video games for mathematics educationkdevlin/presentations/nctm_2011.pdfvideo games for mathematics...

Keith DevlinH-STAR Institute, Stanford University

Video Games for Mathematics Education –They Will Soon Get Better

Just published by AK Peters(CRC Press)

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.

Learning math in a videogame. The current state of the art.

How do we think of “doing math”?

How do we think of “doing math”?

How do we think of “doing math”?

How do we think of “doing math”?

How do we think of “doing math”?

Leonardo of PisaʼsLiber abbaci

completed in 1202

Something to think about

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

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

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

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

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

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

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

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

The lesson from Street MathematicsStreet Mathematics and School Mathematics, by Terezinha Nunes, Analucia Dias Schliemann, and David William Carraher, C.U.P. (1993)

The lesson from Street MathematicsStreet Mathematics and School Mathematics, by Terezinha Nunes, Analucia Dias Schliemann, and David William Carraher, C.U.P. (1993)

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)

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)

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

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

✦ Motivation – drives exploration, time-on-task

✦ Context, meaning – facilitate situated learning

What do video games offer?

Video game environments

✦ Motivation – drives exploration, time-on-task

✦ Context, meaning – facilitate situated learning

What do video games offer?

Video game environments

Game dynamics

✦ Motivation – drives exploration, time-on-task

✦ Context, meaning – facilitate situated learning

What do video games offer?

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?

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?

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?

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?

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?

CONTEXT

If you could design the ideal environment for learning everyday math, what properties would it have?

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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

What most current mathematicseducation videogames utilize

1. Compelling engagement that motivates learning/practice/ repetition and drives time-on-task

What most current mathematicseducation videogames utilize

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

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

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

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

Most current video games

Most current video games

Marry traditional curriculum to videogames

Most current video games

Use the compelling engagement of video games to motivate practice and drive time-on-task

Marry traditional curriculum to videogames

Most current video games

Use the compelling engagement of video games to motivate practice and drive time-on-task

Marry traditional curriculum to videogames

Most current video games

Use the compelling engagement of video games to motivate practice and drive time-on-task

Marry traditional curriculum to videogames

One problem

Inappropriate representations

Inappropriate representationsSymbols are for paper-and-pencil math

Inappropriate representationsSymbols are for paper-and-pencil math

Videogames are about using math in a context

Inappropriate representationsSymbols are for paper-and-pencil math

Videogames are about using math in a context

ENVIRONMENT

Inappropriate representationsSymbols are for paper-and-pencil math

Videogames are about using math in a context

ENVIRONMENT

Inappropriate representationsSymbols are for paper-and-pencil math

Videogames are about using math in a context

REPRESENTATIVEMEDIUM

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

ACTIVITY

What is the best way to learn how to do something?

The activity:

Just do it!

What is the best way to learn how to do something?

The activity:

Learning by doing

(simulator learning)Learning by doing

(simulator learning)

Tell me (or let me read it) and I will forget

Learning by doing

(simulator learning)

Tell me (or let me read it) and I will forget

Show me and I will remember

Learning by doing

(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

What is the best way to learn the piano?

What is the best way to learn math?

What is the best way to learn math?

What is the best way to learn math?

What is the best way to learn math?

?

What is the best way to learn math?

?Coming this year

How should we teach everyday math?

98% 37%?

How should we teach everyday math?

98% 37%?We should start on the left and move to the right!

1. Experience/use mathematical thinking in the game

2. Do it symbolically in the real-world (including the classroom)

Our philosophy

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.

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)!

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

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

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

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

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

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

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

For more details, see

For more details, see

devlin@stanford.edu

For more details, see

devlin@stanford.edu

PDF file of talk, NCTM_2011.pdf, available for download from:http://www.stanford.edu/~kdevlin/Presentations