The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of...
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The Art of Problem Solving Instruction
Richard Brown, Director of Undergraduate Studies
Mathematics Department
August 30, 2013
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 1 / 8
![Page 2: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/2.jpg)
Why teach
Being an effective scholar requires one to not only
be a good researcher, but to
be a very good communicator of that research.
Being able to effectively and compellingly communicate all aspects of yourdiscipline to audiences at all levels (from peer scholars to students at alllevels to the lay audience) is absolutely vital to your success as aresearcher.
Being a TA helps
It’s a way to start to develop those muscles that allow you to educate theworld on the wonders of your field.
This part of your training as a scholar is an essential aspect of yourpost-graduate experience.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 2 / 8
![Page 3: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/3.jpg)
Why teach
Being an effective scholar requires one to not only
be a good researcher, but to
be a very good communicator of that research.
Being able to effectively and compellingly communicate all aspects of yourdiscipline to audiences at all levels (from peer scholars to students at alllevels to the lay audience) is absolutely vital to your success as aresearcher.
Being a TA helps
It’s a way to start to develop those muscles that allow you to educate theworld on the wonders of your field.
This part of your training as a scholar is an essential aspect of yourpost-graduate experience.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 2 / 8
![Page 4: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/4.jpg)
Why teach
Being an effective scholar requires one to not only
be a good researcher, but to
be a very good communicator of that research.
Being able to effectively and compellingly communicate all aspects of yourdiscipline to audiences at all levels (from peer scholars to students at alllevels to the lay audience) is absolutely vital to your success as aresearcher.
Being a TA helps
It’s a way to start to develop those muscles that allow you to educate theworld on the wonders of your field.
This part of your training as a scholar is an essential aspect of yourpost-graduate experience.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 2 / 8
![Page 5: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/5.jpg)
Why teach
Being an effective scholar requires one to not only
be a good researcher, but to
be a very good communicator of that research.
Being able to effectively and compellingly communicate all aspects of yourdiscipline to audiences at all levels (from peer scholars to students at alllevels to the lay audience) is absolutely vital to your success as aresearcher.
Being a TA helps
It’s a way to start to develop those muscles that allow you to educate theworld on the wonders of your field.
This part of your training as a scholar is an essential aspect of yourpost-graduate experience.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 2 / 8
![Page 6: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/6.jpg)
Why teach
Being an effective scholar requires one to not only
be a good researcher, but to
be a very good communicator of that research.
Being able to effectively and compellingly communicate all aspects of yourdiscipline to audiences at all levels (from peer scholars to students at alllevels to the lay audience) is absolutely vital to your success as aresearcher.
Being a TA helps
It’s a way to start to develop those muscles that allow you to educate theworld on the wonders of your field.
This part of your training as a scholar is an essential aspect of yourpost-graduate experience.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 2 / 8
![Page 7: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/7.jpg)
Problem Solving Sessions
Also called sections, or recitations.
Exist alongside a set of lectures as a compliment.
Exist to understand theory in the context of applications, practice,examples, extensions, etc.
Are different from lectures
smaller class size.more interactive and conversational.As reactive as they are proactive.
Are more like tutoring sessions (many-to-one)
each query is a conversation overheard by the entire class, andeach conversation is directed toward the student’s lack ofunderstanding.
Are the places where one can gauge the effectiveness of the lectures.
In this format, the discussions are livelier, interactive and more fun andfulfilling for the instructor, but more work is needed to prepare for them.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 3 / 8
![Page 8: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/8.jpg)
Problem Solving Sessions
Also called sections, or recitations.
Exist alongside a set of lectures as a compliment.
Exist to understand theory in the context of applications, practice,examples, extensions, etc.
Are different from lectures
smaller class size.more interactive and conversational.As reactive as they are proactive.
Are more like tutoring sessions (many-to-one)
each query is a conversation overheard by the entire class, andeach conversation is directed toward the student’s lack ofunderstanding.
Are the places where one can gauge the effectiveness of the lectures.
In this format, the discussions are livelier, interactive and more fun andfulfilling for the instructor, but more work is needed to prepare for them.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 3 / 8
![Page 9: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/9.jpg)
Problem Solving Sessions
Also called sections, or recitations.
Exist alongside a set of lectures as a compliment.
Exist to understand theory in the context of applications, practice,examples, extensions, etc.
Are different from lectures
smaller class size.more interactive and conversational.As reactive as they are proactive.
Are more like tutoring sessions (many-to-one)
each query is a conversation overheard by the entire class, andeach conversation is directed toward the student’s lack ofunderstanding.
Are the places where one can gauge the effectiveness of the lectures.
In this format, the discussions are livelier, interactive and more fun andfulfilling for the instructor, but more work is needed to prepare for them.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 3 / 8
![Page 10: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/10.jpg)
Problem Solving Sessions
Also called sections, or recitations.
Exist alongside a set of lectures as a compliment.
Exist to understand theory in the context of applications, practice,examples, extensions, etc.
Are different from lectures
smaller class size.more interactive and conversational.As reactive as they are proactive.
Are more like tutoring sessions (many-to-one)
each query is a conversation overheard by the entire class, andeach conversation is directed toward the student’s lack ofunderstanding.
Are the places where one can gauge the effectiveness of the lectures.
In this format, the discussions are livelier, interactive and more fun andfulfilling for the instructor, but more work is needed to prepare for them.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 3 / 8
![Page 11: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/11.jpg)
Problem Solving Sessions
Also called sections, or recitations.
Exist alongside a set of lectures as a compliment.
Exist to understand theory in the context of applications, practice,examples, extensions, etc.
Are different from lectures
smaller class size.more interactive and conversational.As reactive as they are proactive.
Are more like tutoring sessions (many-to-one)
each query is a conversation overheard by the entire class, andeach conversation is directed toward the student’s lack ofunderstanding.
Are the places where one can gauge the effectiveness of the lectures.
In this format, the discussions are livelier, interactive and more fun andfulfilling for the instructor, but more work is needed to prepare for them.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 3 / 8
![Page 12: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/12.jpg)
Problem Solving Sessions
Also called sections, or recitations.
Exist alongside a set of lectures as a compliment.
Exist to understand theory in the context of applications, practice,examples, extensions, etc.
Are different from lectures
smaller class size.more interactive and conversational.As reactive as they are proactive.
Are more like tutoring sessions (many-to-one)
each query is a conversation overheard by the entire class, andeach conversation is directed toward the student’s lack ofunderstanding.
Are the places where one can gauge the effectiveness of the lectures.
In this format, the discussions are livelier, interactive and more fun andfulfilling for the instructor, but more work is needed to prepare for them.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 3 / 8
![Page 13: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/13.jpg)
Philosophy of the medium
You are not the primary evaluator of the course. Your role is different fromthat of the professor.
You are the coach of the students, their advocate,and cheerleader. Your goal is to get them to excel.
Every question is a gateway to instruction/re-instruction and not a simplerequest for an answer.
Every problem is an introduction/re-introduction to relevant theoreticalmaterial via practical application.
Every interaction is a means to teach the organizational skills necessary tosolve any set of problems, not just the current ones.
Every worked problem is an exposure of the process you use to analyze,deduce, and discover.
Students aren’t looking for an answer (even when they say they are). Theyare looking for understanding. Their real question lies inside their query.
Your role is to answer this real question.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 4 / 8
![Page 14: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/14.jpg)
Philosophy of the medium
You are not the primary evaluator of the course. Your role is different fromthat of the professor. You are the coach of the students, their advocate,and cheerleader. Your goal is to get them to excel.
Every question is a gateway to instruction/re-instruction and not a simplerequest for an answer.
Every problem is an introduction/re-introduction to relevant theoreticalmaterial via practical application.
Every interaction is a means to teach the organizational skills necessary tosolve any set of problems, not just the current ones.
Every worked problem is an exposure of the process you use to analyze,deduce, and discover.
Students aren’t looking for an answer (even when they say they are). Theyare looking for understanding. Their real question lies inside their query.
Your role is to answer this real question.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 4 / 8
![Page 15: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/15.jpg)
Philosophy of the medium
You are not the primary evaluator of the course. Your role is different fromthat of the professor. You are the coach of the students, their advocate,and cheerleader. Your goal is to get them to excel.
Every question is a gateway to instruction/re-instruction and not a simplerequest for an answer.
Every problem is an introduction/re-introduction to relevant theoreticalmaterial via practical application.
Every interaction is a means to teach the organizational skills necessary tosolve any set of problems, not just the current ones.
Every worked problem is an exposure of the process you use to analyze,deduce, and discover.
Students aren’t looking for an answer (even when they say they are). Theyare looking for understanding. Their real question lies inside their query.
Your role is to answer this real question.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 4 / 8
![Page 16: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/16.jpg)
Philosophy of the medium
You are not the primary evaluator of the course. Your role is different fromthat of the professor. You are the coach of the students, their advocate,and cheerleader. Your goal is to get them to excel.
Every question is a gateway to instruction/re-instruction and not a simplerequest for an answer.
Every problem is an introduction/re-introduction to relevant theoreticalmaterial via practical application.
Every interaction is a means to teach the organizational skills necessary tosolve any set of problems, not just the current ones.
Every worked problem is an exposure of the process you use to analyze,deduce, and discover.
Students aren’t looking for an answer (even when they say they are). Theyare looking for understanding. Their real question lies inside their query.
Your role is to answer this real question.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 4 / 8
![Page 17: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/17.jpg)
Philosophy of the medium
You are not the primary evaluator of the course. Your role is different fromthat of the professor. You are the coach of the students, their advocate,and cheerleader. Your goal is to get them to excel.
Every question is a gateway to instruction/re-instruction and not a simplerequest for an answer.
Every problem is an introduction/re-introduction to relevant theoreticalmaterial via practical application.
Every interaction is a means to teach the organizational skills necessary tosolve any set of problems, not just the current ones.
Every worked problem is an exposure of the process you use to analyze,deduce, and discover.
Students aren’t looking for an answer (even when they say they are). Theyare looking for understanding. Their real question lies inside their query.
Your role is to answer this real question.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 4 / 8
![Page 18: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/18.jpg)
Philosophy of the medium
You are not the primary evaluator of the course. Your role is different fromthat of the professor. You are the coach of the students, their advocate,and cheerleader. Your goal is to get them to excel.
Every question is a gateway to instruction/re-instruction and not a simplerequest for an answer.
Every problem is an introduction/re-introduction to relevant theoreticalmaterial via practical application.
Every interaction is a means to teach the organizational skills necessary tosolve any set of problems, not just the current ones.
Every worked problem is an exposure of the process you use to analyze,deduce, and discover.
Students aren’t looking for an answer (even when they say they are). Theyare looking for understanding. Their real question lies inside their query.
Your role is to answer this real question.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 4 / 8
![Page 19: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/19.jpg)
Philosophy of the medium
You are not the primary evaluator of the course. Your role is different fromthat of the professor. You are the coach of the students, their advocate,and cheerleader. Your goal is to get them to excel.
Every question is a gateway to instruction/re-instruction and not a simplerequest for an answer.
Every problem is an introduction/re-introduction to relevant theoreticalmaterial via practical application.
Every interaction is a means to teach the organizational skills necessary tosolve any set of problems, not just the current ones.
Every worked problem is an exposure of the process you use to analyze,deduce, and discover.
Students aren’t looking for an answer (even when they say they are). Theyare looking for understanding. Their real question lies inside their query.
Your role is to answer this real question.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 4 / 8
![Page 20: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/20.jpg)
Things you should do:
Prepare for your sessions
Know well what the current focus is of the lectures. Look for/resolve pitfalls.
Have material ready to generate questions if needed.
While fully prepared, be able and willing to “wing it”. Be reactive, whilemanaging the class time well.
Prepare for multiple directions the discussion may lead.
Engage the class
Force students to take part in resolving their questions. Get them to owntheir work.
Allow other students to take part in resolving questions.
Listen and look for the cues of understanding; nodding heads, puzzled looks,the moment of perfect clarity, snoring?
Challenge them to solve at the board, play “Stump the TA” with you, etc.
Keep in mind always: Queries are the start of conversations.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 5 / 8
![Page 21: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/21.jpg)
Things you should do:
Prepare for your sessions
Know well what the current focus is of the lectures. Look for/resolve pitfalls.
Have material ready to generate questions if needed.
While fully prepared, be able and willing to “wing it”. Be reactive, whilemanaging the class time well.
Prepare for multiple directions the discussion may lead.
Engage the class
Force students to take part in resolving their questions. Get them to owntheir work.
Allow other students to take part in resolving questions.
Listen and look for the cues of understanding; nodding heads, puzzled looks,the moment of perfect clarity, snoring?
Challenge them to solve at the board, play “Stump the TA” with you, etc.
Keep in mind always: Queries are the start of conversations.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 5 / 8
![Page 22: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/22.jpg)
Things you should do:
Prepare for your sessions
Know well what the current focus is of the lectures. Look for/resolve pitfalls.
Have material ready to generate questions if needed.
While fully prepared, be able and willing to “wing it”. Be reactive, whilemanaging the class time well.
Prepare for multiple directions the discussion may lead.
Engage the class
Force students to take part in resolving their questions. Get them to owntheir work.
Allow other students to take part in resolving questions.
Listen and look for the cues of understanding; nodding heads, puzzled looks,the moment of perfect clarity, snoring?
Challenge them to solve at the board, play “Stump the TA” with you, etc.
Keep in mind always: Queries are the start of conversations.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 5 / 8
![Page 23: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/23.jpg)
Things you should do:
Present solutions instead of giving them
You are not giving answers, you are teaching them to think. Showthem how thinking is done by exposing your own analytical process.
Design your boards as if the students are deaf?
Design your explanations as if the students are blind?
Design both to be compatible with each other.
Develop your own style in the classroom
Think about how you help friends trying to understand your discipline.
Play to your strengths. Use your personality and thinking process.
Assess yourself. Learn what works and what doesn’t and adaptaccordingly.
You’d be amazed how much one can learn by teaching.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 24: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/24.jpg)
Things you should do:
Present solutions instead of giving them
You are not giving answers, you are teaching them to think. Showthem how thinking is done by exposing your own analytical process.
Design your boards as if the students are deaf?
Design your explanations as if the students are blind?
Design both to be compatible with each other.
Develop your own style in the classroom
Think about how you help friends trying to understand your discipline.
Play to your strengths. Use your personality and thinking process.
Assess yourself. Learn what works and what doesn’t and adaptaccordingly.
You’d be amazed how much one can learn by teaching.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 25: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/25.jpg)
Things you should do:
Present solutions instead of giving them
You are not giving answers, you are teaching them to think. Showthem how thinking is done by exposing your own analytical process.
Design your boards as if the students are deaf?
Design your explanations as if the students are blind?
Design both to be compatible with each other.
Develop your own style in the classroom
Think about how you help friends trying to understand your discipline.
Play to your strengths. Use your personality and thinking process.
Assess yourself. Learn what works and what doesn’t and adaptaccordingly.
You’d be amazed how much one can learn by teaching.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 26: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/26.jpg)
Things you should do:
Present solutions instead of giving them
You are not giving answers, you are teaching them to think. Showthem how thinking is done by exposing your own analytical process.
Design your boards as if the students are deaf?
Design your explanations as if the students are blind?
Design both to be compatible with each other.
Develop your own style in the classroom
Think about how you help friends trying to understand your discipline.
Play to your strengths. Use your personality and thinking process.
Assess yourself. Learn what works and what doesn’t and adaptaccordingly.
You’d be amazed how much one can learn by teaching.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 27: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/27.jpg)
Things you should do:
Present solutions instead of giving them
You are not giving answers, you are teaching them to think. Showthem how thinking is done by exposing your own analytical process.
Design your boards as if the students are deaf?
Design your explanations as if the students are blind?
Design both to be compatible with each other.
Develop your own style in the classroom
Think about how you help friends trying to understand your discipline.
Play to your strengths. Use your personality and thinking process.
Assess yourself. Learn what works and what doesn’t and adaptaccordingly.
You’d be amazed how much one can learn by teaching.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 28: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/28.jpg)
Things you should do:
Present solutions instead of giving them
You are not giving answers, you are teaching them to think. Showthem how thinking is done by exposing your own analytical process.
Design your boards as if the students are deaf?
Design your explanations as if the students are blind?
Design both to be compatible with each other.
Develop your own style in the classroom
Think about how you help friends trying to understand your discipline.
Play to your strengths. Use your personality and thinking process.
Assess yourself. Learn what works and what doesn’t and adaptaccordingly.
You’d be amazed how much one can learn by teaching.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 29: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/29.jpg)
Things you should do:
Present solutions instead of giving them
You are not giving answers, you are teaching them to think. Showthem how thinking is done by exposing your own analytical process.
Design your boards as if the students are deaf?
Design your explanations as if the students are blind?
Design both to be compatible with each other.
Develop your own style in the classroom
Think about how you help friends trying to understand your discipline.
Play to your strengths. Use your personality and thinking process.
Assess yourself. Learn what works and what doesn’t and adaptaccordingly.
You’d be amazed how much one can learn by teaching.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 30: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/30.jpg)
Things you should do:
Present solutions instead of giving them
You are not giving answers, you are teaching them to think. Showthem how thinking is done by exposing your own analytical process.
Design your boards as if the students are deaf?
Design your explanations as if the students are blind?
Design both to be compatible with each other.
Develop your own style in the classroom
Think about how you help friends trying to understand your discipline.
Play to your strengths. Use your personality and thinking process.
Assess yourself. Learn what works and what doesn’t and adaptaccordingly.
You’d be amazed how much one can learn by teaching.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 31: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/31.jpg)
Things you should do:
Present solutions instead of giving them
You are not giving answers, you are teaching them to think. Showthem how thinking is done by exposing your own analytical process.
Design your boards as if the students are deaf?
Design your explanations as if the students are blind?
Design both to be compatible with each other.
Develop your own style in the classroom
Think about how you help friends trying to understand your discipline.
Play to your strengths. Use your personality and thinking process.
Assess yourself. Learn what works and what doesn’t and adaptaccordingly.
You’d be amazed how much one can learn by teaching.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 32: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/32.jpg)
Things you should do:
Care
Again, you are not the primary evaluator of performance.
You are more like an Olympic sports coach trying to get the bestperformance out of each student.
You are their advocate, not their adversary.
(Hint: Try to remember names. When you do, use it.)
Note the first and foremost thing an educator transfers to students in theclassroom is... ATTITUDE!
If you are not interested, they won’t take interest.
If you do not respect them or the environment, neither will they.
If you do not care, they won’t bother to.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 33: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/33.jpg)
Things you should do:
Care
Again, you are not the primary evaluator of performance.
You are more like an Olympic sports coach trying to get the bestperformance out of each student.
You are their advocate, not their adversary.
(Hint: Try to remember names. When you do, use it.)
Note the first and foremost thing an educator transfers to students in theclassroom is... ATTITUDE!
If you are not interested, they won’t take interest.
If you do not respect them or the environment, neither will they.
If you do not care, they won’t bother to.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 34: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/34.jpg)
Things you should do:
Care
Again, you are not the primary evaluator of performance.
You are more like an Olympic sports coach trying to get the bestperformance out of each student.
You are their advocate, not their adversary.
(Hint: Try to remember names. When you do, use it.)
Note the first and foremost thing an educator transfers to students in theclassroom is... ATTITUDE!
If you are not interested, they won’t take interest.
If you do not respect them or the environment, neither will they.
If you do not care, they won’t bother to.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 35: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/35.jpg)
Things you should do:
Care
Again, you are not the primary evaluator of performance.
You are more like an Olympic sports coach trying to get the bestperformance out of each student.
You are their advocate, not their adversary.
(Hint: Try to remember names. When you do, use it.)
Note the first and foremost thing an educator transfers to students in theclassroom is... ATTITUDE!
If you are not interested, they won’t take interest.
If you do not respect them or the environment, neither will they.
If you do not care, they won’t bother to.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 36: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/36.jpg)
Things you should do:
Care
Again, you are not the primary evaluator of performance.
You are more like an Olympic sports coach trying to get the bestperformance out of each student.
You are their advocate, not their adversary.
(Hint: Try to remember names. When you do, use it.)
Note the first and foremost thing an educator transfers to students in theclassroom is...
ATTITUDE!
If you are not interested, they won’t take interest.
If you do not respect them or the environment, neither will they.
If you do not care, they won’t bother to.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 37: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/37.jpg)
Things you should do:
Care
Again, you are not the primary evaluator of performance.
You are more like an Olympic sports coach trying to get the bestperformance out of each student.
You are their advocate, not their adversary.
(Hint: Try to remember names. When you do, use it.)
Note the first and foremost thing an educator transfers to students in theclassroom is... ATTITUDE!
If you are not interested, they won’t take interest.
If you do not respect them or the environment, neither will they.
If you do not care, they won’t bother to.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 38: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/38.jpg)
Things you should do:
Care
Again, you are not the primary evaluator of performance.
You are more like an Olympic sports coach trying to get the bestperformance out of each student.
You are their advocate, not their adversary.
(Hint: Try to remember names. When you do, use it.)
Note the first and foremost thing an educator transfers to students in theclassroom is... ATTITUDE!
If you are not interested, they won’t take interest.
If you do not respect them or the environment, neither will they.
If you do not care, they won’t bother to.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 39: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/39.jpg)
Things you should do:
Care
Again, you are not the primary evaluator of performance.
You are more like an Olympic sports coach trying to get the bestperformance out of each student.
You are their advocate, not their adversary.
(Hint: Try to remember names. When you do, use it.)
Note the first and foremost thing an educator transfers to students in theclassroom is... ATTITUDE!
If you are not interested, they won’t take interest.
If you do not respect them or the environment, neither will they.
If you do not care, they won’t bother to.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 40: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/40.jpg)
Things you should do:
Care
Again, you are not the primary evaluator of performance.
You are more like an Olympic sports coach trying to get the bestperformance out of each student.
You are their advocate, not their adversary.
(Hint: Try to remember names. When you do, use it.)
Note the first and foremost thing an educator transfers to students in theclassroom is... ATTITUDE!
If you are not interested, they won’t take interest.
If you do not respect them or the environment, neither will they.
If you do not care, they won’t bother to.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 6 / 8
![Page 41: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/41.jpg)
Things you should NOT do:
Their work
Never directly solve homework problems that are yet to be submitted.Offering hints may be appropriate. Doing like problems may work.
Waste valuable section time
There are only 13 sections hours in a semester.
Don’t spend 40 minutes on one topic.
Don’t refuse to accept that you are stuck.
Don’t do three of the exact same problems in a row.
And never go in cold!
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 7 / 8
![Page 42: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/42.jpg)
Things you should NOT do:
Their work
Never directly solve homework problems that are yet to be submitted.Offering hints may be appropriate. Doing like problems may work.
Waste valuable section time
There are only 13 sections hours in a semester.
Don’t spend 40 minutes on one topic.
Don’t refuse to accept that you are stuck.
Don’t do three of the exact same problems in a row.
And never go in cold!
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 7 / 8
![Page 43: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/43.jpg)
Things you should NOT do:
Their work
Never directly solve homework problems that are yet to be submitted.Offering hints may be appropriate. Doing like problems may work.
Waste valuable section time
There are only 13 sections hours in a semester.
Don’t spend 40 minutes on one topic.
Don’t refuse to accept that you are stuck.
Don’t do three of the exact same problems in a row.
And never go in cold!
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 7 / 8
![Page 44: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/44.jpg)
Things you should NOT do:
Their work
Never directly solve homework problems that are yet to be submitted.Offering hints may be appropriate. Doing like problems may work.
Waste valuable section time
There are only 13 sections hours in a semester.
Don’t spend 40 minutes on one topic.
Don’t refuse to accept that you are stuck.
Don’t do three of the exact same problems in a row.
And never go in cold!
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 7 / 8
![Page 45: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/45.jpg)
Final Note
There is no canonical style to effective teaching
Teaching is just directed conversation.
You are at your most lucid, compelling and persuasive when you arecomfortable.
Develop your own style based on your personality, and keep theenvironment professional and engaging.
There is no need to perform or entertain as a teacher. Simply “lead thechatter” in this environment.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 8 / 8
![Page 46: The Art of Problem Solving Instruction - Mathematicsbrown/Documents/TATraining.pdf · The Art of Problem Solving Instruction Richard Brown, Director of Undergraduate Studies Mathematics](https://reader031.fdocuments.in/reader031/viewer/2022022420/5a79e8c97f8b9a3d058b997b/html5/thumbnails/46.jpg)
Final Note
There is no canonical style to effective teaching
Teaching is just directed conversation.
You are at your most lucid, compelling and persuasive when you arecomfortable.
Develop your own style based on your personality, and keep theenvironment professional and engaging.
There is no need to perform or entertain as a teacher. Simply “lead thechatter” in this environment.
Richard Brown (Mathematics Department) The Art of Problem Solving Instruction August 30, 2013 8 / 8