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Math Puzzle
- 1. Math-Puzzle:Math-Puzzle: Equation Tutor forSighted andEquation Tutor for Sighted and Visually-Impaired ChildrenVisually-Impaired Children Jarno Jokinen Department of Computer Sciences University of Tampere Finland jarno.jokinen@uta.fi April, 2005 AAFG 2005
- 2. Math-Puzzle • Communication ofmathematics is usually visual • Formulas, diagrams, graphs etc. • It is very difficult for blind and partially sighted people/ students to do mathematics and is one of the biggest obstacles for them in school and at the university. Introduction
- 3. Math-Puzzle Most of thework reported in developing techniques that deal with mathematics can be presented through next categories: • Tactile as in Braille and other raised representations • Audio aids that read equations with tools to help in reading process • Tonal representing equations and graphs (sonification / audification) • Haptic or forced feedback devices represent shapes and curves • Integrated /multimodal approaches
- 4. Introduction Into TheGames Math-Puzzle p://www.boowakwala.com/kids/math-game-kids.html http://www.learn4good.com/games/kids/double_digits.htm
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- 6. Math-Puzzle Project Impetus • Createda game instead of making tests with an existing game • Mathematical game for blind children • After different ideas, Math-Puzzle was chosen • Training in logics, memory and equations’ manipulation strategy
- 7. The Problems InQuestion • Is it possible to solve equations using only short speech cues? • What are the limitations? • What is the easy way for blind interaction to edit the equations in static or dynamical puzzle? (memory capacity or external memory aid see next slide) • How long does it take to solve a puzzle? • What are the parameters of the gameplay progress and player performance? • How much does it make difference when player has visual feedback or all the tasks (including navigation within the game-field) are presented through sounds? • How and in which order the equations could be solved? (strategies) Math-Puzzle
- 8. Math-Puzzle Different Matrix Approaches •static puzzle on the left • dynamic puzzle on the right
- 9. Game Concept • 5x5matrix with one equation in each row • Equations are predefined and randomly picked for the matrix • The goal of the game is to change the places of the equation members so that all of the equations are true • The figures (only in the same column) can be swapped by clicking one number and then the other one • Operators cannot be swapped as well other controls are: • alt+R -> new game (reset) • alt+M -> minimize / maximize browser window • alt+S -> show / hide figures and operators • The puzzle completion time and the number of moves are calculated • The game is currently implemented only in www with limitations Math-Puzzle
- 10. Testing Procedure • 5technically aware adults (age ranged from 26 to 34) • 10 games per player with all three playing modes: 1st visual, 2nd blind (hidden labels with sound cues), 3rd blindfolded • Laptop pc with external mouse and headphones Math-Puzzle
- 11. Problems • Sound feedbackis not supported with mozilla browsers • Completing the fourth equation usually completes also the fifth • If not, the answers are crossing each other in a way that makes it very difficult to solve the puzzle • The program sometimes gives 1 or more correct equations at the start which may also result in an error on the browser Math-Puzzle
- 12. Results And Discussions •The game (blind mode) is hard for adults that can see • What about kids that can’t? They have better spatial understanding • Some matrixes can be a lot faster solved than others – repetitions needed for a good estimate of skills • If you wan’t to hear the sound cues you need to be patient • Sound is heard when the mouse is moved over the square, so if you want to hear it again you must move the mouse away and over again • Completing the fourth equation is crucial as explained on next slide Math-Puzzle
- 13. About The FourthEquation Math-Puzzle OK OK OK OK
- 14. Conclusions • Game requiresa lot of memorizing, but there are strategies that help • Completing equations in some order • Using mathematical rules (division and multiplication) • When playing the game blindfolded, the increase in speed was bigger than when playing the visual version Math-Puzzle
- 15. Math-Puzzle References http://www.boowakwala.com/kids/math-game-kids.html http://www.learn4good.com/games/kids/double_digits.htm http://www.gamealbum.com/keyword/math/ Children’s math projecthttp://www.udel.edu/educ/cmp2/ http://www.educational-software-directory.net/math/ Lambda-project: Linear Access to Mathematic for Braille Device and Audio-synthesis http://www.lambdaproject.org/ Karshmer, A.I., Gupta, G., Gillan, D. Architecting an Auditory Browser for Navigating Mathematical Expressions, ICCHP 2002, LNCS 2398, p. 477 http://link.springer.de/link/service/series/0558/papers/2398/23980477.pdf Gaura, P. REMathEx - Reader and Editor of the Mathematical Expressions for Blind Students, 2002, LNCS 2398, p. 486, http://link.springer-ny.com/link/service/series/0558/papers/2398/23980486.pdf Fitzpatrick D. Speaking Technical Documents: Using Prosody to Convey Textual and Mathematical Material, ICCHP 2002, LNCS 2398, p. 494, http://link.springer.de/link/service/series/0558/papers/2398/23980494.pdf http://www.computing.dcu.ie/~dfitzpat/publications.html Math project, http://www.cs.york.ac.uk/maths/index.html Prosody in Mathtalk http://www.cs.york.ac.uk/maths/robert/prosody.html Mathematical Access for Technology and Science, http://www.papenmeier.de/reha/research/mathe.htm Edwards, A. D. N., Stevens, R. D. and Pitt, I. J. Représentation non visuelle des mathématiques, (translated by A. Assimacopoulos) in A. B. Safran and A. Assimacopoulos (editors) Le Déficit Visuel, Éditions Masson, pp. 169–178 (1995), http://www.cs.york.ac.uk/ftpdir/pub/alistair/publications/ps/geneva.ps Karshmer, A.I., Gupta, G., Geiger, S., and Weaver, C.: Reading and Writing Mathematics: The MAVIS Project, BIT (Behaviour & Information Technology), January 1999
Editor's Notes
- #2 Hi! My name is Jarno Jokinen and I am going to tell you about a game that I created for visually-impaired children.
- #3 Mathematics is visual. You may start with counting your fingers and other objects you can see. Mathematic formulas, diagrams and graphs are presented as visually understandable objects.
- #4 People doing work on this subject have found various ways of solving the problems. These solutions can be divided into five categories. Tactile Haptic or forced feedback Tonal representation Reading equations (like was the case in my solution) Multimodality
- #5 Here are two examples of math games for kids found in the internet.
- #6 Here are some screenshots of games found from the gamealbum.
- #7 Right from the start, my target in this course was to create a game, rather than making tests and studying an existing game. I believe it will tell you more if you try to develope something new. At least it gives you a totally different view of things and gives you perspective on the subject. Personally, I have always liked mathematical and logical problems and making a game of my own sounded like an interesting task. Equations seemed like a good project task. Not too hard yet not too easy. The project resulted as a game for developing logics, memory and strategy for manipulating equations.
- #8 My goal, with this game, was to find out if it is possible to solve the puzzle and equations using only short speech cues. And what limitations does the system have. There were two approaches on how the equations could be solved. Using a static or a dynamic matrix. Which is better? I wanted to know how long does it take to solve a puzzle and what kind of affect does the players experience of the game have. Including the previous aspects, I also wanted to know what kind of affect does the visual interface (or the lack of it) have to the game and how it is progressing. What kind of strategies are used.
- #9 Here is a quick example of the two ways that the matrix could have been used. On the static matrix, each of the equations are selected by clicking the squares in the right order. On a dynamic matrix, the squares are swapped so that in the end you would have one true equation on each row. The dynamic way was chosen, because of the smaller need of memorizing.
- #10 As seen on the previous slide, the equations are shown on a 5x5 matrix. The equations are written in the game source code and randomly selected for each game. The player changes the places of the equation members and this way tries to get all of the equations in the matrix true. You can only change the places of the numbers. And only inside the same column. There are also some shortcuts that the player can use. The game is still very much a prototype, but includes all required functionality
- #11 Tests were done in two rounds. I asked a few people to test the game before the actual testing session so that the bugs in the could be found. This was a good decision, and forced me to do some corrections and limitations about the testing sessions. I was following all the testing sessions. Each session consisted of 30 games, 10 for each playing mode. Visual was in a way rehearsing for the actual game. In this mode you can see the equations. Blind was the same thing, but without seeing the using sound as the only help. Blindfolded was a situation where I could see the equations, but the user had a scarf preventing seeing and the puzzle was done using only sound. This was a good way to evaluate the strategies.
- #12 There were some errors in the game that I couldn’t solve. And some features that could be considered as design problems. Nothing major I think.
- #13 Rather than knowing in what time the puzzle was solved or the number of moves it took, I spent time talking with the participants. I asked them to be blunt and rude, since they knew I had made the game myself. People are usually too polite in these situations. The game determines pretty well peoples’ way of seeing things spatially. The game forces you to memorize places of many of the numbers. Strategies may help with this. There are a lot of matrix variations. Some are very close to being solved and some are more complex. If you want to find out how good the participant is in this task, you need to run more games for reducing the meaning of luck. The game includes sound. The sound cues are so long that you really need to stop and listen to them. As a result, the speed was significantly slower when playing the game using only sound. Three players complained about the fact that you couldn’t hear the sound when the mouse is not moving. It is heard only when the mouse is moved over the square. Sometimes they forgot what square they were on. Usually, when you complete the fourth equation, the fifth gets solved too, because all of the pieces are on their correct places. Sometimes, though, there are two possible correct equations but only the other can lead you to a correct puzzle. An example of this is found later.
- #14 Small explanation on the dilemma of the fourth equation. In some some matrixes it is possible to solve four equations without solving the fifth. Here is an example of a certain situation. <click> To solve the matrix you need to break one equation to solve the remaining, fifth, equation. The problem is to find out which one is the incorrect, yet true, equation. <click> After swapping the numbers you have solved the puzzle. <click>
- #15 When following the participants playing the game, I could find some patterns in their puzzle solving methods. Since the game requires a lot of memorizing, you may want to reduce the load. Completing the equations in some order (for example from top to bottom) lets you forget what rows are already completed and just concentrate on the next row. One of the participants seemed to first find the equations that include divisions and multiplications These equations also include the biggest numbers, either as the result of a multiplication or as the number to be divided. The first tries of the blindfolded version took several minutes to complete (if they were not totally aborted due to frustration). Later the speed increased significantly, as the mind started to use the correct sences.