video games for mathematics educationkdevlin/presentations/nctm_2011.pdfvideo games for mathematics...
TRANSCRIPT
![Page 1: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/1.jpg)
Keith DevlinH-STAR Institute, Stanford University
Video Games for Mathematics Education –They Will Soon Get Better
![Page 2: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/2.jpg)
Just published by AK Peters(CRC Press)
![Page 3: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/3.jpg)
EVERYDAY MATH
Counting, arithmetic, proportional reasoning, numerical estimation, elementary geometry and trigonometry, elementary algebra, basic probability and statistics, logical thinking, algorithm use, problem formation (modeling), problem solving, and sound calculator use.
![Page 4: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/4.jpg)
Learning math in a videogame. The current state of the art.
![Page 5: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/5.jpg)
How do we think of “doing math”?
![Page 6: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/6.jpg)
How do we think of “doing math”?
![Page 7: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/7.jpg)
How do we think of “doing math”?
![Page 8: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/8.jpg)
How do we think of “doing math”?
![Page 9: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/9.jpg)
How do we think of “doing math”?
![Page 10: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/10.jpg)
![Page 11: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/11.jpg)
Leonardo of PisaʼsLiber abbaci
completed in 1202
![Page 12: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/12.jpg)
Something to think about
![Page 13: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/13.jpg)
Though much advanced mathematics is linguistically defined, everyday math is directly abstracted from the world, and can be done without formal notation (symbols).
Something to think about
![Page 14: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/14.jpg)
Though much advanced mathematics is linguistically defined, everyday math is directly abstracted from the world, and can be done without formal notation (symbols).
So why do we teach it using formal, symbolic representations?
Something to think about
![Page 15: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/15.jpg)
Though much advanced mathematics is linguistically defined, everyday math is directly abstracted from the world, and can be done without formal notation (symbols).
So why do we teach it using formal, symbolic representations?
After all, mathematics is about doing, not knowing.
Something to think about
![Page 16: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/16.jpg)
Though much advanced mathematics is linguistically defined, everyday math is directly abstracted from the world, and can be done without formal notation (symbols).
So why do we teach it using formal, symbolic representations?
After all, mathematics is about doing, not knowing. Everyday math is primarily a way of thinking about
entities, issues, and problems in the world.
Something to think about
![Page 17: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/17.jpg)
Though much advanced mathematics is linguistically defined, everyday math is directly abstracted from the world, and can be done without formal notation (symbols).
So why do we teach it using formal, symbolic representations?
After all, mathematics is about doing, not knowing. Everyday math is primarily a way of thinking about
entities, issues, and problems in the world. Well, for over two thousand years, books were the only
means to store and disseminate information to a large audience.
Something to think about
![Page 18: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/18.jpg)
Though much advanced mathematics is linguistically defined, everyday math is directly abstracted from the world, and can be done without formal notation (symbols).
So why do we teach it using formal, symbolic representations?
After all, mathematics is about doing, not knowing. Everyday math is primarily a way of thinking about
entities, issues, and problems in the world. Well, for over two thousand years, books were the only
means to store and disseminate information to a large audience.
But textbook delivery has shaped our view of what mathematics is and how to do it.
Something to think about
![Page 19: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/19.jpg)
Though much advanced mathematics is linguistically defined, everyday math is directly abstracted from the world, and can be done without formal notation (symbols).
So why do we teach it using formal, symbolic representations?
After all, mathematics is about doing, not knowing. Everyday math is primarily a way of thinking about
entities, issues, and problems in the world. Well, for over two thousand years, books were the only
means to store and disseminate information to a large audience.
But textbook delivery has shaped our view of what mathematics is and how to do it.
Is it the best way to teach (everyday) mathematics today?
Something to think about
![Page 20: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/20.jpg)
![Page 21: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/21.jpg)
Go back to the beginning and rethink what we want to achieve
We need to
In the case of using video games for math learning
![Page 22: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/22.jpg)
The lesson from Street MathematicsStreet Mathematics and School Mathematics, by Terezinha Nunes, Analucia Dias Schliemann, and David William Carraher, C.U.P. (1993)
![Page 23: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/23.jpg)
The lesson from Street MathematicsStreet Mathematics and School Mathematics, by Terezinha Nunes, Analucia Dias Schliemann, and David William Carraher, C.U.P. (1993)
![Page 24: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/24.jpg)
The lesson from Street Mathematics
98%
Street Mathematics and School Mathematics, by Terezinha Nunes, Analucia Dias Schliemann, and David William Carraher, C.U.P. (1993)
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The lesson from Street Mathematics
98% 37%
Street Mathematics and School Mathematics, by Terezinha Nunes, Analucia Dias Schliemann, and David William Carraher, C.U.P. (1993)
![Page 26: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/26.jpg)
The lesson from Street Mathematics
98% 37%
Street Mathematics and School Mathematics, by Terezinha Nunes, Analucia Dias Schliemann, and David William Carraher, C.U.P. (1993)
✦ Context, meaning – facilitate situated learning
![Page 27: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/27.jpg)
The lesson from Street Mathematics
98% 37%
Street Mathematics and School Mathematics, by Terezinha Nunes, Analucia Dias Schliemann, and David William Carraher, C.U.P. (1993)
✦ Context, meaning – facilitate situated learning
✦ Motivation – drives exploration, time-on-task
![Page 28: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/28.jpg)
✦ Motivation – drives exploration, time-on-task
✦ Context, meaning – facilitate situated learning
What do video games offer?
![Page 29: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/29.jpg)
Video game environments
✦ Motivation – drives exploration, time-on-task
✦ Context, meaning – facilitate situated learning
What do video games offer?
![Page 30: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/30.jpg)
Video game environments
Game dynamics
✦ Motivation – drives exploration, time-on-task
✦ Context, meaning – facilitate situated learning
What do video games offer?
![Page 31: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/31.jpg)
Video game environments
Game dynamics – leveling, acquiring stuff, competition, transactions
✦ Motivation – drives exploration, time-on-task
✦ Context, meaning – facilitate situated learning
What do video games offer?
![Page 32: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/32.jpg)
Video game environments
Game dynamics – leveling, acquiring stuff, competition, transactionsActivities
✦ Motivation – drives exploration, time-on-task
✦ Context, meaning – facilitate situated learning
What do video games offer?
![Page 33: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/33.jpg)
Video game environments
Game dynamics – leveling, acquiring stuff, competition, transactionsActivities – solving puzzles, building things
✦ Motivation – drives exploration, time-on-task
✦ Context, meaning – facilitate situated learning
What do video games offer?
![Page 34: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/34.jpg)
Video game environments
Game dynamics – leveling, acquiring stuff, competition, transactionsActivities – solving puzzles, building thingsSocial dynamics
✦ Motivation – drives exploration, time-on-task
✦ Context, meaning – facilitate situated learning
What do video games offer?
![Page 35: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/35.jpg)
Video game environments
Game dynamics – leveling, acquiring stuff, competition, transactionsActivities – solving puzzles, building thingsSocial dynamics – status
✦ Motivation – drives exploration, time-on-task
✦ Context, meaning – facilitate situated learning
What do video games offer?
![Page 36: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/36.jpg)
CONTEXT
![Page 37: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/37.jpg)
If you could design the ideal environment for learning everyday math, what properties would it have?
![Page 38: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/38.jpg)
If you could design the ideal environment for learning everyday math, what properties would it have?
1. It would have to be a “real-world environment,” as similar as possible to the environment(s) in which people will use what they learn.
![Page 39: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/39.jpg)
If you could design the ideal environment for learning everyday math, what properties would it have?
1. It would have to be a “real-world environment,” as similar as possible to the environment(s) in which people will use what they learn.
2. It would have to be possible to provide unlimited numbers of learners with exactly the same learning environment.
![Page 40: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/40.jpg)
If you could design the ideal environment for learning everyday math, what properties would it have?
1. It would have to be a “real-world environment,” as similar as possible to the environment(s) in which people will use what they learn.
2. It would have to be possible to provide unlimited numbers of learners with exactly the same learning environment.
3. It should be possible to repeat an experience, to allow for a post mortem analysis of what took place.
![Page 41: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/41.jpg)
If you could design the ideal environment for learning everyday math, what properties would it have?
1. It would have to be a “real-world environment,” as similar as possible to the environment(s) in which people will use what they learn.
2. It would have to be possible to provide unlimited numbers of learners with exactly the same learning environment.
3. It should be possible to repeat an experience, to allow for a post mortem analysis of what took place.
4. It should be possible to provide the learner with variation along a single dimension.
![Page 42: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/42.jpg)
If you could design the ideal environment for learning everyday math, what properties would it have?
1. It would have to be a “real-world environment,” as similar as possible to the environment(s) in which people will use what they learn.
2. It would have to be possible to provide unlimited numbers of learners with exactly the same learning environment.
3. It should be possible to repeat an experience, to allow for a post mortem analysis of what took place.
4. It should be possible to provide the learner with variation along a single dimension.
5. There should be some uniform means of assessing students’ performance
![Page 43: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/43.jpg)
If you could design the ideal environment for learning everyday math, what properties would it have?
1. It would have to be a “real-world environment,” as similar as possible to the environment(s) in which people will use what they learn.
2. It would have to be possible to provide unlimited numbers of learners with exactly the same learning environment.
3. It should be possible to repeat an experience, to allow for a post mortem analysis of what took place.
4. It should be possible to provide the learner with variation along a single dimension.
5. There should be some uniform means of assessing students’ performance
6. It should be possible for the student to explore new concepts and practice new techniques at his or her own pace.
![Page 44: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/44.jpg)
If you could design the ideal environment for learning everyday math, what properties would it have?
1. It would have to be a “real-world environment,” as similar as possible to the environment(s) in which people will use what they learn.
2. It would have to be possible to provide unlimited numbers of learners with exactly the same learning environment.
3. It should be possible to repeat an experience, to allow for a post mortem analysis of what took place.
4. It should be possible to provide the learner with variation along a single dimension.
5. There should be some uniform means of assessing students’ performance
6. It should be possible for the student to explore new concepts and practice new techniques at his or her own pace.
7. The learning tool/environment should store pre-planned learning experiences that the student is presented with, some of them in a certain order.
![Page 45: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/45.jpg)
If you could design the ideal environment for learning everyday math, what properties would it have?
1. It would have to be a “real-world environment,” as similar as possible to the environment(s) in which people will use what they learn.
2. It would have to be possible to provide unlimited numbers of learners with exactly the same learning environment.
3. It should be possible to repeat an experience, to allow for a post mortem analysis of what took place.
4. It should be possible to provide the learner with variation along a single dimension.
5. There should be some uniform means of assessing students’ performance
6. It should be possible for the student to explore new concepts and practice new techniques at his or her own pace.
7. The learning tool/environment should store pre-planned learning experiences that the student is presented with, some of them in a certain order.
8. The student should be given feedback about performance immediately after each action.
![Page 46: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/46.jpg)
If you could design the ideal environment for learning everyday math, what properties would it have?
1. It would have to be a “real-world environment,” as similar as possible to the environment(s) in which people will use what they learn.
2. It would have to be possible to provide unlimited numbers of learners with exactly the same learning environment.
3. It should be possible to repeat an experience, to allow for a post mortem analysis of what took place.
4. It should be possible to provide the learner with variation along a single dimension.
5. There should be some uniform means of assessing students’ performance
6. It should be possible for the student to explore new concepts and practice new techniques at his or her own pace.
7. The learning tool/environment should store pre-planned learning experiences that the student is presented with, some of them in a certain order.
8. The student should be given feedback about performance immediately after each action.
9. There should be sufficient “cost” to getting something wrong to motivate correction, but not so great it leads to the student losing heart and giving up.
![Page 47: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/47.jpg)
If you could design the ideal environment for learning everyday math, what properties would it have?
1. It would have to be a “real-world environment,” as similar as possible to the environment(s) in which people will use what they learn.
2. It would have to be possible to provide unlimited numbers of learners with exactly the same learning environment.
3. It should be possible to repeat an experience, to allow for a post mortem analysis of what took place.
4. It should be possible to provide the learner with variation along a single dimension.
5. There should be some uniform means of assessing students’ performance
6. It should be possible for the student to explore new concepts and practice new techniques at his or her own pace.
7. The learning tool/environment should store pre-planned learning experiences that the student is presented with, some of them in a certain order.
8. The student should be given feedback about performance immediately after each action.
9. There should be sufficient “cost” to getting something wrong to motivate correction, but not so great it leads to the student losing heart and giving up.
10.The learning environment should provide a stimulating and, if possible, enjoyable experience.
![Page 48: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/48.jpg)
If you could design the ideal environment for learning everyday math, what properties would it have?
1. It would have to be a “real-world environment,” as similar as possible to the environment(s) in which people will use what they learn.
2. It would have to be possible to provide unlimited numbers of learners with exactly the same learning environment.
3. It should be possible to repeat an experience, to allow for a post mortem analysis of what took place.
4. It should be possible to provide the learner with variation along a single dimension.
5. There should be some uniform means of assessing students’ performance
6. It should be possible for the student to explore new concepts and practice new techniques at his or her own pace.
7. The learning tool/environment should store pre-planned learning experiences that the student is presented with, some of them in a certain order.
8. The student should be given feedback about performance immediately after each action.
9. There should be sufficient “cost” to getting something wrong to motivate correction, but not so great it leads to the student losing heart and giving up.
10.The learning environment should provide a stimulating and, if possible, enjoyable experience.
VIDEO GAMES OFFER ALL OF THESE IN SPADES
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What most current mathematicseducation videogames utilize
![Page 50: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/50.jpg)
1. Compelling engagement that motivates learning/practice/ repetition and drives time-on-task
What most current mathematicseducation videogames utilize
![Page 51: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/51.jpg)
1. Compelling engagement that motivates learning/practice/ repetition and drives time-on-task
2. Compelling engagement that motivates learning/practice/repetition and drives time-on-task
What most current mathematicseducation videogames utilize
![Page 52: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/52.jpg)
1. Compelling engagement that motivates learning/practice/ repetition and drives time-on-task
2. Compelling engagement that motivates learning/practice/repetition and drives time-on-task
3. Compelling engagement that motivates learning/practice/repetition and drives time-on-task
What most current mathematicseducation videogames utilize
![Page 53: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/53.jpg)
1. Compelling engagement that motivates learning/practice/ repetition and drives time-on-task
2. Compelling engagement that motivates learning/practice/repetition and drives time-on-task
3. Compelling engagement that motivates learning/practice/repetition and drives time-on-task
4. Compelling engagement that motivates learning/practice/repetition and drives time-on-task
What most current mathematicseducation videogames utilize
![Page 54: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/54.jpg)
1. Compelling engagement that motivates learning/practice/ repetition and drives time-on-task
2. Compelling engagement that motivates learning/practice/repetition and drives time-on-task
3. Compelling engagement that motivates learning/practice/repetition and drives time-on-task
4. Compelling engagement that motivates learning/practice/repetition and drives time-on-task
5. Compelling engagement that motivates learning/practice/repetition and drives time-on-task
What most current mathematicseducation videogames utilize
![Page 55: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/55.jpg)
Most current video games
![Page 56: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/56.jpg)
Most current video games
Marry traditional curriculum to videogames
![Page 57: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/57.jpg)
Most current video games
Use the compelling engagement of video games to motivate practice and drive time-on-task
Marry traditional curriculum to videogames
![Page 58: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/58.jpg)
Most current video games
Use the compelling engagement of video games to motivate practice and drive time-on-task
Marry traditional curriculum to videogames
![Page 59: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/59.jpg)
Most current video games
Use the compelling engagement of video games to motivate practice and drive time-on-task
Marry traditional curriculum to videogames
![Page 60: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/60.jpg)
One problem
![Page 61: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/61.jpg)
Inappropriate representations
![Page 62: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/62.jpg)
Inappropriate representationsSymbols are for paper-and-pencil math
![Page 63: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/63.jpg)
Inappropriate representationsSymbols are for paper-and-pencil math
Videogames are about using math in a context
![Page 64: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/64.jpg)
Inappropriate representationsSymbols are for paper-and-pencil math
Videogames are about using math in a context
ENVIRONMENT
![Page 65: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/65.jpg)
Inappropriate representationsSymbols are for paper-and-pencil math
Videogames are about using math in a context
ENVIRONMENT
![Page 66: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/66.jpg)
Inappropriate representationsSymbols are for paper-and-pencil math
Videogames are about using math in a context
REPRESENTATIVEMEDIUM
![Page 67: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/67.jpg)
Inappropriate representationsSymbols are for paper-and-pencil math
BETTER TO
1. Experience/use mathematical thinking in the game
2. Do it symbolically in the real-world (including the classroom)
Videogames are about using math in a context
![Page 68: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/68.jpg)
ACTIVITY
![Page 69: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/69.jpg)
What is the best way to learn how to do something?
The activity:
![Page 70: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/70.jpg)
Just do it!
What is the best way to learn how to do something?
The activity:
![Page 71: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/71.jpg)
Learning by doing
![Page 72: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/72.jpg)
(simulator learning)Learning by doing
![Page 73: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/73.jpg)
(simulator learning)
Tell me (or let me read it) and I will forget
Learning by doing
![Page 74: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/74.jpg)
(simulator learning)
Tell me (or let me read it) and I will forget
Show me and I will remember
Learning by doing
![Page 75: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/75.jpg)
(simulator learning)
Tell me (or let me read it) and I will forget
Show me and I will remember Let me experience it and I will know how to do it for ever
Learning by doing
![Page 76: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/76.jpg)
What is the best way to learn the piano?
![Page 77: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/77.jpg)
What is the best way to learn math?
![Page 78: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/78.jpg)
What is the best way to learn math?
![Page 79: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/79.jpg)
What is the best way to learn math?
![Page 80: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/80.jpg)
What is the best way to learn math?
?
![Page 81: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/81.jpg)
What is the best way to learn math?
?Coming this year
![Page 82: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/82.jpg)
How should we teach everyday math?
98% 37%?
![Page 83: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/83.jpg)
How should we teach everyday math?
98% 37%?We should start on the left and move to the right!
![Page 84: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/84.jpg)
1. Experience/use mathematical thinking in the game
2. Do it symbolically in the real-world (including the classroom)
Our philosophy
![Page 85: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/85.jpg)
1. Experience/use mathematical thinking in the game
2. Do it symbolically in the real-world (including the classroom)
Our philosophy
Symbolic representations are for doing math with paper-and-pencil. Videogames offer other ways to represent mathematical problems that are natural to the medium.
![Page 86: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/86.jpg)
1. Experience/use mathematical thinking in the game
2. Do it symbolically in the real-world (including the classroom)
Our philosophy
Symbolic representations are for doing math with paper-and-pencil. Videogames offer other ways to represent mathematical problems that are natural to the medium.
The player may need to stop playing and do some symbolic math – or ask the teacher for help – in order to solve the puzzle when s/he resumes the game. That’s fine, indeed desirable. The idea is to design games that assist teachers (not replace them)!
![Page 87: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/87.jpg)
The underlying pedagogy
Teacher assigns homework:
“Try to get to level 3.”
Student does homework:
Gets to level 2
Teacher explains the math that can help the student
get to level 3
![Page 88: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/88.jpg)
The underlying pedagogy
Teacher assigns homework:
“Try to get to level 4.”
Student does homework:
Gets to level 3
Teacher explains the math that can help the student
get to level 4
![Page 89: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/89.jpg)
The underlying pedagogy
Teacher assigns homework:
“Try to get to level 4.”
Student does homework:
Gets to level 3
Teacher explains the math that can help the student
get to level 4
Assignment
![Page 90: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/90.jpg)
The underlying pedagogy
Teacher assigns homework:
“Try to get to level 4.”
Student does homework:
Gets to level 3
Teacher explains the math that can help the student
get to level 4
Assignment
Exploration/grounding/
testing
![Page 91: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/91.jpg)
The underlying pedagogy
Teacher assigns homework:
“Try to get to level 4.”
Student does homework:
Gets to level 3
Teacher explains the math that can help the student
get to level 4
Assignment
Exploration/grounding/
testing
Teaching
![Page 92: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/92.jpg)
The underlying pedagogy
Teacher assigns homework:
“Try to get to level 4.”
Student does homework:
Gets to level 3
Teacher explains the math that can help the student
get to level 4
Assignment
Exploration/grounding/
testing
Teaching
LEARNING
![Page 93: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/93.jpg)
Factors to consider Immersive 3D environment High resolution graphics Avatar identity Action Interaction Game? Multi-player Collaborative or PvP? Social networking Massively multi-player Real world context of play Teacher education/training
![Page 94: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/94.jpg)
For more details, see
![Page 96: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/96.jpg)
For more details, see
PDF file of talk, NCTM_2011.pdf, available for download from:http://www.stanford.edu/~kdevlin/Presentations
![Page 97: Video Games for Mathematics Educationkdevlin/Presentations/NCTM_2011.pdfVideo Games for Mathematics Education ... audience.! But textbook delivery has shaped our view of what mathematics](https://reader033.vdocuments.site/reader033/viewer/2022050311/5f730a429a6f5e083b2030b4/html5/thumbnails/97.jpg)