.1.3      Empowerment of Creativity and Feedback

Yu-kai Chou compares this part of gamification to building Lego blocks. A user is engaged in a creative process where they must try different combinations. Users can then receive the feedback they crave and be provi (Koop, 2017) (V, E, Easterday, & Organ, 2010) (Bilham, 2021)ded with the result of their creativity.

A Duolingo user will inevitably get some questions wrong during their time on the app. While being incorrect can sometimes be projected as something negative, Duolingo takes it as an opportunity to allow its users to learn and grow.

2.1.4      Ownership and possession

The Ownership and Possession Pillar is based on the principle that because you own something, you want to improve it, protect it, and get more of it. This pillar is often associated with elements such as virtual goods and currencies.

Multiple components:

– Profile picture

– Streak

– XP

– Gems

– Outfits

2.1.5      Social influence and relatedness

“Social Influence and Relatedness is a Right Brain Core Drive that bases its success off the common, and sometimes inevitable human desire to connect and compare with one another. When utilised properly, it can serve as one of the strongest and long-lasting motivations for people to become connected and engaged.” – Yu-kai Chou.

Duolingo encourages you to invite friends (something that almost every app does nowadays), follow people, check out your friends’ progressions and your place on league leaderboards.

These features allow an aspect of comparison to others on the app which can, when used effectively, encourage the user to continue using Duolingo or interact with it a little more to progress alongside their friends.

2.1.6      Scarcity and Impatience

There is a natural human tendency to want what we cannot have. Scarcity and impatience is the drive that motivates us simply because we cannot obtain something immediately, or because there is difficulty in obtaining it. This pillar can sometimes overlap into the Loss and Avoidance Pillar, where users do not want to lose progress or points in case, they miss out on something amazing.

– Duolingo’s exclusive club

– Duolingo won’t let just anybody in

– XP Ramp Up Challenge

– this event ends in 21 hours

Unpredictability and Curiosity taps into the human desire to find out what happens next. According to Yu-kai Chou, our intellectual consciousness is inherently lazy, and if tasks at hand don’t demand immediate attention, the neocortex delegates the mental legwork to our subconscious mind, or “System 1” according to Economics Nobel Prize winner and psychologist Daniel Kahneman.

Duolingo taps into this pillar when trying to get users to progress to another level. When something is ‘locked’ there is a desire to view and progress to the unknown. In the middle image below, users are given the opportunity to spend some of their gems take a test to skip to the unknown level. Will it be so hard that you will not progress? Or, by chance will you succeed and progress further than before. It is a gamble that many users are willing to take.

2.1.7      Loss and Avoidance

The Loss and Avoidance Pillar is simply motivating through the fear of losing something or having undesirable events transpire. It goes hand in hand with Ownership and Possession, where something you once earned could be taken away from you.

The primary example in Duolingo’s product is the use of the Streak feature. Although this has been touched on in the previous pillars, one core drive for withholding your streak is the fear of losing it.

2.2        DULVAFT model

The DULVAFT (Koops, 2017) model was created by Martijn Koops. A DULVAFT is a list of the essential components of a game. DULVAFT is a short Dutch form for doel, uitdaging, levels, voortgangindicatie, autonimie, feedback, and thema. These are the goal, a challenge, levels, a progress indicator, autonomy, feedback, and a theme in English. In any case, the best games provide their players with the following features:

  • Goal:

The intended outcome desired by the player.

  •  Challenge:

The obstacle that must be overcome to achieve the goal is.

  • Levels:

The levels into which the obstacles are classified.

  • Progress Indicator:

An indication of the player’s progress in the game

  • Autonomy:

The player’s ability to make his own decisions.

  •  Feedback:

Information that updates the player on how things are going.

  • Theme:

The game’s presentation style

Martijn Koops (2017) believes that an educational game should have these features in any circumstance. The term “goal” refers to the game’s goal rather than the learning objectives of the game.

The sort of game you play has a big impact on what you learn. According to Martijn Koops (2017), there are four sorts of games: knowledge games, practice games, understanding games, and exploration games. This is based on the learning objective that is contained in it.

  • Knowledge games:

can be used to either provide or test knowledge.  For example, pim-pam-pet, triviviant.
The aim of learning these kinds of games is knowledge.

  • Practice games:

allow the player to use a skill.  Practice will help you get better and better. For example: doctor shiver, mikido, and tag.

The aim of learning these kinds of games is skills.

  • Understanding games:

is about understanding structure, rules, and coherence between elements.
For example, chess, monopoly, and risk.  The aim of learning these kinds of games is concept.

  • Exploration games:

It is about being exposed to new social and cultural contexts. The acts of the players decide the outcome of these games. 

For example, role play, such as mother and father, and werewolves.

The aim of learning these kinds of games is attitude.

2.3        Framework digital educational games by Aleven

The framework described in Aleven’s (2010) paper coordinates the several levels at which an educational game must succeed to be effective. This paper proposes a framework to help designers identify and analyse the essential design decisions that must be made while developing an educational game. The framework is composed of three components: learning objectives, MDA, and Instructional Design Principles, along with a strategy for combining them.

2.3.1      Learning objectives

A well-defined set of learning objectives assists designers in ensuring that the game they create really satisfies an intended and coherent set of educational goals. If the educational goals are unclear, it is difficult for a designer to imagine how to create a game that is educational and effective. Specifying the learning objective requires answering three questions:

  1. (Prior knowledge) What knowledge or skills do student/players need to have before starting the game?
  2. (Learning and retention) What knowledge or skills can student/players reasonably be expected to learn from the game?
  3. (Potential transfer) What knowledge and skills might they learn that go beyond what they encountered in the game?

2.3.2      MDA

LeBlanc’s MDA framework helps game analysts and designers in thinking about games in three mutually dependent layers. The letter “M” stands for Mechanics. The letter “D” stands for dynamics. The letter “A” stands for Aesthetics.


Mechanics are the core components of the game around which it is developed. Think about the basics of movement, explicit goals, control mechanics, rules, and materials. (Aleven, Myers, Easterday, & Ogan, 2010)


“Dynamics of the game are the runtime behaviors of the game mechanics acting on the players’ input and each other’s output over time.” (LeBlanc, R, & Zubek, July 2004)

The aesthetics of the game capture the emotional responses of the player as they interact with the game. Aesthetics’ vocabulary moves away from “fun” and “gameplay” and toward a more straightforward vocabulary (LeBlanc, R, & Zubek, July 2004). This includes, but is not limited to, the taxonomies stated below:

  • Sensation

Game as sense-pleasure

  •  Fantasy

Game as make-believe

  • Narrative

Game as drama

  • Challenge

Game as obstacle course

  • Fellowship

Game as social framework

  • Discovery

Game as uncharted territory

  • Expression

Game as self-discovery

  •  Submission

Game as pastime

2.3.3      Instructional Design Principles

The use of research-based principles for instructional design is the third component. There are numerous collections like this. (For a list of lists, see ) A key assumption is that instructional design principles established in other types of learning environments will carry over to the design of educational games and can aid in the creation of educationally effective games.

2.4        Analyze the frameworks.

To be able to decide which framework I want to use for my project. I’ve beforehand weighed the advantages and disadvantages of each framework. And I decided based on that.

8 pilar OctasisConsists of 8 ‘parts’Focus on productivenot specific to education
On daily useFocus on creativity
(which can be advantageous during learning because there are frequently multiple options)
On daily use
(not relevant for my project now)
 The concept of ownership
(could be useful in tracking your development.)
The focus on comparison can be beneficial and destructive. 
(There is some doubt)
  Scarcity and impatience are the reasons that motivate us however, learning something new is not immediately useful.
  Fear of loss or unwanted events may motivate people.
  Motivated by the fear of losing something or allowing unwanted events to take place.
DulvastConsists of 7 “parts”focused on educational gamesfocused on in-person rather than digital
The games are divided into 4 types.Examples are provided with this framework.The parts are not clearly measured, therefore there is less focus on how to learn.
Alevenconsists of 3 componentsThere are three large but different parts.If you want good results, look further into the theory.
 All of the individual components are simple to understand.Think about incorporating everything.

Aleven’s framework is the most helpful when it comes to creating an educational digital game. This framework is the easiest to follow while designing the game because it consists of three components, each with its own tool set. Also, you are not instantly assigned to a specific type of game. It can be good to grab specific pieces of 8 pilar Octalysis to motivate the player during the game.

3.     My Game Idea

When designing a new game, you don’t have to come up with something completely original. So I started looking for math games to get some inspiration. Finally, I had something to play around with.

3.1        Original Game

(LeBlanc, Hunick, & Zubek, july 2004)When I started looking for digital math games, I came across quite a few of them. I already knew that I wanted to create a simple game. I discovered the game Snake Blockade ( and immediately had ideas on how to tweak it for my own game.

Snake Blockade is a browser-based game. Where the player is a snake that moves with the movement of your mouse. The snake is a specific length and must pass through various obstacles along the route. These blocks contain values, and those values can pass through them if they are the correct length. There are several points throughout the game where the snake grows in length / value. Throughout the game, you can gather stars to unlock skins.

3.2        My twist

The concept is that the snake can only pass through the correct block. It was an excellent beginning point for me to put my mathematical learning objective into it. My main mathematics learning objective is the Priority order. Because order is critical in this case, traveling through the correct block worked nicely.

3.2.1      Explaining

The core mechanic remains the same: you move the snake with your mouse. Instead of being concerned with the snake’s length, you must instead be concerned with the formula that wraps it. The formula shrinks as it passes through the correct block until it is completely solved. When the formula completely breaks down, the snake is free. You must do all of this within a certain time frame.

3.2.2      Visuals

3.3        Framework Aleven

3.3.1      Learning Objectives

Specifying the learning objective requires answers three questions:

1 (Prior knowledge) What knowledge or skills do student/players need to have before starting the game?

Before they can start playing the game as intended, the students need to have the following prior knowledge:

  • Basic math skills such as – + × /
    • Calculate with formulas.

2 (Learning and retention) What knowledge or skills can student/players reasonably be expected to learn from the game?

By playing my game, the student learns how to solve the formulas in the correct order. And, because of the numerous repetitions, people are likely to remember it.

3 (Potential transfer) What knowledge and skills might they learn that go beyond what they encountered in the game?

Because the focus is on the order of solving, several formula alternatives will be instructed. As a result, they are exposed to a variety of formulas, allowing them to solve more than one type of formula later.

3.3.2      MDA

LeBlanc’s MDA framework helps game analysts and designers in thinking about games in three mutually dependent layers.


The core mechanic is the mouse movement, which moves the snake from left to right.

The goal of the game is to free the snake from its formula. You accomplish this by passing through the appropriate block. The formula can be solved with the right block, and the snake can be freed once more.


This game has a time constraint to keep it challenging while also increasing competition so that the player wants to keep playing.


Challenge is the best fit for this game out of the eight kinds of fun. The player is under time pressure not only to free the snake, but also to free as many snakes as possible in the time frame given to them.

3.3.3      Instructional Design Principles

The goal of this game is to remember how to solve a formula in the correct order. This relates to the instructional Design principle of Practice at Retrieval. This means that the learner uses their own memory to retrieve information rather than relying on external memory aids.

4.     Paper prototype

5.     Resources

Bilham, J. (. (2021, juli 13). Case Study: How Duolingo Utilises Gamification To Increase User Interest – Raw.Studio. Retrieved from Raw.Studio:

Chou, Y. (2015). Actionable Gamification.

Koop, M. C. (2017). Game didatiek. Uitgerverij Didactica.

LeBlanc, M., Hunick, R., & Zubek, R. (july 2004). MDA: A formal approach to game design and game research. Proceedings of the AAAI Workshop onn Challenges in Game AI, Vol.4 No.1, p. 1722.

V, A., E, M., Easterday, M., & Organ, A. (2010). Toward a Framework for the Anakysis and Design of Educational Games. Third IEEE International Confernce on Digital Game and Intelligent Toy Enhanced Learning, 69-76.