9:00-9:50

Session 1  -  Choose One

Estimating Area Using the Monte Carlo Method

Ken Collins, Charlotte Latin School, Charlotte, NC

We will use the TI-83 and its random number generator to estimate the area of various geometric regions with the Monte Carlo method.  This will also allow us to estimate pi and e.

 (Also Friday 3:55 )

Watts 301

Connecting Euler’s Method and Simpson’s Rule

Dan Teague, NCSSM, Durham, NC

Calculus students learn to use Euler’s method to generate approximate solutions to differential equations.  If students have used differential equations software, they may have heard about the improvement in Euler’s method called Runge-Kutta.  Calculus students also learn several methods of numerical integration such as Rectangle and Midpoint rules, the Trapezoid Rule, and Simpson’s rule. In this talk we will show that the numerical methods for solving differential equations and the numerical methods for integration are one and the same.  We will use the methods of numerical integration and Taylor’s Theorem to estimate the error in Euler’s method.  This talk will try to bring unity to what appear to be several different topics in calculus.  

 (Also Saturday 11:15)

ETC

Lecture Hall

Linear Transformations for All                                      

Jon Choate, The Groton School, Groton,  MA 

Computer algebra systems and geometric construction packages such as the Geometer’s Sketchpad can be used to do new and exciting things with matrix algebra, systems of equations, and transformational

geometry.  This talk will make a case for the study of linear

transformations in the post-algebra 2/pre-calculus curriculum.

 (Also Friday 2:30)

Hill 19

Mathematical Wind Chimes                                                                                  

Landy Godbold, The Westminster Schools, Atlanta, GA

Wind chimes look pretty.  Some even sound pretty.  We will examine the relationships among pitch, note names, and pipe length to take the guesswork out of tuning your chimes.  CBL data collection and fitting non-linear functions to data form the mathematical backbone of this project.  Discussion will include the differences between what’s SUPPOSED to happen and what REALLY happens in class. 

 (Also Friday 2:30)

Hill 10

Fun Activities for Precalculus

Margaret Wirth, J H Rose High School, Greenville, NC

We will look at a collection of activities to enhance student learning in advanced mathematics (precalculus) classes.  Topics include exponentials, logarithms, trigonometry, probability, and graph theory.

(Also Saturday 8:45)

Watts 306

9:50-10:20

CONTINENTAL BREAKFAST

ETC Student Center

10:25-11:15

Session 2  - Choose One

What Goes Around Comes Around

Tom Walters, UCLA, Los Angeles, CA

We will explore some “Möbius like” sequences based on function iteration which provide opportunities for students to practice algebraic and visualization skills.

 (Also Saturday 8:45)

Hill 10

Introducing the Logic of Significance Testing through Simulation                  

Josh Tabor, Glen A. Wilson High School, CA

The concepts of simulation and inference are two of the most important in a modern statistics course. In this session, we will use simulations with manipulatives and the TI-83 to explore the logic of significance testing, including sampling distributions and p-values.

(Also Friday 1:25)

Watts 301

CAS-Intensive Mathematics: Making Mathematical Connections through CAS and Dynamic Geometry Environments                                                                              Kathy Heid, Penn State University, PA 

Continuous student access to CAS and a dynamic geometry tool can open interesting connections among traditionally separate mathematics areas.  Examples will be drawn from the CAS-Intensive Mathematics curriculum materials, a joint project of the Mathematics Education faculty at Penn State and the University of Iowa.

 (Also Friday 3:55)

Hill 19

Basins of Attraction

David Chan, NCSSM, Durham, NC

Basins of attraction are a mathematical tool that can help describe how models behave in the long run.  They also can help describe how iterative processes behave.  One example is Newton’s Method, which is taught in calculus.  Furthermore, basins of attraction can be used to create fractals.  In this talk we will learn how these basins are formed and see how they can be used in different classes.

 (Also Friday 2:30)

Watts 306

Constructing An Equal Area World Map                                                       

Joanie Zia, Phillips Exeter Academy, Exeter, NH

For many problems it is useful to be able to visualize data on a map that shows regions of the Earth in their correct proportions; for example, studying animal migration patterns or determining the extent of old-growth forests.  This kind of map is called an equal area or equivalent map by cartographers.  A map known as the Mollweide projection is an example of an equal area map.  A Mollweide map is in the shape of an ellipse with area equivalent to the surface area of the Earth.  In this session, we will apply right triangle trigonometry, solid geometry, and informal limits to derive the longitude and latitude equations needed to create an image of this map using Winplot software.

(Also Friday 1:25)

ETC

Lecture Hall

11:30-12:20

Session 3  -  Choose One

Teaching to the Standards—Whose Standards?

Helen Compton, NCSSM, Durham, NC

Algebra 2 is a course in North Carolina that has state goals and an end of course test.  Through collaborations with several Algebra 2 teachers in our state, many of the major issues of the impact of testing and state mandates have become our issues.  There is a place for applications and use of technology in this setting.  Just drill and practice does not adequately prepare students for the test.  Sample lessons show that you can make choices to address both state and NCTM Standards.  

 (Also Saturday 10:10)

Watts 301

A Discussion of AP Statistics Exam Free Response Experimental Design Questions

Gloria Barrett, NCSSM, Durham, NC

In this session we will review the experimental design problems from the first five AP Statistics exams.  As we discuss solutions to these problems we will focus on the topics of randomization, confounding, and blocking.  Teachers in the North Carolina School of Science and Mathematics Statistics Leadership Institute have developed classroom-ready activities that help students better understand these concepts; several will be shared.

 (Also Friday 3:55)

Hill 10

Rearranging the Alternating Harmonic Series         

Dan Teague, NCSSM, Durham, NC

Calculus students learn that the sum of the alternating harmonic series is In (2).

So, if 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + 1/9 - 1/10 +…= In (2),

what is the value of

1 - 1/2 - 1/4 + 1/3 - 1/6 - 1/8 + 1/5 - 1/10  - 1/12 + 1/7…?

We will prove that this infinite sum is actually (1/2)ln(2).  We will show that there is a rearrangement of the alternating harmonic series that

converges to your favorite real number, and derive (using only algebra) a formula for computing other rearrangements of the terms of the alternating series.

 (Not Repeated)

ETC

Lecture

Hall

Dynamic Spreadsheets

Nils Ahbel, Deerfield Academy, MA

Spreadsheets can be used to create dynamic graphs through the use of scroll bars, making it easier to convey mathematical concepts to students.  Examples will include transformations, binomial probabilities, Pascal’s Triangle, and a method of finding bivariate models without using a regression tool; these and many more spreadsheets are available online.

(Also Saturday 8:45)

Hill 19

The Mover’s Dilemma: Variations on a Theme                                                     

Chris Jones, Horace Mann School, NY

Tired of the same solutions to the same optimization problems included by every calculus textbook under the sun?  While looking for new problems is always a worthwhile endeavor, you may be surprised by the mathematics that an in-depth examination of these old standards can generate.  In this talk we will look at the classic “mover’s dilemma” problem.  Will an object of a certain length with negligible thickness fit around a specific corner?  The multiple solutions presented will incorporate iteration on the graphing calculator and locus hunting with Geometer’s Sketchpad and will introduce the geometric notion of an “envelope.”

(Also Saturday 11:15)

Watts 306

12:20-1:20

LUNCH

NCSSM Cafeteria

1:25-2:15

Session 4  -  Choose One

Growth, the Great Math/Science Disconnect

Alan Bellman, University of California at Davis, CA

In this session the topic of growth, first exponential but mostly logistic, will be investigated.  A simulation, a game, and a couple of CBL experiments will be used to give experience with logistic growth.  Recursion will be the reward.  These lessons are Algebra II/Pre-Calculus ready.  

 (Also Saturday 10:10)

Hill 10

Introducing the Logic of Significance Testing through Simulation                  

Josh Tabor, Glen A. Wilson High School, CA

The concepts of simulation and inference are two of the most important in a modern statistics course. In this session, we will use simulations with manipulatives and the TI-83 to explore the logic of significance testing, including sampling distributions and p-values.

 (Also Friday 10:25)

Watts 301

The Slingshot Around the Moon                                               

Floyd Bullard, NCSSM, Durham, NC

All of the Apollo lunar missions had flight paths that followed a “free-return trajectory”: if for some reason thrusters failed to put the spacecraft into lunar orbit, the gravitational forces of the earth and the moon would “slingshot” the spacecraft around the moon and return it to the earth following a figure-eight path.  This precaution saved the lives of the crew of Apollo 13.  Using Euler’s method, calculus students can design such a flight path, sending their own spacecraft on a round-trip lunar voyage.   

 (Also Saturday 8:45)

Parametric Equations, Motion Problems and Understanding Trigonometry

David Bannard, Collegiate School, Richmond, VA

Parametric equations are an important tool for understanding the wrapping function.  See some fun problems that help introduce students to parametric equations and interesting applications.

(Also Saturday 10:10)

Watts 306

Hill 19

Constructing An Equal Area World Map                                                      

Joanie Zia, Phillips Exeter Academy, Exeter, NH

For many problems it is useful to be able to visualize data on a map that shows regions of the Earth in their correct proportions; for example, studying animal migration patterns or determining the extent of old-growth forests.  This kind of map is called an equal area or equivalent map by cartographers.  A map known as the Mollweide projection is an example of an equal area map.  A Mollweide map is in the shape of an ellipse with area equivalent to the surface area of the Earth.  In this session, we will apply right triangle trigonometry, solid geometry, and informal limits to derive the longitude and latitude equations needed to create an image of this map using Winplot software.   

 (Also Friday 10:25)

ETC

Lecture

Hall

2:30 - 3:20

Session 5  -  Choose One

How Old is Mr. Rogers Anyway?

Donita Robinson, NCSSM, Durham, NC

Through collaborations with several teachers across NC in the teaching of block schedule Algebra 2 classes, we have had the experience of planning and conducting lessons that support the mandated state goals and end of course test.  One of the first lessons we taught introduced the idea of data analysis.  In this activity students guessed the ages of famous people and then tried to determine the best guesser in the room.  Lots of things were new to the students: graphing calculators, interpretation of linear models, and residuals, just to name a few.  In this session we will quickly work through this introductory lesson and look at a follow-up problem taken from the North Carolina Algebra II Indicators.

 (Also Saturday 11:15)

Watts 301

Experiments, Observational Studies, and Sample Surveys:  How can we distinguish among them? 

Linda Young, University of Nebraska, Lincoln, NE

Random assignment of treatments and random selection of units are two different types of randomization that can be present in a study.  These randomizations, or lack of them, are key in determining whether a study is an experiment, an observational study, or a sample survey.  Random selection is also fundamental to determining the scope of inference.  Real-life examples of studies will be used to illustrate these ideas. 

 (Also Saturday 10:10)

Watts 306

Basins of Attraction

David Chan, NCSSM, Durham, NC

Basins of attraction are a mathematical tool that can help describe how models behave in the long run.  They also can help describe how iterative processes behave.  One example is Newton’s Method, which is taught in calculus.  Furthermore, basins of attraction can be used to create fractals.  In this talk we will learn how these basins are formed and see how they can be used in different classes.

 (Also Friday 10:25)

ETC

Lecture

Hall

Linear Transformations for All                                      

Jon Choate, The Groton School, Groton,  MA 

Computer algebra systems and geometric construction packages such as the Geometer’s Sketchpad can be used to do new and exciting things with matrix algebra, systems of equations, and transformational geometry.  This talk will make a case for the study of linear transformations in the post-algebra 2/pre-calculus curriculum.

 (Also Friday 9:00)

Hill 19

Mathematical Wind Chimes                                                                                  

Landy Godbold, The Westminster Schools, Atlanta, GA

Wind chimes look pretty.  Some even sound pretty.  We will examine the relationships among pitch, note names, and pipe length to take the guesswork out of tuning your chimes.  CBL data collection and fitting non-linear functions to data form the mathematical backbone of this project.  Discussion will include the differences between what’s SUPPOSED to happen and what REALLY happens in class.

(Also Friday 9:00) 

Hill 10

3:20-3:50

REFRESHMENTS

ETC Student Center

3:55-4:45

Session 6  -  Choose One

Estimating Area Using the Monte Carlo Method

Ken Collins, Charlotte Latin School, Charlotte, NC

We will use the TI-83 and its random number generator to estimate the area of various geometric regions with the Monte Carlo method.  This will also allow us to estimate pi and e.

 (Also Friday 9:00)

Hill 10

A Discussion of AP Statistics Exam Free Response Experimental Design Questions

Gloria Barrett, NCSSM, Durham, NC

In this session we will review the experimental design problems from the first five AP Statistics exams.  As we discuss solutions to these problems we will focus on the topics of randomization, confounding, and blocking.  Teachers in the North Carolina School of Science and Mathematics Statistics Leadership Institute have developed classroom-ready activities that help students better understand these concepts; several will be shared.

 (Also Friday 11:30)

Watts 306

Using Math to Make Decisions

Dot Doyle, NCSSM, Durham, NC

How do your students decide which college they will attend?  We will discuss a way to use matrices to help make decisions when many attributes are involved.

(Also Saturday 11:15)

Watts 301

Cubic Splines

Julie Graves, NCSSM, Durham, NC

The method of cubic splines fits a piecewise differentiable function to a set of data.  We will look at the mathematics involved and then discuss a calculus project in which students use cubic splines to model a lake bottom.

(Also Saturday 10:10)

ETC

Lecture

Hall

CAS-Intensive Mathematics: Making Mathematical Connections through CAS and Dynamic Geometry Environments                                                                              Kathy Heid, Penn State University, PA 

Continuous student access to CAS and a dynamic geometry tool can open interesting connections among traditionally separate mathematics areas.  Examples will be drawn from the CAS-Intensive Mathematics curriculum materials, a joint project of the Mathematics Education faculty at Penn State and the University of Iowa.

(Also Friday 10:25)

Hill 19

5:00-5:30

Shuttles from Watts Lobby to the Durham Marriott Hotel

BANQUET AT DURHAM MARRIOTT HOTEL

6:00

Social Hour (Cash Bar)

Durham Marriott Hotel

7:00

DINNER

Durham Marriott Hotel

Saturday, February 2, 2002

7:45-8:30

Shuttle from Durham Marriott Hotel

8:15-8:45

COFFEE

ETC Student Center

8:45-9:35

Session 7  -  Choose One

What Goes Around Comes Around

Tom Walters, UCLA, Los Angeles, CA

We will explore some “Möbius like” sequences based on function iteration which provide opportunities for students to practice algebraic and visualization skills.

 (Also Friday 10:25)

Hill 10

Extending the Chi Square Test: Putting Meat on the Two-Way Table     

Chris Olsen, George Washington High School, Cedar Rapids, IA

The simplicity of the chi square calculations for independence and homogeneity of proportions hides some interesting statistics and probability well within the scope of the AP Statistics syllabus. Ideas for connecting chi square to the rest of the AP syllabus will be presented, with examples you can take into the classroom.  

 (Also Saturday 11:15)

Watts 301

The Slingshot Around the Moon                                               

Floyd Bullard, NCSSM, Durham, NC

All of the Apollo lunar missions had flight paths that followed a “free-return trajectory”: if for some reason thrusters failed to put the spacecraft into lunar orbit, the gravitational forces of the earth and the moon would “slingshot” the spacecraft around the moon and return it to the earth following a figure-eight path.  This precaution saved the lives of the crew of Apollo 13.  Using Euler’s method, calculus students can design such a flight path, sending their own spacecraft on a round-trip lunar voyage.  

(Also Friday 1:25)

ETC

Lecture

Hall

Dynamic Spreadsheets

Nils Ahbel, Deerfield Academy, MA

Spreadsheets can be used to create dynamic graphs through the use of scroll bars, making it easier to convey mathematical concepts to students.  Examples will include transformations, binomial probabilities, Pascal’s Triangle, and a method of finding bivariate models without using a regression tool; these and many more spreadsheets are available on-line. 

 (Also Friday 11:30)

Hill 19

Fun Activities for Precalculus

Margaret Wirth, J H Rose High School, Greenville, NC

We will look at a collection of activities to enhance student learning in advanced mathematics (precalculus) classes.  Topics include exponentials, logarithms, trigonometry, probability, and graph theory.

(Also Friday 9:00)

Watts 306

9:35-10:05

CONTINENTAL BREAKFAST

ETC Student Center

10:10-11:00

Session 8  -  Choose One

Teaching to the Standards—Whose Standards?

Helen Compton, NCSSM, Durham, NC

Algebra 2 is a course in North Carolina that has state goals and an end of course test.  Through collaborations with several Algebra 2 teachers in our state, many of the major issues of the impact of testing and state mandates have become our issues.  There is a place for applications and use of technology in this setting.  Just drill and practice does not adequately prepare students for the test.  Sample lessons show that you can make choices to address both state and NCTM Standards.  

 (Also Friday 11:30)

Watts 301

Growth, the Great Math/Science Disconnect

Alan Bellman, University of California at Davis, CA

In this session the topic of growth, first exponential but mostly logistic, will be investigated.  A simulation, a game, and a couple of CBL experiments will be used to give experience with logistic growth.  Recursion will be the reward.  These lessons are Algebra II/Pre-Calculus ready.  

 (Also Friday 1:25)

Hill 10

Experiments, Observational Studies, and Sample Surveys:  How can we distinguish among them? 

Linda Young, University of Nebraska, Lincoln, NE

Random assignment of treatments and random selection of units are two different types of randomization that can be present in a study.  These randomizations, or lack of them, are key in determining whether a study is an experiment, an observational study, or a sample survey.  Random selection is also fundamental to determining the scope of inference.  Real-life examples of studies will be used to illustrate these ideas. 

 (Also Friday 2:30)

Watts 306

Cubic Splines

Julie Graves, NCSSM, Durham, NC

The method of cubic splines fits a piecewise differentiable function to a set of data.  We will look at the mathematics involved and then discuss a calculus project in which students use cubic splines to model a lake bottom.

 (Also Friday 3:55)

ETC

Lecture

Hall

Parametric Equations, Motion Problems and Understanding Trigonometry

David Bannard, Collegiate School, Richmond, VA

Parametric equations are an important tool for understanding the wrapping function.  See some fun problems that help introduce students to parametric equations and interesting applications.

(Also Friday 1:25)

Hill 19

11:15-12:05

Session 9  -  Choose One

How Old Is Mr. Rogers Anyway?

Donita Robinson, NCSSM, Durham, NC

Through collaborations with several teachers across NC in the teaching of block schedule Algebra 2 classes, we have had the experience of planning and conducting lessons that support the mandated state goals and end of course test.  One of the first lessons we taught introduced the idea of data analysis.  In this activity students guessed the ages of famous people and then tried to determine the best guesser in the room.  Lots of things were new to the students: graphing calculators, interpretation of linear models, and residuals, just to name a few.  In this session we will quickly work through this introductory lesson and look at a follow-up problem taken from the North Carolina Algebra II Indicators.

(Also Friday 2:30)

Watts 301

Extending the Chi Square Test: Putting Meat on the Two-Way Table     

Chris Olsen, George Washington High School, Cedar Rapids, IA

The simplicity of the chi square calculations for independence and homogeneity of proportions hides some interesting statistics and probability well within the scope of the AP Statistics syllabus. Ideas for connecting chi square to the rest of the AP syllabus will be presented, with examples you can take into the classroom.  

 (Also Saturday 8:45)

Hill 10

Using Math to Make Decisions

Dot Doyle, NCSSM, Durham, NC

How do your students decide which college to attend?  We will discuss a way to use matrices to help make decisions when many attributes are involved.

 (Also Friday 3:55)

Hill 19

Connecting Euler’s Method and Simpson’s Rule

Dan Teague, NCSSM, Durham, NC

Calculus students learn to use Euler’s method to generate approximate solutions to differential equations.  If students have used differential equations software, they may have heard about the improvement in Euler’s method called Runge-Kutta.  Calculus students also learn several methods of numerical integration such as Rectangle and Midpoint rules, the Trapezoid Rule, and Simpson’s rule. In this talk we will show that the numerical methods for solving differential equations and the numerical methods for integration are one and the same.  We will use the methods of numerical integration and Taylor’s Theorem to estimate the error in Euler’s method.  This talk will try to bring unity to what appear to be several different topics in calculus.  

 (Also Friday 9:00)

ETC

Lecture

Hall

The Mover’s Dilemma: Variations on a Theme                                                      

Chris Jones, Horace Mann School, NY

Tired of the same solutions to the same optimization problems included by every calculus textbook under the sun?  While looking for new problems is always a worthwhile endeavor, you may be surprised by the mathematics that an in-depth examination of these old standards can generate.  In this talk we will look at the classic “mover’s dilemma” problem.  Will an object of a certain length with negligible thickness fit around a specific corner?  The multiple solutions presented will incorporate iteration on the graphing calculator and locus hunting with Geometer’s Sketchpad and will introduce the geometric notion of an “envelope.”

(Also Friday 11:30)   

Watts 306

12:05-1:05

1:15-2:15

2:30-3:00

2:30

3:00

LUNCH

Closing Address: Factors to Convince Us Not to Factor

Tom Seidenberg, Phillips Exeter Academy, Exeter, NH

Speakers’ Meeting

Shuttle from the ETC Lobby to Durham Marriott Hotel

Shuttle from the Watts Lobby to Durham Marriott Hotel

NCSSM Cafeteria

ETC

Auditorium

Watts 301