The Elusive Perfect Problem Outline Do No Harm activities in an - PowerPoint PPT Presentation

The Elusive Perfect Problem Paul Zeitz The Elusive Perfect Problem Outline “Do No Harm” activities in an enrichment program for Introduction “unenriched” students The San Francisco Math Circle Good and Bad Problems Paul Zeitz Example: Trapezoidal Numbers University of San Francisco Example: San Francisco Math Circle Codes and Communica- tion Jun. 3, 2011

The Elusive Perfect Problem 1 Introduction Paul Zeitz Outline Introduction 2 The San Francisco Math Circle The San Francisco Math Circle 3 Good and Bad Problems Good and Bad Problems Example: Trapezoidal 4 Example: Trapezoidal Numbers Numbers Example: Codes and Communica- 5 Example: Codes and Communication tion

SF Math Circle: Joint Work The Elusive Perfect Problem Paul Zeitz Started Fall 2005 Outline Introduction The San Francisco Math Circle Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

SF Math Circle: Joint Work The Elusive Perfect Problem Paul Zeitz Started Fall 2005 Outline Introduction Matthias Beck (SFSU), Brandy Wiegers The San Francisco (MSRI), PZ (USF) Math Circle Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

SF Math Circle: Joint Work The Elusive Perfect Problem Paul Zeitz Started Fall 2005 Outline Introduction Matthias Beck (SFSU), Brandy Wiegers The San Francisco (MSRI), PZ (USF) Math Circle Good and Bad MSRI Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

SF Math Circle: Joint Work The Elusive Perfect Problem Paul Zeitz Started Fall 2005 Outline Introduction Matthias Beck (SFSU), Brandy Wiegers The San Francisco (MSRI), PZ (USF) Math Circle Good and Bad MSRI Problems Example: Trapezoidal Generous Donors Numbers Example: Codes and Communica- tion

SF Math Circle: Joint Work The Elusive Perfect Problem Paul Zeitz Started Fall 2005 Outline Introduction Matthias Beck (SFSU), Brandy Wiegers The San Francisco (MSRI), PZ (USF) Math Circle Good and Bad MSRI Problems Example: Trapezoidal Generous Donors Numbers Example: Instructors, Teachers, Students, Parents Codes and Communica- tion

What Type of Circle? The Elusive Perfect Problem Paul Zeitz Students: Unenriched —— Already enriched Outline Diversity: High —— Low Introduction The San Recruitment: Teacher — Self — Parents Francisco Math Circle Time: After-school —— Evening/Weekend Good and Bad Problems Example: Length: Short —— Long Trapezoidal Numbers Level: Math doesn’t suck! —— Olympiad Example: Codes and Communica- Instruction: Small groups —— Pure Lecture tion

What Type of Circle? The Elusive Perfect Problem Paul Zeitz Students: Unenriched —— Already enriched Outline Diversity: High —— Low Introduction The San Recruitment: Teacher — Self — Parents Francisco Math Circle Time: After-school —— Evening/Weekend Good and Bad Problems Example: Length: Short (50 min) —— Long Trapezoidal Numbers Level: Math doesn’t suck! —— Olympiad Example: Codes and Communica- Instruction: Small groups —— Pure Lecture tion

The Circle in Action The Elusive Perfect Problem Paul Zeitz Outline Introduction The San Francisco Math Circle Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

The Circle in Action The Elusive Perfect Problem Paul Zeitz Outline Introduction The San Francisco Math Circle Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

The Circle in Action The Elusive Perfect Problem Paul Zeitz Outline Introduction The San Francisco Math Circle Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

The Circle in Action The Elusive Perfect Problem Paul Zeitz Outline Introduction The San Francisco Math Circle Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

What Makes a Problem Bad? The Elusive Perfect Problem Paul Zeitz Anything that inhibits Outline Introduction The San Francisco Math Circle Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

What Makes a Problem Bad? The Elusive Perfect Problem Paul Zeitz Anything that inhibits Outline Introduction Confidence The San Francisco Math Circle Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

What Makes a Problem Bad? The Elusive Perfect Problem Paul Zeitz Anything that inhibits Outline Introduction Confidence The San Francisco Conversation/Argument Math Circle Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

What Makes a Problem Bad? The Elusive Perfect Problem Paul Zeitz Anything that inhibits Outline Introduction Confidence The San Francisco Conversation/Argument Math Circle Good and Bad Quick mathematical feedback Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

What Makes a Problem Bad? The Elusive Perfect Problem Paul Zeitz Anything that inhibits Outline Introduction Confidence The San Francisco Conversation/Argument Math Circle Good and Bad Quick mathematical feedback Problems Example: Trapezoidal Physical, tangible interaction with the world Numbers Example: Codes and Communica- tion

What Makes a Problem Bad? The Elusive Perfect Problem Paul Zeitz Anything that inhibits Outline Introduction Confidence The San Francisco Conversation/Argument Math Circle Good and Bad Quick mathematical feedback Problems Example: Trapezoidal Physical, tangible interaction with the world Numbers Example: INVESTIGATION Codes and Communica- tion

Examples of Bad Problems The Elusive Perfect Problem Paul Zeitz Outline Introduction The San Francisco Math Circle Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

Examples of Bad Problems The Elusive Perfect Problem Paul Zeitz Outline “Count . . . ” Introduction The San Francisco Math Circle Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

Examples of Bad Problems The Elusive Perfect Problem Paul Zeitz Outline “Count . . . ” Introduction (without easy verification) The San Francisco Math Circle Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

Examples of Bad Problems The Elusive Perfect Problem Paul Zeitz Outline “Count . . . ” Introduction (without easy verification) The San Francisco “Prove. . . ” Math Circle Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

Examples of Bad Problems The Elusive Perfect Problem Paul Zeitz Outline “Count . . . ” Introduction (without easy verification) The San Francisco “Prove. . . ” Math Circle Good and Bad (without student-generated question) Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

Examples of Bad Problems The Elusive Perfect Problem Paul Zeitz Outline “Count . . . ” Introduction (without easy verification) The San Francisco “Prove. . . ” Math Circle Good and Bad (without student-generated question) Problems Example: “Is it possible to . . . ?” Trapezoidal Numbers Example: Codes and Communica- tion

Examples of Bad Problems The Elusive Perfect Problem Paul Zeitz Outline “Count . . . ” Introduction (without easy verification) The San Francisco “Prove. . . ” Math Circle Good and Bad (without student-generated question) Problems Example: “Is it possible to . . . ?” Trapezoidal Numbers (without student-generated question) Example: Codes and Communica- tion

Two Styles for Good Problems The Elusive Perfect Problem Paul Zeitz Outline Introduction The San Francisco Math Circle Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

Two Styles for Good Problems The Elusive Perfect Problem Paul Zeitz Outline Hard, but with “scaffolding” Introduction The San Francisco Math Circle Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

Two Styles for Good Problems The Elusive Perfect Problem Paul Zeitz Outline Hard, but with “scaffolding” Introduction The San Warm-up problems Francisco Math Circle Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

Two Styles for Good Problems The Elusive Perfect Problem Paul Zeitz Outline Hard, but with “scaffolding” Introduction The San Warm-up problems Francisco Math Circle Hint rationing Good and Bad Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion

Two Styles for Good Problems The Elusive Perfect Problem Paul Zeitz Outline Hard, but with “scaffolding” Introduction The San Warm-up problems Francisco Math Circle Hint rationing Good and Bad Trained helpers Problems Example: Trapezoidal Numbers Example: Codes and Communica- tion