Welcome to the 30th Anja S. Greer Conference on Mathematics, Science and Technology being held June 22 - June 27, 2014 at Phillips Exeter Academy. If this is your first time to the conference, use our interactive map to get to know the campus. Registration is held at the Phelps Academy Center and classes are primarily in the Phelps Science Center or the Academy Center. You can find your dorm by using the buiding filters. Your conference "Welcome Letter" includes your dorm assignment. Please note on the map, the dorms are listed as male or female. The gender assignment of the dorms may change the week of the conference based on our needs.

Using the schedule below, you can build your individual schedule by clicking on the "star" of the sessions you will attend. For your (2) weeklong courses, please refer to your "Welcome Letter" for courses listed by period.

Our Conference within a Conference (CWIC) sessions are included in this schedule. During your free time, you can attend as many CWIC sessions as you’d like. You do not have to pre-register for CWIC sessions, these are open to all to attend. Just "star" the sessions you are interested in attending. Your individual schedule will be created. You can print it or push it to a mobile device.

Using the schedule below, you can build your individual schedule by clicking on the "star" of the sessions you will attend. For your (2) weeklong courses, please refer to your "Welcome Letter" for courses listed by period.

Our Conference within a Conference (CWIC) sessions are included in this schedule. During your free time, you can attend as many CWIC sessions as you’d like. You do not have to pre-register for CWIC sessions, these are open to all to attend. Just "star" the sessions you are interested in attending. Your individual schedule will be created. You can print it or push it to a mobile device.

Getting Started with the TI-84 PlusC (C is for Color)

**Leaders**
## Ken Collins

Get a jump start on the week with an introduction to the new TI-84 C (C is for Color). We'll look at a few tricks for navigating through HomeScreen, Graphing, and Data Entry menus. We'll look at how to paste a photograph onto the graph screen and analyze it with concepts from beginning algebra.

Charlotte Latin School, Charlotte, NC

Ken has a B.S. in physics and M.S. in math from BPI/NYU and a Ph.D. from Purdue University. He has taught for forty seven years in middle school through graduate school. His focus is on effective use of technology in teaching and learning mathematics. He teaches calculus, precalculus... Read More →

Sunday June 22, 2014 10:00am - 12:00pm

Grainger Hall

Grainger Hall

Charlotte Latin School, Charlotte, NC

Ken has a B.S. in physics and M.S. in math from BPI/NYU and a Ph.D. from Purdue University. He has taught for forty seven years in middle school through graduate school. His focus is on effective use of technology in teaching and learning mathematics. He teaches calculus, precalculus... Read More →

Sunday June 22, 2014 10:00am - 12:00pm

Grainger Hall

Grainger Hall

Am I a frequentist or a Bayesian or a likelihoodist? The big inference debate explained.

**Leaders**
## Floyd Bullard

The last century has seen a lot of discussion about how statistical inference should be conducted. The three main contenders today are Frequentism (the prevailing champion), Bayesianism (the hot contender), and Likelihoodism (the longshot with a powerful one-two!). Some recent academic buzz suggests that the times may be ripe for an upset. In this session I will try not to play favorites, but only provide commentary: who are the players and what do they stand for? What are their chances?

The North Carolina School of Science and Mathematics, Durham, NC

Instructor of Mathematics, NCSSM

The Mathematical Mechanic

**Leaders**
## Philip Todd

In his book __The Mathematical Mechanic__, Mark Levi uses physical insight to solve mathematical problems. I will examine some of his examples, using the new software Mechanical Expressions to create interactive digital models of the analog thought computers used by Levi in his book.

Founder, Saltire Software, Tigard, OR

I am a mathematically trained software engineer who started programming in high school in Scotland at the same time as Bill Gates in Seattle. Except he had access to a computer. Our teacher graded our programs by hand. I graduated from college when Steve Jobs brought out the Apple... Read More →

Monday June 23, 2014 8:15am - 9:00am

Grainger Hall

Grainger Hall

Folded Quadratics

**Leaders**
## Ira Nirenberg

First of all, you're folding the quadratic algebraically, not geometrically. If that's not enough to whet your appetite, then you are clearly not the kid who stood in a corner at a school dance. But come anyway, you could probably use the rest after all that dancing. The talk is divided into three parts: Part 1: A concrete, very specific example, of what we're doing and what will get (some) kids saying: NO WAY! Part 2: We generalize the concrete example in order to see why it works. To which everyone says: No way. Part 3 (newly minted): We may finally have a proof of the Nirenberg Conjecture! You won't find this anywhere else!

Benjamin Franklin High School, New Orleans, LA (retired)

Ira worked for Shell Oil as a geophysicist for six years prior to entering the teaching field. From 1985 to 2005 he taught at Benjamin Franklin High School in New Orleans, LA. 2006-2007 academic year was spent at University of Chicago Laboratory Schools and Lusher High School in 2009... Read More →

Quadratic Models without Quad Reg

When we want to find quadratic or exponential models for data, we have the option of having our calculator perform QuadReg or ExpReg. Neither of these regression techniques helps students deepen their understanding of transformations or sheds light on the graphs of the resulting models. We will use linear regression to find both quadratic and exponential models; the process can help students see how parabolas or exponential curves have been transformed to fit a particular data set.

Monday June 23, 2014 9:15am - 10:00am

Grainger Hall

Grainger Hall

Flatland, The Movie

**Leaders**
## Jonathan Choate

Edwin A. Abbot's geometry classic Flatland has been made into a movie that can be shown in any geometry classroom. It is well done and contains a lot of nice mathematics. Tom Banchoff's classic video, Slicing The Hypercube, will also be shown.

Groton School, Groton, MA

Jonathan has taught mathematics at Groton School since 1966. He is the co-author of The Dynamics Toolkit, four books covering topics in fractal geometry and chaos theory. He has served on both NCTM's Algebra and Discrete Mathematics Task Forces. His column, Geometer's Corner, is a... Read More →

Using Anscombe's Quartet to Study Bivariate Data

Informed data analysis should be both numerical and graphical in nature. In this session, participants will use a cleverly devised data set, namely, Anscombe's Quartet, to numerically and graphically study the effect of outliers on Pearson's product-moment correlation coefficient and least squares regression analysis.

Monday June 23, 2014 10:30am - 11:15am

Grainger Hall

Grainger Hall

Mathematical Modeling in Abu Dhabi: Architecture, design and mathematics
Mathematical modeling can be done with buildings anywhere in the world. The focus of this session will be on mathematical models and activities related to astonishing buildings in Abu Dhabi, including one that responds to sunlight and another in the shape of a circle. The mathematical content from this session will involve linear, quadratic and sinusoidal functions; algebra, geometry, trigonometry and the golden ratio.

Teaching Mathematics in a Wireless Classroom: New Communication Opportunities

In this session, participants will experience a wireless mathematics classroom setting where the teacher can pose a question and obtain immediate feedback on student understanding. Various question types and questioning techniques will be showcased. This session is suitable for mathematics teachers interested in formative assessment.

Monday June 23, 2014 11:30am - 12:15pm

Grainger Hall

Grainger Hall

Mobius transformations as a complex number exercise

**Leaders**
## Jeff Ibbotson

Some simple complex number algebra can be used to develop intricate knowledge of a linear fractional transformation. The project reveals a visual perspective on rotation of a sphere followed by stereographic projection.

Mathematics, Phillips Exeter Academy

Jeff has been teaching mathematics at private schools since 1995. Prior to that, he taught at a local four-year college. His fields of expertise involve functional analysis, geometry and logic. He has been working on a history of mathematics text for high school use for several years... Read More →

Monday June 23, 2014 1:45pm - 2:30pm

Grainger Hall

Grainger Hall

What lawyers, doctors, and the MLB don't know: digging deeper with probability
Conditional probability is the probability that some event A happens, given event B happens (conditional upon event B) fools the experts every day, and often with dire consequences. What are some examples where we have seen this go very wrong? What makes conditional probability so anti-intuitive? How can we teach students to think about it differently so that they don't make the same mistakes? These are the kind of questions that we will investigate using some interesting real world examples (assuming no prior knowledge of probability rules and topics).

Assessment in PBL: Being Consistent with Your Learning Goals

**Leaders**
## Carmel Schettino

With the onset of the CCSS and the increasing desire for teachers to use PBL and inquiry methods in their classes, how can teacher adapt assessment practices to best measure the strengths and weaknesses of their students' learning? Come and hear this presenter's experiences with many years of classroom PBL methods and different techniques of assessment from self-evaluation to metacognitive writing to group problem sets to more traditional quizzes.

Senior Academic Advisor for Mathematics, Avenues: The World School

With Problem-Based Learning as her specialization, Carmel obtained a Ph.D. in Math Education while teaching at the secondary level for many years. She is passionate about helping teachers grapple with the pedagogical and curricular questions that rise when PBL is brought into the... Read More →

The Axioms of Origami

**Leaders** *PM*
## Philip Mallinson

In origami an axiom is a permitted type of fold. They are more powerful than Euclid's in that they permit the trisection of a general angle and the construction of cube roots. I will provide appropriate paper to explore these axioms.

Mathematics, Phillips Exeter Academy

Philip started his math teaching career in 1970 at a tiny private school, now defunct, in Vermont. From there he went to the University of Washington in Seattle to earn a license to teach mathematics. He was an instructor briefly at the University of Washington and then taught at... Read More →

Monday June 23, 2014 2:45pm - 3:30pm

Grainger Hall

Grainger Hall

Bring American History Into The Math Classroom: Teach Probability With Punchboards

**Leaders**
## Stuart Moskowitz

Gambling takes on many forms. A fascinating part of American gambling history is the Punchboard. Though now illegal for gambling, punchboards can be brought into math class to enhance an introduction to probability. A typical punchboard is made of pressed cardboard, anywhere from 3 by 5 inches up to 11 by 17 inches and about an inch thick. It has lots of small holes drilled in it, perhaps as many as 2000. Each hole contains a tiny piece of folded paper with a number on it and each hole would be covered with paper or foil. The rules for each board would be printed on the board along with a colorful theme/story about something that was popular in America at the time. Between 1910 and 1960, in states where they were legal, punchboards were commonly found in stores and bars. A customer would pay money for the opportunity to punch out one of the papers hidden in the holes. If the number on the hidden paper matched a winning number as described on the board, the patron wins. Winnings often were money, candy, or cigarettes. Because the winning numbers and their payouts are stated on the board, probabilities and expected values are relatively easy to calculate. This makes punchboards an excellent way to introduce probability to our students. It's hard to get students excited when we use contrived data out of a textbook. But when I take my colorful punchboards out of the cupboard and let them punch out a few of the hidden papers, all my students are motivated, curious, and attentive.

Retired, Humboldt State University Math Dept

Stuart loves to play with puzzles when he's not teaching math. Even more, Stuart loves to use puzzles to teach math. Besides puzzles, Stuart has a passion for history and technology as ways to make math come alive for students. Throughout Stuart's 20 years teaching teacher-prep courses... Read More →

Monday June 23, 2014 3:45pm - 4:30pm

Grainger Hall

Grainger Hall

Engaging all Learners with iTunesU

**Leaders**
## Anthony DiLaura

Have you ever wondered where you can go to find endless amounts of free reusable content from the top universities and k-12 institutions? Ever pondered how you can impact education beyond your classroom walls? Have you been debating which learning management system is right for you and best for your students? iTunesU is the answer to all these questions and so many more. With iTunesU you can teach and learn anything from anywhere. Come and find out how you can engage all learners with iTunesU.

Teacher, Zeeland Public Schools, Zeeland, MI

Anthony is a high school math teacher, STEM educator, and instructional technology specialist. In 2013 he was award the “Apple Distinguished Educator” title and in 2015 he was nationally recognized as the “iBooks Author Trainer of the Year” for his innovative workshops that... Read More →

Graphing and Modeling with Desmos

Desmos, both the free app and the web-based interface, offer intuitive yet powerful tools for exploring and transforming graphs and modeling physical phenomena. Introducing this tool early and putting it directly into students hands provides them with dynamic ways to quickly visualize and access concepts that are typically static, or require more elaborate software and teacher direction.

Monday June 23, 2014 3:45pm - 4:30pm

Academy Building, Mayer Auditorium

Academy Building, Mayer Auditorium

Using GeoGebra to teach Statistics

**Leaders**
## Mike May

GeoGebra is an open source, cross-platform, program that can be used for most math courses in a high school or junior college curriculum. On of the newer features is the ability to demonstrate most of the statistics used in an introductory statistics course. We will explore those features.

Saint Louis University, St. Louis, MO

I use a variety of technology in teaching.Recently I have been using GeoGebra for demonstration, SAGE for number theory, Excel and Wolfram Alpha for Business Calculus, and WeBWorK for automated homework. I am also a Jesuit priest

Monday June 23, 2014 3:45pm - 4:30pm

PSC Rm 127

PSC Rm 127

Common Core Statistics: A Simple Introduction to Statistical Significance

The concept of "statistical significance" is included in the Common Core State Standards and as such will soon be part of the middle school and high school curriculum for many students. We will consider an example about driving and cell phone use to explain the idea of statistical significance. This presentation will be geared to teachers who do not teach statistics.

Monday June 23, 2014 4:45pm - 5:30pm

Academy Building, Mayer Auditorium

Academy Building, Mayer Auditorium

My Favorite Angle

**Leaders**
## Philip Todd

Since high school I have had a favorite angle. It charms me by not being a whole number of degrees, but it does have a name and turns up as the solution to three apparently unrelated problems. I'll share these problems, and their solution: my favorite angle.

Founder, Saltire Software, Tigard, OR

I am a mathematically trained software engineer who started programming in high school in Scotland at the same time as Bill Gates in Seattle. Except he had access to a computer. Our teacher graded our programs by hand. I graduated from college when Steve Jobs brought out the Apple... Read More →

Monday June 23, 2014 4:45pm - 5:30pm

Grainger Hall

Grainger Hall

The 1954 AP Exam in Mathematics

**Leaders**
## Doug Kuhlmann

Wait, the AP exam was not given until 1956. Yes, but the College Board had a couple of years of trial runs experimenting with types of exams before settling on multiple choice and free response. Come see what the 1954 and 1955 questions looked like. The 1954 exam had a short answer section in addition to the MC and FR section. We can probably guess why short answer questions did not make the final cut.

Doug has been teaching in secondary boarding schools for 38 years, the last 29 at Philips Academy. He received his B.S. in math from St. Louis U. in 1968, and his Ph.D. from Northwestern in 1978. He enjoys learning and teaching mathematics and is particularly interested in using GeoGebra... Read More →

The Geometry of Salt

**Leaders** *PM*
## Philip Mallinson

Let salt fall uniformly on a plane surface - imagine snow on a flat roof. As the salt - or snow - builds up, interesting patterns in ridges and curves develop. Come and explore them.

Mathematics, Phillips Exeter Academy

Philip started his math teaching career in 1970 at a tiny private school, now defunct, in Vermont. From there he went to the University of Washington in Seattle to earn a license to teach mathematics. He was an instructor briefly at the University of Washington and then taught at... Read More →

Monday June 23, 2014 4:45pm - 5:30pm

PSC Rm 216

PSC Rm 216

Constructing Parallelograms and Circles on the IPad with TINspire to Discover Properties

A quick overview of how to construct parallelograms and circles to allow students to discover their properties and theorems. This method means students can play around with the objects to "see" what happens to the angles, lengths or slopes, when changes occur to shapes.

Tuesday June 24, 2014 8:15am - 9:00am

Grainger Hall

Grainger Hall

Manipulatives to Explore Limits
In this session, we will explore how to find limits of sequences using manipulatives. This hands-on activity builds upon students' intuition and could be used to bring students to an understanding of limits equivalent to the epsilon-N definition while addressing some common misconceptions.

Enhancing Algebra, Pre-Calculus, and Calculus using Sketchpad 5

Sketchpad 5 is a very versatile cross-platform software that can be used to make many mathematical concepts visual. Some of the important techniques for programming will be demonstrated, and a variety of sketches will be shown. All of the presenter's completed Sketchpad work will be given to anyone in attendance

Tuesday June 24, 2014 9:15am - 10:00am

Grainger Hall

Grainger Hall

Gateway Exams: Let the Party Begin

**Leaders**
## Dan Butler

Gateway exams are like the multiplication tests in elementary school. Come in and see how I took the technical skills out of my unit tests to leave room for the juicier problems.

Mathematics Teacher, Mounds View High School, Arden Hills, MN

Dan has taught mathematics for twenty-seven years; 9 years in middle school and 18 years in high school. In addition, he teaches an enriched and accelerated course for middle school students at the University of Minnesota. He has been involved in professional development workshops... Read More →

Using Mapping Diagrams to Understand Linear Functions

**Leaders** *MF*
## Martin Flashman

Mapping diagrams provide a very illuminating tool to visualize functions that complement the more commonly used graph. I will present an introduction to mapping diagrams and their use for understanding linear functions including linear function composition and inverses for understanding solving equations with mapping diagrams and connections with other elementary functions. Worksheets and interactive on-line apps (using GeoGebra) will be provided.

Professor of Mathematics, Humboldt State University

Martin ("Flash") holds a BA, MA, and PhD in Math from Brandeis. He has taught calculus and preparation for calculus for more than 40 years-Bard College (6 yrs)-Humboldt State Univ(33 yrs). He has given presentations around the US and recently a webinar for AMATYC on mapping diagrams... Read More →

Tuesday June 24, 2014 9:15am - 10:00am

Academy Building, Mayer Auditorium

Academy Building, Mayer Auditorium

Reading Ancient Mathematics

**Leaders**
## Philip Todd

Does your school have a classics department? Have you ever considered collaborating? I will follow Sir Thomas Little Heath in arguing that reading Euclid in Greek (or pseudo-Archimedes in Latin) is not piling inutility upon inutility, but exposing the student (or yourself) to classically precise mathematical exposition which is surprisingly accessible in its original tongue. I will give you a flavor of the experience of reading the ancient mathematics in its original form and present (in English) the arguments from short snippets of Euclid and Archimedes. Like me, you may be surprised at how modern and elegant this ancient mathematics seems when read on its own terms.

Founder, Saltire Software, Tigard, OR

I am a mathematically trained software engineer who started programming in high school in Scotland at the same time as Bill Gates in Seattle. Except he had access to a computer. Our teacher graded our programs by hand. I graduated from college when Steve Jobs brought out the Apple... Read More →

Working Mathematically

**Leaders** *SP*
## Simon Purdue

Wesley College Mathematics Department wants students to experience mathematics as an engaging, personally relevant, problem-solving activity. We want to support students to work like a 'mathematician'. Lower School 'Problems of the Week' and complex Upper School Investigations from our Specialist stream will be discussed. All resources will available for attendees at the conclusion of the conference.

Mathematics Teacher, Wesley College

Education; trying new strategies, utilizing technology, making learning fun!

Tuesday June 24, 2014 10:30am - 11:15am

Grainger Hall

Grainger Hall

Challenging the Mathematically Challenged and Others

**Leaders**
## Ray Williams

This session will explain how problem solving projects can allow students a great degree of success.

Ray has been a teacher of mathematics and science for the past 40 years and is currently the Head of Mathematics at St Mark's Anglican Community School in Perth, Western Australia. St Mark's mathematics classrooms all have TI-Nspire Navigator Wireless Networks and wireless data projection... Read More →

Tuesday June 24, 2014 11:30am - 12:15pm

Academy Building, Mayer Auditorium

Academy Building, Mayer Auditorium

Learning Styles in the Math Classroom

**Leaders**
## Nils Ahbel

We know that everyone has a different learning style such as left brain, right brain, auditory, visual, and kinesthetic. To connect more effectively with all of our students we need to be able to teach in all of these modes. Many teachers teach in different modes, but presenting ideas to students becomes so much more powerful when the teacher choses the mode more deliberately based on the student's learning style. But... how do we recognize the learning style of an individual student? How can we present material more effectively by addressing each of these modalities? What is the result when a teacher is not aware of his/her own learning style? Drawing from his experience in the classroom, Nils will share his answers to these questions. He will also "teach" mini-lessons with the same content, addressing drastically different modalities of learning.

Deefield Academy

Nils studied Mechanical Engineering and then earned his MBA from the University of Chicago in 1984, with a concentration in Microeconomics. Following graduate school he worked in Germany as a project engineer for five years and then, searching for his passion he returned to the US... Read More →

Origami's Amazing Fold-And-One-Cut Theorem

**Leaders** *PM*
## Philip Mallinson

If you draw a polygon on a sheet of paper then you can cut it out with as many straight cuts as the polygon has sides. There is a theorem in origami that it is possible to fold the paper in such a way that you can cut out the polygon with a just one straight cut. Don't believe me? Scissors and paper provided.

Mathematics, Phillips Exeter Academy

Philip started his math teaching career in 1970 at a tiny private school, now defunct, in Vermont. From there he went to the University of Washington in Seattle to earn a license to teach mathematics. He was an instructor briefly at the University of Washington and then taught at... Read More →

Tuesday June 24, 2014 11:30am - 12:15pm

Grainger Hall

Grainger Hall

Enhancing Algebra, Pre-Calculus, and Calculus using Sketchpad 5
Sketchpad 5 is a very versatile cross-platform software that can be used to make many mathematical concepts visual. Some of the important techniques for programming will be demonstrated, and a variety of sketches will be shown. All of the presenter's completed Sketchpad work will be given to anyone in attendance

Tuesday June 24, 2014 1:45pm - 2:30pm

Grainger Hall

Grainger Hall

Using Anscombe's Quartet to Study Bivariate Data
Informed data analysis should be both numerical and graphical in nature. In this session, participants will use a cleverly devised data set, namely, Anscombe's Quartet, to numerically and graphically study the effect of outliers on Pearson's product-moment correlation coefficient and least squares regression analysis.

Quadratic Models without Quad Reg
When we want to find quadratic or exponential models for data, we have the option of having our calculator perform QuadReg or ExpReg. Neither of these regression techniques helps students deepen their understanding of transformations or sheds light on the graphs of the resulting models. We will use linear regression to find both quadratic and exponential models; the process can help students see how parabolas or exponential curves have been transformed to fit a particular data set.

Tuesday June 24, 2014 2:45pm - 3:30pm

Grainger Hall

Grainger Hall

Teaching Mathematics in a Wireless Classroom: New Communication Opportunities
In this session, participants will experience a wireless mathematics classroom setting where the teacher can pose a question and obtain immediate feedback on student understanding. Various question types and questioning techniques will be showcased. This session is suitable for mathematics teachers interested in formative assessment.

Students Teaching Parents

In my algebra and precalculus classes I help students learn to apply the mathematics they study and learn to use technology appropriately. Since parents often purchase calculators, or iPads, or laptops to help their students with schoolwork, I like to give the parents the opportunity to see one example of how the students use technology in math. To accomplish this, I assign a "parent project" in which the student teaches one of his or her parents (or another adult relative if that is more appropriate) one of the applied projects we have done during the course. In this session, I will describe the components of the parent project, suggest some problems that students have used with their parents in the past, and share student and parent reactions to the activity.

Tuesday June 24, 2014 3:45pm - 4:30pm

Academy Building, Mayer Auditorium

Academy Building, Mayer Auditorium

Technical Problem Solving: MacGuyver Meets the Math Classroom.

**Leaders**
## Dan Butler

Come in and solve some interesting geometry problems where time and materials are limited and imagination rules the day.

Mathematics Teacher, Mounds View High School, Arden Hills, MN

Dan has taught mathematics for twenty-seven years; 9 years in middle school and 18 years in high school. In addition, he teaches an enriched and accelerated course for middle school students at the University of Minnesota. He has been involved in professional development workshops... Read More →

Tuesday June 24, 2014 3:45pm - 4:30pm

PSC Rm 304

PSC Rm 304

The Babylonians to Newton to Mandelbrot

**Leaders** *DB*
## David Bannard

This talk will trace mathematics begun in Babylonian times, advanced by Newton and culminating in the fractal geometry of Mandelbrot. I am giving this talk in memory of Rick Parris whose fractal geometry class I was fortunate to take several years ago at this conference.

Collegiate School, Richmond, VA

David has been teaching since 1969 including 17 years at the Groton School and the past 21 years at the Collegiate School in Richmond, Virginia. As one of the original beta testers for The Geometer's Sketchpad, he has been using the program in the classroom for almost 18 years. He... Read More →

Viete's formula and infinite operations

**Leaders**
## Jeff Ibbotson

The early history of the Calculus is littered with interesting use of infinite expansions of various types. One of the lesser known is Viete's infinite product expansion for pi. Another is the Wallis product expansion for pi/2. We will show both and derive through some interesting trigonometric expansions. Connections with the gamma function will also be highlighted.

Mathematics, Phillips Exeter Academy

Jeff has been teaching mathematics at private schools since 1995. Prior to that, he taught at a local four-year college. His fields of expertise involve functional analysis, geometry and logic. He has been working on a history of mathematics text for high school use for several years... Read More →

Tuesday June 24, 2014 3:45pm - 4:30pm

Grainger Hall

Grainger Hall

KenKen puzzles and the iPad
KenKen puzzles are immensely satisfying to solve and they can be done in a very short time. We will discuss ways that mathematics teachers can use KenKen puzzles in their classes and how students can use an iPad to teach each other how to solve these puzzles.

Thoughts on the Harmonic Mean

**Leaders**
## Ira Nirenberg

We often overlook the harmonic mean paying more attention to the arithmetic mean and the geometric mean; somehow that seems mean, right? We use the harmonic mean more often than we realize because, well, it's subtle. I would claim that the poor old HM is the underappreciated member of the Mean family. Want to see why?

Benjamin Franklin High School, New Orleans, LA (retired)

Ira worked for Shell Oil as a geophysicist for six years prior to entering the teaching field. From 1985 to 2005 he taught at Benjamin Franklin High School in New Orleans, LA. 2006-2007 academic year was spent at University of Chicago Laboratory Schools and Lusher High School in 2009... Read More →

Tuesday June 24, 2014 4:45pm - 5:30pm

Grainger Hall

Grainger Hall

The Complexity of Linear Equations
One of my favorite classroom activities is an open-ended investigation into the relationship between the algebraic structure of a family of linear equations and the geometric representation of that family in the plane. In the equation , if we define a family of lines by requiring a, b, and c satisfy some constraint ( , for example), what common features do the graphs of these lines share? In the activity, students will generate their own individual conjectures and write their first original proof.

Vectors and Regression

Most of us know that the regression line minimizes the sum of squared residuals, but most of us don’t know how our calculators actually produce a slope and intercept for a regression line. This session will provide an answer to the question “How did my calculator do that?” It turns out that our calculators and other software use vectors to compute regression equations. We will look at the vector basis of regression; a certain level of comfort with vectors will be assumed.

Wednesday June 25, 2014 8:15am - 9:00am

Grainger Hall

Grainger Hall

Students' Problem-Solving Approaches to Counting
This session will provide an overview of three categories of students' ways of thinking about basic combinatorics problems. Some of these approaches came naturally to students, while others required students to build upon previous techniques. We will discuss how to guide students to develop these new, often more sophisticated, approaches.

Why pi is wrong. Celebrate tau day on June 28.

**Leaders**
## Doug Kuhlmann

A few mathematicians are realizing that pi is wrong. Not incorrect, mind you, but the real constant should not be the circumference of a circle divided by the diameter but the circumference divided by the radius. This is tau. Hear how I introduced the unit circle in trig class using tau and discover the advantages.

Doug has been teaching in secondary boarding schools for 38 years, the last 29 at Philips Academy. He received his B.S. in math from St. Louis U. in 1968, and his Ph.D. from Northwestern in 1978. He enjoys learning and teaching mathematics and is particularly interested in using GeoGebra... Read More →

Wednesday June 25, 2014 9:15am - 10:00am

Grainger Hall

Grainger Hall

A very nice hyperbola problem.

This session will take a close look at a very nice application that introduces the two focal point locus definition of the hyperbola. After analyzing the problem algebraically, we will look at two different approaches for sketching hyperbolas on Sketchpad or Geogebra, with a bonus feature at the end.

Wednesday June 25, 2014 10:30am - 11:15am

Grainger Hall

Grainger Hall

The Mathematical Mechanic
In his book __The Mathematical Mechanic__, Mark Levi uses physical insight to solve mathematical problems. I will examine some of his examples, using the new software Mechanical Expressions to create interactive digital models of the analog thought computers used by Levi in his book.

**Leaders**
## Philip Todd

I am a mathematically trained software engineer who started programming in high school in Scotland at the same time as Bill Gates in Seattle. Except he had access to a computer. Our teacher graded our programs by hand. I graduated from college when Steve Jobs brought out the Apple... Read More →

Founder, Saltire Software, Tigard, OR

Students Teaching Parents
In my algebra and precalculus classes I help students learn to apply the mathematics they study and learn to use technology appropriately. Since parents often purchase calculators, or iPads, or laptops to help their students with schoolwork, I like to give the parents the opportunity to see one example of how the students use technology in math. To accomplish this, I assign a "parent project" in which the student teaches one of his or her parents (or another adult relative if that is more appropriate) one of the applied projects we have done during the course. In this session, I will describe the components of the parent project, suggest some problems that students have used with their parents in the past, and share student and parent reactions to the activity.

The Axioms of Origami
In origami an axiom is a permitted type of fold. They are more powerful than Euclid's in that they permit the trisection of a general angle and the construction of cube roots. I will provide appropriate paper to explore these axioms.

**Leaders** *PM*
## Philip Mallinson

Philip started his math teaching career in 1970 at a tiny private school, now defunct, in Vermont. From there he went to the University of Washington in Seattle to earn a license to teach mathematics. He was an instructor briefly at the University of Washington and then taught at... Read More →

Mathematics, Phillips Exeter Academy

Wednesday June 25, 2014 11:30am - 12:15pm

Grainger Hall

Grainger Hall

Common Core Statistics: A Simple Introduction to Statistical Significance
The concept of "statistical significance" is included in the Common Core State Standards and as such will soon be part of the middle school and high school curriculum for many students. We will consider an example about driving and cell phone use to explain the idea of statistical significance. This presentation will be geared to teachers who do not teach statistics.

Wednesday June 25, 2014 1:45pm - 2:30pm

Grainger Hall

Grainger Hall

Flatland 2: Sphereland, The Movie

**Leaders**
## Jonathan Choate

Flatland 2 is a follow up to the movie Flatland and continues the story line developed in the first movie. Like the first movie the animation is terrific and does a good job of introducing the idea of a higher dimension.

Groton School, Groton, MA

Jonathan has taught mathematics at Groton School since 1966. He is the co-author of The Dynamics Toolkit, four books covering topics in fractal geometry and chaos theory. He has served on both NCTM's Algebra and Discrete Mathematics Task Forces. His column, Geometer's Corner, is a... Read More →

Circular Reasoning: PI Shows Up In The Strangest Places

**Leaders**
## Stuart Moskowitz

It's impossible to know exact values for both the circumference and diameter of a circle, but that hasn't stopped us from trying. From before the time Archimedes squeezed a circle between polygons, we've tried to find PI by cutting circles up to make them rectangles or triangles, dropping needles onto grids, and even legislating exact ratios. This CWIC will be a 45 minute historical tour that brings unusual applications of algebra, geometry, probability, and politics all together for a common goal.

Retired, Humboldt State University Math Dept

Stuart loves to play with puzzles when he's not teaching math. Even more, Stuart loves to use puzzles to teach math. Besides puzzles, Stuart has a passion for history and technology as ways to make math come alive for students. Throughout Stuart's 20 years teaching teacher-prep courses... Read More →

How to Find a Spouse

You are seeking a life-partner and, obviously, want to find the best match possible. As you meet and date "candidates", you have the opportunity to determine how well matched you are as a couple. There are several rules to this dating game: 1) It is generally considered bad form to date seriously two different people simultaneously, so you consider each person one at a time. 2) You can date someone for any length of time, but eventually, you must either "select" them or say "no", and move on to another candidate. 3) No is forever. Once someone has been passed over, you cannot go back. Given that one must make their selection before seeing all the "candidates", how can you maximize the probability that you select your best match? This problem combines ideas of probability, discrete optimization, and calculus.

Wednesday June 25, 2014 2:45pm - 3:30pm

Grainger Hall

Grainger Hall

Maps and Math: Using maps to enrich tasks

**Leaders**
## David Sabol

With the volume, variety, and detail offered in online maps and satellite imagery today, countless inquiry-driven tasks can be developed for all levels of math learning. In this session, we will look at a handful of tasks developed for the high school geometry classroom and one for calculus/precalculus. We will play Thales of Miletus in the modern era, take a long look at Voronoi maps which define regions of closest proximity to individual points, compare zoom on Google Maps to dilation factors in similar polygons, and examine average rate of change by trapping speeders in front of a middle school. The technology resources demoed will include browser-based google maps, websites, and GeoGebra.

Math Department Chair, Saint Ignatius High School

I teach Algebra I, Geometry, and Calculus in Cleveland, Ohio. I was selected in the first cohort of the Desmos Teaching Fellowship and have since become a Desmos Certified Presenter. I also love a good map, but who doesn't?

Wednesday June 25, 2014 3:45pm - 4:30pm

Grainger Hall

Grainger Hall

Twitter basics: Connecting, Learning, & Sharing with the World

**Leaders**
## Anthony DiLaura

Ever hear one of your students say "hashtag YOLO" and wondered what they were talking about? Ever wonder what the greatest agent of innovation in education is? Ever consider that the answer to both of these questions is the same- Twitter! This CWiC session will give you an overview of how educators around the world are connecting and growing in their profession using Twitter. This is an intro session to Twitter so it is very safe for those timid teachers wondering the basic what, why, and how's of Tweeting. Come learn how you can connect, learn, and share with the world!

Teacher, Zeeland Public Schools, Zeeland, MI

Anthony is a high school math teacher, STEM educator, and instructional technology specialist. In 2013 he was award the “Apple Distinguished Educator” title and in 2015 he was nationally recognized as the “iBooks Author Trainer of the Year” for his innovative workshops that... Read More →

“Webale Kwegesiya” – A Math Teacher’s Experience in an African Village

Come and hear stories about moving from an elite boarding school in the US to spend a decade in a remote, impoverished, war-torn village in Uganda. How do you establish a community school in a place beyond the end of the road? How do the practices of a student-centered classroom interact with an exam-driven culture? What do you do when everyone in the district is failing “maths”?

Wednesday June 25, 2014 3:45pm - 4:30pm

Academy Building, Mayer Auditorium

Academy Building, Mayer Auditorium

A Math Trail at the Phillips Exeter Academy
Starting at the entrance to the Phelps Science Center, we will take a mathematical walk to the Exeter Library. We will answer and pose mathematical questions related to architecture, public art, and patterns encountered along this path. This workshop will be of interest to teachers wanting to provide their students with opportunities to be active learners, to collaborate and to develop their own mathematical questions related to their interests. Participants are encouraged to bring a mobile device.

Dynamic and Dynamite Desmos Demos

**Leaders** *CR*
## Chip Rollinson

Explore the powerful (and free) online graphing software from Desmos.com and hopefully discover a few ways that you and your students would benefit from using it. Desmos is incredibly elegant and easy to use, while also being a versatile tool capable of graphing equations in many different forms. Learn how Desmos makes exploring transformations so easy and (I dare say!) fun. See examples of student artwork created by transforming an assortment of basic toolkit equations. Observe how easily Desmos graphs (and animates) parametric and polar functions. Calculus lovers will also enjoy seeing Desmos beautifully graph functions defined as Taylor Series in their sigma notation! Bring your laptop or tablet and play around with this amazing graphing tool.

Buckingham Browne and Nichols

I've been teaching high school math at Buckingham Browne & Nichols (BB&N) in Cambridge, MA since 2005. At BB&N, I've taught just about everything up to AP Calculus BC. I also coach BB&N's math team. Before BB&N, I taught high school math at Beaver Country Day in Chestnut Hill, MA... Read More →

Wednesday June 25, 2014 4:45pm - 5:30pm

Academy Building, Mayer Auditorium

Academy Building, Mayer Auditorium

It Started with the French Garden Problem: Teachers Modeling Inquiry

**Leaders**
## Carmel Schettino

One of the goals of the math classroom today is to create innovative, creative thinkers with resilience and grit. A major question for math teachers is how to do this and an answer to that question is to model perseverance and curiosity in all that we do. But how do we do that with the material that we teach? We already know the answers and the methods, so how can we create for ourselves an ongoing community of inquiry and investigation with each other that we can share with our students. Come hear the story of the ways in which I have found inquiry through my own PLC and how I shared it with my own students in a project this spring. Wonderful eBook inquiry projects from students will be shared.

Senior Academic Advisor for Mathematics, Avenues: The World School

With Problem-Based Learning as her specialization, Carmel obtained a Ph.D. in Math Education while teaching at the secondary level for many years. She is passionate about helping teachers grapple with the pedagogical and curricular questions that rise when PBL is brought into the... Read More →

Modeling the Cycloid: From Geometry to Calculus

**Leaders**
## Maria Hernandez

Participants will explore the motion of a cycloid modeled by parametric equations. We will demonstrate how to capture the data from a video and explore the geometric underpinnings that verify the models. Data will be shared in various formats along with a GeoGebra file that helps students visualize the concepts.

Mathematics Instructor, The North Carolina School of Science and Mathematics, Durham, NC

I have taught math for over 25 years and have focused my teacher development efforts on incorporating real-world modeling problems and the effective use of technology in the classroom . I have recently taught Complex Systems, Precalculus, Calculus and Multivariable at NCSSM. I am... Read More →

Wednesday June 25, 2014 4:45pm - 5:30pm

Grainger Hall

Grainger Hall

Retired, Humboldt State University Math Dept

Stuart loves to play with puzzles when he's not teaching math. Even more, Stuart loves to use puzzles to teach math. Besides puzzles, Stuart has a passion for history and technology as ways to make math come alive for students. Throughout Stuart's 20 years teaching teacher-prep courses... Read More →

Modeling the Cycloid: From Geometry to Calculus
Participants will explore the motion of a cycloid modeled by parametric equations. We will demonstrate how to capture the data from a video and explore the geometric underpinnings that verify the models. Data will be shared in various formats along with a GeoGebra file that helps students visualize the concepts.

**Leaders**
## Maria Hernandez

Mathematics Instructor, The North Carolina School of Science and Mathematics, Durham, NC

I have taught math for over 25 years and have focused my teacher development efforts on incorporating real-world modeling problems and the effective use of technology in the classroom . I have recently taught Complex Systems, Precalculus, Calculus and Multivariable at NCSSM. I am... Read More →

Thursday June 26, 2014 8:15am - 9:00am

Grainger Hall

Grainger Hall

Reading Ancient Mathematics
Does your school have a classics department? Have you ever considered collaborating? I will follow Sir Thomas Little Heath in arguing that reading Euclid in Greek (or pseudo-Archimedes in Latin) is not piling inutility upon inutility, but exposing the student (or yourself) to classically precise mathematical exposition which is surprisingly accessible in its original tongue. I will give you a flavor of the experience of reading the ancient mathematics in its original form and present (in English) the arguments from short snippets of Euclid and Archimedes. Like me, you may be surprised at how modern and elegant this ancient mathematics seems when read on its own terms.

**Leaders**
## Philip Todd

I am a mathematically trained software engineer who started programming in high school in Scotland at the same time as Bill Gates in Seattle. Except he had access to a computer. Our teacher graded our programs by hand. I graduated from college when Steve Jobs brought out the Apple... Read More →

Founder, Saltire Software, Tigard, OR

Thursday June 26, 2014 9:15am - 10:00am

Grainger Hall

Grainger Hall

The Gini Index for Income Inequity
The Gini Index, a commonly used index for income inequality, is a real-world application of the area of a region bounded by a curve. The index uses basic concepts from data analysis and integral calculus to arrive at a measure for the relative degree of inequity of income distribution in a society. The Gini Index also can be applied to measuring the inequity of the distribution of other resources as well.

Animations, Visualizations, and Simulations

Dynamic visuals and animations can make math come alive for your students and help them to see powerful connections. Abstract concepts suddenly become clearer. This session will highlight my favorite and most effective classroom animations, visuals, and statistical simulation activities from algebra, geometry, trigonometry, calculus, probability, and statistics. Ready to use demos using the TI-84, GeoGebra, and Wolfram demonstrations will be shared, and resources will be provided.

Thursday June 26, 2014 10:30am - 11:15am

Grainger Hall

Grainger Hall

Using Mapping Diagrams to Understand Linear Functions
Mapping diagrams provide a very illuminating tool to visualize functions that complement the more commonly used graph. I will present an introduction to mapping diagrams and their use for understanding linear functions including linear function composition and inverses for understanding solving equations with mapping diagrams and connections with other elementary functions. Worksheets and interactive on-line apps (using GeoGebra) will be provided.

**Leaders** *MF*
## Martin Flashman

Professor of Mathematics, Humboldt State University

Martin ("Flash") holds a BA, MA, and PhD in Math from Brandeis. He has taught calculus and preparation for calculus for more than 40 years-Bard College (6 yrs)-Humboldt State Univ(33 yrs). He has given presentations around the US and recently a webinar for AMATYC on mapping diagrams... Read More →

Thursday June 26, 2014 10:30am - 11:15am

Academy Building, Mayer Auditorium

Academy Building, Mayer Auditorium

What's an English Teacher Doing in a Math Classroom

**Leaders**
## Ray Williams

This session provides a concrete example of how both English and mathematics can achieve quality learning using and integrated approach in the analysis of what initially appears to be an “English Only” resource.

Ray has been a teacher of mathematics and science for the past 40 years and is currently the Head of Mathematics at St Mark's Anglican Community School in Perth, Western Australia. St Mark's mathematics classrooms all have TI-Nspire Navigator Wireless Networks and wireless data projection... Read More →

The North Carolina School of Science and Mathematics, Durham, NC

Instructor of Mathematics, NCSSM

Working Mathematically
Wesley College Mathematics Department wants students to experience mathematics as an engaging, personally relevant, problem-solving activity. We want to support students to work like a 'mathematician'. Lower School 'Problems of the Week' and complex Upper School Investigations from our Specialist stream will be discussed. All resources will available for attendees at the conclusion of the conference.

**Leaders** *SP*
## Simon Purdue

Mathematics Teacher, Wesley College

Education; trying new strategies, utilizing technology, making learning fun!

Thursday June 26, 2014 11:30am - 12:15pm

Grainger Hall

Grainger Hall

Constructing Parallelograms and Circles on the IPad with TINspire to Discover Properties
A quick overview of how to construct parallelograms and circles to allow students to discover their properties and theorems. This method means students can play around with the objects to "see" what happens to the angles, lengths or slopes, when changes occur to shapes.

Vectors and Regression
Most of us know that the regression line minimizes the sum of squared residuals, but most of us don’t know how our calculators actually produce a slope and intercept for a regression line. This session will provide an answer to the question “How did my calculator do that?” It turns out that our calculators and other software use vectors to compute regression equations. We will look at the vector basis of regression; a certain level of comfort with vectors will be assumed.

Thursday June 26, 2014 1:45pm - 2:30pm

Grainger Hall

Grainger Hall

Animations, Visualizations, and Simulations
Dynamic visuals and animations can make math come alive for your students and help them to see powerful connections. Abstract concepts suddenly become clearer. This session will highlight my favorite and most effective classroom animations, visuals, and statistical simulation activities from algebra, geometry, trigonometry, calculus, probability, and statistics. Ready to use demos using the TI-84, GeoGebra, and Wolfram demonstrations will be shared, and resources will be provided.

Viete's formula and infinite operations
The early history of the Calculus is littered with interesting use of infinite expansions of various types. One of the lesser known is Viete's infinite product expansion for pi. Another is the Wallis product expansion for pi/2. We will show both and derive through some interesting trigonometric expansions. Connections with the gamma function will also be highlighted.

**Leaders**
## Jeff Ibbotson

Mathematics, Phillips Exeter Academy

Jeff has been teaching mathematics at private schools since 1995. Prior to that, he taught at a local four-year college. His fields of expertise involve functional analysis, geometry and logic. He has been working on a history of mathematics text for high school use for several years... Read More →

Thursday June 26, 2014 2:45pm - 3:30pm

Grainger Hall

Grainger Hall

An introduction to WeBWorK

**Leaders**
## Mike May

Webwork is an open source automated homework system for mathematics used at over 700 colleges and Universities. It uses algorithmically generated questions with automatic grading. The problem bank has more than 20,000 questions. The CWIC session will walk through the student and teacher experience and provide references if you wish to use the system at home.

Saint Louis University, St. Louis, MO

I use a variety of technology in teaching.Recently I have been using GeoGebra for demonstration, SAGE for number theory, Excel and Wolfram Alpha for Business Calculus, and WeBWorK for automated homework. I am also a Jesuit priest

Thursday June 26, 2014 3:45pm - 4:30pm

PSC Rm 127

PSC Rm 127

Explain Everything

A quick introduction to Explain Everything, a great App to get students to record solutions or explanations of concepts and likewise for teachers.

Thursday June 26, 2014 3:45pm - 4:30pm

Academy Building, Mayer Auditorium

Academy Building, Mayer Auditorium

The Fibonacci Sequence and Systems of Linear Equations

It is important to highlight links and connections between mathematical ideas. In this session, participants will use technology to explore patterns in systems of linear equations involving the Fibonacci sequence.

Thursday June 26, 2014 3:45pm - 4:30pm

Grainger Hall

Grainger Hall

2014 A.P. Calculus Grading

**Leaders**
## Ken Collins

This session will review the grading of 2014 AP Calculus exam and share the rubrics that were used during the grading. It will include suggestions for teachers based on the grading and a discussion period if time permits.

Charlotte Latin School, Charlotte, NC

Ken has a B.S. in physics and M.S. in math from BPI/NYU and a Ph.D. from Purdue University. He has taught for forty seven years in middle school through graduate school. His focus is on effective use of technology in teaching and learning mathematics. He teaches calculus, precalculus... Read More →

Thursday June 26, 2014 4:45pm - 5:30pm

Grainger Hall

Grainger Hall

A very nice hyperbola problem.
This session will take a close look at a very nice application that introduces the two focal point locus definition of the hyperbola. After analyzing the problem algebraically, we will look at two different approaches for sketching hyperbolas on Sketchpad or Geogebra, with a bonus feature at the end.

FluidMath on the iPad

**Leaders**
## Nils Ahbel

FluidMath is an iPad app that recognizes mathematics you write with your finger or stylus. Write an equation like y-3=2(x+1) and with a flick of the wrist you have a graph and table. FluidMath recognizes and graphs inequalities, systems of equations, implicitly defined functions, relations (like conic sections), polar functions, and discrete functions (like the Fibonacci Sequence). Dozens of FluidMath applets will be shared that are aligned with the Common Core State Standards.

Deefield Academy

Nils studied Mechanical Engineering and then earned his MBA from the University of Chicago in 1984, with a concentration in Microeconomics. Following graduate school he worked in Germany as a project engineer for five years and then, searching for his passion he returned to the US... Read More →

Thursday June 26, 2014 4:45pm - 5:30pm

Academy Building, Mayer Auditorium

Academy Building, Mayer Auditorium