mathematical and arithmetical computer games computer ga… · curriculum - integration of...

NWO-FWO project version 1 P. Wouters

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Mathematical and arithmetical computer games Purpose We have classified existing math/arithmetic games on several dimensions (see table below). The classification may provide us an overview of the current state of affairs and guide our thinking about the structure of our own game(s) and some decisions that we have to make such as the game contexts we are going to use, the type of game or which type of visual design. At the end the results are summarized in three tables and a conclusion is drawn. Game dimensions Game type Which game type is used (e.g. role playing game, arcade game, action

game etc.) Visual design How elaborate is the visual design (e.g., cartoon-like, realistic, text-

based etc.) Context Is there a context or narrative, a description of what the player has to

do? If there are several (sub)games, is there an overarching context? Assignment - Symbolic assignments: assignments are mathematical or arithmetical,

for example the player is asked to calculate 24+25. - Contextualized assignments: Assignments are embedded in the

context, for example the player has to shop and buy three products of which the added prices come as close to 10 euro as possible.

Answer - Player explicitly gives an answer: the player enters the answer in a textbox or clicks the correct answer with the mouse. - Player acts in the game world: in order to answer the player has to

act in the game world, for example in an action game the player has to navigate his/her avatar to a location in the game where the correct answer can be found

Feedback - A numerical score: a correct answer increases the score - Feedback is reflected in the game world: The answer may change the

game world, for example when a player gives a correct answer his/her car in a mathematical race will drive faster

Motivation The proposal identifies four ways to enhance motivation: learner control (opportunity to make choices), competency (need for challenge and feeling of being effective), uncertainty (chance of being rewarded), situatedness (challenging context).

Cognition The proposal also identifies some ways to foster cognitive processes: self explanations, collaboration (some games had multiplayer variants, but this was not equaled with collaboration), information gaps (i.e., curiosity), integration, clarifications, part task practice

Domain Which topics in arithmetic and/or math are presented Curriculum - Integration of curriculum topics: Diverse curriculum topics (e.g.,

addition, division, making estimations) are integrated. - Isolated curriculum topics: Separated games are developed for each

curriculum subject (e.g., addition, division, making estimations). Age For what age is the game?


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1. http://www.arcademicskillbuilders.com/ Game type Action: arcade games (simple fast action games) Visual design 2D cartoonlike (see picture of Grand Prix game) Context There is no overall context or narrative that connects the different games.

In the example the context is a race match Assignment The player receives symbolic assignments (e.g., 8 x 1 in the picture below) Answer Player answers by clicking an alternative, so multiple choice Feedback A correct answer changes the game world, that is, the car of the player will

get a boost, but there is also a score indicator (rate) Motivation Control, competency, situatedness Cognition None Domain Basic operations of addition, subtraction, division, multiplication Curriculum Topics are presented in isolation Age unknown


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2. http://www.aplusmath.com/Games/index.html Some of them are motivational with simple means: see for example http://www.aplusmath.com/Games/HiddenPicture/HiddenPicture.php (a nice example also of perceptual curiosity). Game type Puzzle: bingo and hidden picture Visual design 2D Java/Flash schematic games Context There is no overall context or narrative that connects the different games Assignment The player receives symbolic assignments (e.g., 11+7 in the picture below) Answer The player can select the correct answer by clicking a square. It is

classified as acting because an answer sometimes appears several times and the player can decide which is most appropriate in order to see the picture.

Feedback After clicking the correct answer the game world changes, that is, part of the underlying picture becomes visible. There is also a score.

Motivation Control, competency, situatedness Cognition None Domain Addition, subtraction, division, multiplication Curriculum Topics are presented in isolation. Age Unknown


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3. The game Escape from Fraction Manor => http://www.thinkingblocks.com/HauntedFractions/HFGameLoader.html Game type Action: Side-scrolling platform video-game Visual design 2D cartoonlike games Context The player is trapped in a manor and has to solve puzzles to escape from

the manor. Before the player can solve a puzzle he has to collect puzzle cards and in the mean time watch out for guards. This activity involves a certain amount of navigation skills. (i.e., the player moves with move left, move right, and jump (space bar) keys (see left picture)

Assignment The player receives symbolic assignments (see right picture) Answer Typing because the player answers by dragging the numbers to the grey

squares. Feedback When the player solves the puzzle he receives a key for a door that leads to

another room (level) of the manor. So the answer of the player changes the game world. There is also a score.

Motivation Control, competency, situatedness Cognition Feedback (knowledge, directions) that can be regarded as clarifications Domain Fractions Curriculum Topics are presented in isolation. Age Unknown

Legenda: the cat is the players avatar; F is a puzzle card, the green/blue character is the guard.


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4. http://hotmath.com/hotmath_help/games/numbercop/numbercop_hotmath.swf Game type Action: simple race game Visual design 2D realistic Context The player drives a police car on a road with three lanes. Numbers appear

on the lanes. Depending on the assignment the player must switch the police car between the lanes in order to get the correct number (e.g., in the picture the assignment is to catch multiples of 2. The player first has to switch to the left lane to get the 4 and after that to the most right lane)

Assignment Mix of symbolic and contextual Answer The player has to act in the game world (quickly change from lane) Feedback Score because catching correct numbers yields points, incorrect number an

error message. In both situation the game continues Motivation Control, competency, situatedness Cognition There is some level of intrinsic integration (game rules are used to teach

learning material) Domain Multiples, fractions, perfect squares, rational number, prime numbers Curriculum Topics are presented in isolation. Age 11-14 years


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5. The dimension games developed by Tabula Digita => http://www.dimensionu.com/dimu/home/dimugames.aspx?ref=top%20menu%20dimu Game type Action: First-person shooter game Visual design 3D realistic Context The player moves in an imaginary world and has to perform actions to

activate assignments. In this case the player has to collect five balls and then pass a beam (after which the assignment appears) (see left picture)

Assignment The assignment is symbolic (see right picture) Answer Acting because the player answers by clicking the correct alternative Feedback Basically a score because a correct answer yields credits Motivation Control, competency, situatedness Cognition Some collaboration (an option that can be employed by the teacher) Domain In principle the game covers the whole NCTM mathematics standard (US) Curriculum Topics are presented in isolation Age K-12 (16-19 years)


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6. The game TimezAttack => http://www.bigbrainz.com/ Game type Adventure game Visual design 3D realistic Context The player moves through an imaginary world and has to perform actions

(e.g., in the dungeon context collect a golden key, see picture left, and circumvent obstacles).

Assignment After collecting the golden key, a symbolic assignment is shown (see picture right).

Answer A combination of typing (e.g., to open the door the player has to type 132 below 12*11) and acting in the world (the player can use the balls on the floor: the balls are hints, e.g. when the avatar takes the first ball the figure 11 appears, the next ball shows 22, the next 33 to show that is 12*11 is 11+11+11 … etc.) (see picture right).

Feedback When the assignment is answered correctly a door opens and the player can further explore the game world (the next golden key)

Motivation Control, competency, situatedness: Cognition Some basic intrinsic integration and clarifications (hints) Domain Addition, Subtraction, Multiplication, Division Curriculum Topics are presented in isolation. Age Unknown


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7. http://www.edalive.com/au/products/volcanic-panic-v2 Game type Puzzle: Board-adventure game Visual design 3D cartoonlike Context The player has crash-landed on a volcanic island that’s about to blow.

Therefore the player has to race round the island grabbing fuel canisters and, with some strategy and luck, zoom off in a jet-powered escape pod.

Assignment The player has to solve symbolic assignments (see left picture). Answer The player types the answer. Feedback When the assignment is solved correctly the player throws a dice (by

clicking on it) and advances the number of places that is thrown on the game board (see right picture). So the effect of the (correct) answer changes the game world, but there is also a score.

Motivation Control, competency, some uncertainty (throwing the dice), situatedness Cognition None Domain Addition, Subtraction, Division, Multiplication, Numeration,

Fractions/Decimals. Curriculum Topics are presented in isolation. Age 5-15 years


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8. http://www.knowledgeadventure.com/mathblaster/ Game type Action: Action-adventure game Visual design 3D realistic Context Math Blaster has a long history (started in 1987, in 2005 the sixth

generation was launched). In this version the player acts as an astronaut to defend earth from hostile robots in space

Assignment Assignments are symbolic (see picture below) Answer Player acts in the game Feedback Not clear (I did not find a demo) Motivation Control, competency, situatedness Cognition Not clear Domain Addition, subtraction, division, multiplication, problem solving,

equivalents Curriculum Not clear Age 6-12 years


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9. http://www.practicalmoneyskills.com/games/ Game type Strategy: Simulation game Visual design 2D cartoonlike Context There is no overall context or narrative that connects the different games.

In the example the player is placed in a virtual small town and sets a goal (e.g., making a trip costing 400 euro). The player receives a small budget (see left picture).

Assignment The assignment is contextual because the player has to get the 400 euro by doing activities in the game world.

Answer Acting because the player selects and performs activities that either cost money or yields money (e.g., mowing the lawn yields 10 euro, see picture right).

Feedback The game world does not change, but the budget meter increases (or decreases).

Motivation Control, competency, situatedness Cognition There is some level of intrinsic integration Domain Financial literacy Curriculum Not clear Age 7-12 years


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10. Lure of the Labyrinth => http://labyrinth.thinkport.org/www/index.php Game type Action: Action-adventure game Visual design 2D cartoonlike (the story is told in graphic-novel sequences) Context The player acts in an imaginary graphic-novel world. The player’s pet is

missing in this world and he has to find it (as well as other pets), but the player also has to deal with monsters

Assignment The puzzles that can be considered contextual. In the cafeteria puzzle (see picture below), students must fill each monster's tray with food items by selecting a food item and indicating the amount. The proportions of the trays must be corresponding

Answer The player acts in the world by clicking the dispensing button on the food machine and places the food that appears in the correct spot on a monster's tray

Feedback If the food is placed on the correct tray and in the right amount, the monster will respond favorably and that plate of food is locked into place. In order to successfully complete the first level of play, the player must place all plates of food correctly before all of the lights expire on the plate counter. So feedback by changing the game world.

Motivation Control, competency, situatedness Cognition Some basic level of intrinsic integration Domain Pre-algebra curriculum: (1) Proportions (including fractions and ratios); (2)

Variables and Equations; (3) Number and Operations (including geometry, order of operations)

Curriculum Topics are presented in isolation. Age 11-14 years (6-8 grade US)


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11. http://www.unicog.org/main/pages.php?page=NumberRace Game type Puzzle: Board/puzzle game Visual design 2D schematic Context The player engages in a numerical comparison task and plays against the

computer. The player has to choose the larger of two quantities of a treasure (see left picture) before the competitor character (controlled by the computer) does so. They then use the quantity (often represented as a set of gold pieces or coconuts) that they selected to advance on the board screen (right picture). At higher levels, they have to try and avoid hazards, which appear at random on some board squares and cause characters to go backwards when landed on. When a child wins from the computer he receives a reward.

Assignment Symbolic (see left picture) Answer The player makes a choice on the comparison screen, but afterwards the

player also has to move to the board screen (right picture) and move forward the number of places of the quantity they have chosen

Feedback The player receives verbal feedback, but the game world also changes because the player has to move forward on the board screen

Motivation Control, competency, situatedness Cognition There are some, but not those that are mentioned in the proposal Domain Number sense with single digit numbers, numerical comparison,

enumeration, one-to-one correspondence, counting, reading arabic digits, and simple (1-digit) addition and subtraction.

Curriculum Topics are presented in isolation Age 7-9 years


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12. Math game based on ‘How the West was won’ (see Cordova, D, J. & Lepper, M. R., (1996). Intrinsic motivation and the process of learning: Beneficial effects of contextualization, personalization, and choice. Journal of Educational Psychology, 88, 715-730.) Game type Puzzle: Board game Visual design 2D schematic Context The game board consists of a number line ranging from 1 to 50, with four

‘target zones’ located at each multiple of 10 and two ‘shortcuts’(right picture)

Assignment Symbolic because the player receives three numbers Answer The player has to combine the three numbers in an arithmetic expression.

It seems that the player answers by typing because he selects and combines numbers and operation symbols (e.g., +, -, ( ,etc.) in a display (see upper part right picture)

Feedback The correct value of that expression is the number of spaces that the player will advance on the number line. So the answer changes the game world

Motivation Control, competency, situatedness Cognition None (learning is fostered by motivational processes) Domain Arithmetical and problem-solving skills Curriculum Several curriculum topics are integrated Age 9-11 years


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13. Zombie Division (see Habgood, M. P. J. & Ainsworth, S. E. (August, 2009). Does intrinsic integration matter? Exploring the value of intrinsic integration in educational games.. Paper presented at the international symposium ‘Designing engaging and effective serious games’ at the European Association for Research on Learning and Instruction in Amsterdam, The Netherlands) Game type Action: Action-adventure game Visual design 2D cartoonlike Context The player is placed in a world with zombie skeletons that have to be

combated with several weapons. Assignment The assignment is contextual in the integrated version (first picture below),

[but symbolic in the non-integrated version (second picture below)] Answer The player performs by acting in the game world, that is by selecting a

weapon and mathematically divide the opponent Feedback An appropriate attack will have the defeated zombie rise and split in

several smaller ghosts (bearing the quotient). In case of an inappropriate attack the zombie will fight back. So, feedback is provided in the game world, but rewards are provided as well.

Motivation Control, competency, situatedness Cognition Intrinsic integration (upper picture, lower picture is without integration) Domain Recognize and describe number patterns, including two- and three-digit

multiples of 2, 5 and 10, recognizing their patterns and using them to make predictions; recognize prime numbers up to 20 and square numbers up to 10 x 10; find factor pairs and all the prime factors of any two digit integer

Curriculum Topics are presented in isolation. Age 7-11 year


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14. http://www.wizzworld.nl/index_oud.html Game type Puzzle game Visual design 2D cartoonlike Context The game is part of larger learning environment. The player is placed in a

world (either Fractionwood, Meter-O-Polis or Cashba) and engages in missions that deal with number and arithmetic

Assignment The assignments are contextual (see picture below) Answer The player acts in the game. In dividing the two cakes equally for three

persons (see picture) the player uses a knife. Feedback Feedback is in the form of points, but they also receive attributes that they

can use later in the game. Motivation Control, competency, situatedness Cognition Some collaboration Domain Fractions, decimals, addition, subtraction, measurement, money Curriculum Not clear Age 6-12 years


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15. Absurdmath => http://www.learningwave.com/abmath/ Game type Puzzle game Visual design 2D schematic/textual Context The player proceeds on missions in a strange world where the ultimate

power consists of mathematical skill and knowledge. Many of the pages have hidden clues and areas. In the game the player has to solve hidden assignments.

Assignment The assignment is contextual in the sense that the player has to discover it. In the picture below for example, the assignment is -4* (times) 46.

Answer The player types the answer in a textbox Feedback A correct answer leads to another page with an assignment. An incorrect

answer gives a message. Type of feedback is difficult to define. Motivation Control, competency, situatedness Cognition There is some level of intrinsic integration Domain Not clear Curriculum Not clear Age Unknown


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16. http://www.mangahigh.com/en/games Game type Action games Visual design 2D cartoonlike Context There is no overall context or narrative that connects the different games.

In the example game, see picture below, Robots are infected with a virus. They have a shield that can be cracked by using arithmetic skills

Assignment The assignment is symbolic. Above the Robots an arithmetical assignment is shown that have to be resolved.

Answer The player types the answer. Feedback A correct answer deactivates the shield of the Robot so that it can be

destroyed with a weapon. Performance is also reflected in “cash” and points that the player can earn.

Motivation Control, competency, situatedness Cognition There is some level of intrinsic integration Domain All topics from Key Stage 2 up to GCSE (Exam qualification UK) Curriculum Both isolated and integrated Age 7-16 years


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17. http://www.learnalot.com/content/ Game type Puzzle: Quiz Visual design Textual Context Learnalot comprises a learning environment consisting of 18 activities

across 6 resources and 49 games. The games are essentially quizzes with questions

Assignment Symbolic (see picture below) Answer Player types the answer Feedback Feedback is provided by a numerical score Motivation Competency Cognition None Domain Entire KS3 range (UK) Curriculum Several curriculum topics are integrated Age 11-16 years


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18. http://www.sumdog.com/en/About_Sumdog/ Game type Divers: action (arcade) games, but also puzzle games Visual design 2D cartoonlike Context There is no overall context or narrative that connects the different games. Assignment Always symbolic assignments Answer In general de player has to act in the game world Feedback Feedback is provided by changes in the game world Motivation Control, competency, situatedness Cognition There is some level of intrinsic integration Domain Addition, division, subtraction, multiplication, percentages Curriculum Topics are presented in isolation. Age unknown


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Classification of games

In the tables below the results are summarized. Table 1 shows the distribution of the computer games on four important instructional dimensions. Table 2 shows the distribution of the computer games on motivational and cognitive factors as described in the NWO-FWO proposal. Table 3 summarizes the distribution of game type and visual design.

Table 1.

1

2 Assignment

Symbolic or Contextual

3 Answer

Typing or Acting

4 Feedback

Numeric score or Game world changes

Integrated curriculum topics Several arithmetical/mathematical topics are trained in the game

Isolated curriculum topics One arithmetical/mathematical topic is trained in the game

Symbolic Typing Numeric score 16, 17 1, 3, 5, 7, 16 Contextual Typing Numeric score 15(?) Symbolic Acting Numeric score 8(?) 2, 4, 8(?) Contextual Acting Numeric score 9(?) 4, 9(?), 13, 14 Symbolic Typing Game world changes 12 1, 3, 6, 7, 11, 16 Contextual Typing Game world changes 15(?) Symbolic Acting Game world changes 8(?) 2, 6, 8(?), 11, 18 Contextual Acting Game world changes 10, 13 (?) means that is unclear how it can be classified in a dimension. Some games appear in several cells (e.g., many games have both a score and a change in the game world as feedback mechanism)


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Table 2. MOTIVATIONAL FACTORS Learner

control Competency Uncertainty Situatedness

Self explanation Collaboration 5, 14 5, 14 5, 14 Information gaps

Integration 4, 6, 9, 10, 13, 15, 16, 18

4, 6, 9, 10, 13, 15, 16, 18

4, 6, 9, 10, 13, 15, 16, 18

Clarifications 3, 6 3, 6 3, 6 Part-task practice

CO

GN

ITIV

E F

AC

TO

RS

None 1, 2, 7, 8, 11, 12

1, 2, 7, 8, 11, 12, 17

7 1, 2, 7, 8, 11, 12


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Table 3. Game type Action Puzzle Strategy

Schematic/textual 2, 11, 12, 15, 17

Cartoonlike 1, 3, 10, 13, 16, 18

7, 14, 18 9

Vis

ual

de

sig

n

Realistic 4, 5, 6, 8 Action games: action games, arcade games, race games, adventure games, FPS Puzzle games: puzzle games, board games, quizzes Strategy games: strategy games, simulation games


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Some websites with computer games for mathematics/arithmetic Here a list of url’s to other websites with games for mathematics/arithmetic: http://www.apples4theteacher.com/math.html#measurementgames http://mathematics.hellam.net/ http://www.multiplication.com http://hoodamath.com/games/ http://www.abcya.com/ http://www.coolmath-games.com/1-number-games-01.html http://www.sheppardsoftware.com/math.htm http://www.visualfractions.com/FindGrampy/findgrampy.html http://www.math-play.com/index.html http://www.fractionmonkeys.co.uk/ http://www.mrnussbaum.com/derby/index.html http://members.learningplanet.com/act/mayhem/mayhem.asp?type=add http://www.solvemymath.com/math_games/ http://www.mathnook.com/ http://www.sumdog.com/en/About_Sumdog/ http://www.arcadediner.com/games.php?c=number http://www.prongo.com/games/ http://www.woodlands-junior.kent.sch.uk/maths/index.html http://mathsduck.co.uk/number.php (http://mathsduck.co.uk/) http://jmathpage.com/ http://www.gameclassroom.com/math-games/6th-grade http://www.fi.uu.nl/rekenweb/rekenmaar/leerlingen/groepselectie.xml?groep=9&subject=0 http://www.fi.uu.nl/rekenweb/hva/games/ http://eagle.aasdcat.com/login.php http://www.theproblemsite.com/math_games.asp http://www.playkidsgames.com/mathGames.htm# http://www.mathgametime.com/math-games http://www.math-quest.com/math/


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Conclusion Most computer games use symbolic assignments instead of contextual assignments and in the majority of games topics are presented in isolation rather than integrated or combined. With respect to performing assignments, designs in which players could type or click an answer were used equally often (roughly) as designs in which the player had to act in the game world. The same fifty-fifty distribution applies to the feedback mechanism (score vs. changes in the game world). Furthermore, the classification shows that most mathematical/arithmetical computer games capitalize on three of the four motivational factors: learner control, competency and situatedness. With the exception of Volcanic Panic (nr. 7) where the reward of the player depends on the value of a dice that the player has to throw, no examples of uncertainty were found. In the investigated computer games little evidence was found for the factors that foster cognitive or learning processes (as mentioned in the proposal). An exception is intrinsic integration. In several computer games the player became to some extent involved in the learning content by engaging in the game mechanics (the rules that make playing the game fun such as defeating an enemy, avoiding obstacles etc.). With respect to game design most game were either a kind of action game (roughly equal cartoonlike or realistic) or a kind of puzzle game (most schematic/textual, some cartoonlike).

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