Description: Although using dynamic mathematical software programs, such as GeoGebra or Fathom, can be very effective as a teaching tool, it often difficult to find the time to develop the files needed for a classroom experience. The purpose of this session is to provide a jump start to using software in the classroom. We are looking for talks that present one specific mathematics lesson using some dynamic software. The presentation will describe how the software was used in the classroom, and the files used in the lesson will be made available on-line. As a result, the audience will have a ready-made lesson to use. The lesson could be for any mathematical course and use any third-party software including GeoGebra, Fathom, Geometer's Sketchpad, calculator simulators, spreadsheets or a computer algebra system. It is preferred that the lesson include hands-on use of the software by students and not simply a classroom demonstration. Preference will be given to uses of widely used software such as those listed above or freeware.

Abstract #	Title	Presenters	Abstract	Links or Materials
1077-D5-1201	Exploring regressions through Geometer's Sketchpad and Microsoft Excel.	Brandon Milonovich bamilono@syr.edu	The rigorous definition of a limit is often neglected or even omitted in a Calculus class due to the difficulty students have in grasping the concept. I will present an interactive GeoGebra demo designed to illustrate geometrically existence and nonexistence of limits of some chosen functions. The activities are suitable for classroom demonstration or individual student use.
1077-D5-2828	From Dilation to Similarity - an Exploration Using Geometer's Sketchpad.	Margaret L. Morrow morrowml@plattsburgh.edu	Similar figures can be defined in terms of the transformation dilation. We will share a sketchpad worksheet that guides students through an exploration of some interesting properties of dilation. En route students are introduced to similarity of geometric figures, and develop some strong intuitions about similar figures. We use this worksheet in an introductory level College Geometry class.
1077-D5-1499	Epsilons and Deltas with GeoGebra.	Jason McCullough jmccullo@math.ucr.edu	The rigorous denition of a limit is often neglected or even omitted in a Calculus class due to the diculty students have in grasping the concept. I will present an interactive GeoGebra demo designed to illustrate geometrically existence and nonexistence of limits of some chosen functions. The activities are suitable for classroom demonstration or individual student use.
1077-D5-1769	The Euler Line in GeoGebra.	Philip P. Mummert phmummert@taylor.edu	In Euclidean geometry the centroid, circumcenter, and orthocenter of a triangle are collinear (forming the “Euler line”). GeoGebra is a fantastic tool for illustrating t he definition of each of these triangle centers (including the poor, forgotten incenter) and demonstrating their collinearity. Use of the dilation tool makes the proof of this remarkable fact even easier to follow.
1077-D5-700	An iPad-based activity for learning to sketch the graph of the derivative of a given graph.	Hillary Einziger einziger@math.psu.edu	This lesson plan uses graphs created in GeoGebra as the basis for an activity in which students use an iPad and stylus to practice sketching derivative graphs. Students are presented with the graph of a function, shown on a screen through a projector, and then one student at a time volunteers to try to sketch the derivative graph. Other students can offer suggestions and comments, and then they compare the sketch with the actual graph of the derivative. This lesson provides students with instant feedback as to whether they understand the concepts, it encourages students to discuss and experiment with their ideas, and it allows all the students in the class to see several different perspectives on how to solve similar problems. The lesson as planned requires only one iPad and a projector, as well as the presentation app Explain Everything. In a classroom equipped with multiple iPads or other tablets, this could easily be modified into a small group activity, where each group would consider the graphs and discuss how to draw the derivatives. Creating the graphs in GeoGebra and then saving them as PDF files allows the use of the iPads, so that students can draw directly on the given graphs.
1077-D5-468	Rolling Wheels: Explore Curve Sketching via GeoGebra and Mathematica.	David A. Brown dabrown@ithaca.edu	Cycloids, hypocycloids, epitrochoids, and more generally, curve sketching via truncated Fourier series, provide students the opportunity to explore the interplay among geometry, functions, and number theory. This lesson (used in multivariable calculus and a course in mathematical experimentation) asks the students to investigate these topics by first considering rolling wheels and how points on the wheels can trace curves. GeoGebra and Mathematica are used to simulate these evolving curves and we provide lessons using both software packages. As students move on to explore a wheel rolling on a wheel rolling on yet another wheel, they develop functions which are truncated Fourier series. The lesson asks students to explore (via GeoGebra and/or Mathematica) the parameters involved in these functions, leading them to realize that number theory is playing a role in the structure of the resulting curves. The lesson also allows students to experience their artistic side as they manipulate parameters. We even make a connection with automotive engineering.
1077-D5-2854	Motions and Rates: Using GeoGebra to Analyze Video Recordings.	Tibor Marcinek marci1t@cmich.edu	Moving objects are often used to illustrate applications of mathematics and derive important mathematical models. However, students' first-hand experience with these phenomena is problematic and textbooks heavily rely on rather abstract descriptions. Although stroboscopic images and their analysis may provide some experience, video recordings offer greater flexibility and potential to bring hands-on explorations of real motions into the classroom. In the presentation, we will briefly explain how GeoGebra can be turned into a simple video player with play & pause button and a seek bar, and how its mathematical tools can be utilized to analyze recorded motions. We will share ready- to-use applets and ggb files with videos that represent typical mathematical models (free fall, projectile motion) as well as some phenomena recorded using special techniques (candle burning rate recorded in a time-lapse mode).
1077-D5-2542	WeBWorK labs? A case study in differential equations.	Dan Gries, Barbara Margolius, Felipe Martins* luizfelipe.martins@gmail.com	WeBWorK is an online homework system, initially developed at the University of Rochester and currently supported by the MAA and NSF. WeBWorK is traditionally used as a practice and assessment tool. Under our NSF-CCLI grant, DUE-0941388 we have developed a library of Flash applets embedded in WeBWorK homework assignments for entry level university mathematics courses including calculus, pre-calculus and differential equations. This opens the possibility of creating dynamic WeBWorK pages that can be used for instruction, instead of just assessment. In this talk, we will present a case study, where we create a WeBWorK ”lab” for exploring parameter dependency in Ordinary Differential Equations.
1077-D5-787	Becoming One with Bifurcations in 3D!	Itai Seggev Wolfram	In this talk we will argue that bifurcations in ordinary differential equations are best understood by means of ”3D bifurcation diagrams”. By plotting the rate function-as a function of both the dependent variable and the bifurcation parameter-and slicing it with appropriate planes, the stability and nature of a bifurcation can be determined. A Mathematica package for automatically creating these diagrams from a rate function will be presented.
1077-D5-778	Taylor Polynomials in R.	Andrew J Rich* arich@macalester.edu Daniel T Kaplan, kaplan@macalester.edu , Randall J Pruim, rpruim@calvin.edu , Nicholas J Horton, nhorton@smith.edu JJ Allaire, jj.allaire@gmail.com	In keeping with the format of the session, we will present a lesson on Taylor Polynomials that makes use of interactive graphical software in R. Although R is best known for its important uses in statistics and is a professional-level technical computing environment, it is quite suitable for teaching introductory university-level courses such as calculus. It's also free, and can be run using a browser-based interface (RStudio), which makes it easy to deploy to students in the classroom. The Taylor Polynomial lesson will make use of the symbolic differentiation capabilities built in to R. It illustrates how the quality of the approximation varies with the order and highlights the difference between Taylor polynomials and least-squares polynomials.
1077-D5-2604	Student Voice Waves: Investigations using Calculus and Freeware.	Phil Gustafson Colorado Mesa pgustafs@coloradomesa.edu	Modeling and analyzing student generated sound waves is a great way for students to gain a better appreciation for applications of integration and series expansions. In this presentation we share a classroom activity that makes use of the freeware Audacity and FreeMat to capture and display student voice waves as well as to analyze their frequency content.
1077-D5-2616	Communicating calculus concepts using graphically presented functions in Adobe Flash applets embedded in WeBWorK.	Daniel J Gries	We will present a collection of applets created in Adobe Flash, and embedded into WeBWorK problems, which allow for the exploration of calculus concepts using functions which are defined only in terms of graphs. The applets allow for graphical communication of functions in both directions: students see functions only as graphs, while also being asked to draw functions by hand which satisfy certain criteria. This approach allows for a greater conceptual focus by removing algebraic tasks from the assessment of student understanding, while also getting away from the notion that all functions need to be defined by algebraic formulas. We will talk about some of the different techniques for randomly generating a sufficiently rich collection of well-behaved functions, along with some of the computational care required in finding features such as extrema and inflection points. This work has been supported by the NSF-CCLI grant DUE-0941388.
1077-D5-2453	Team Activities for the First Day of Class Using a Computer Algebra System.	J Alfredo Jimenez jaj4@psu.edu	I would like to present an activity that I use the first day of class to create an environment where students work collaboratively in teams, review some basic mathematical concepts, and use the computer algebra system Mathematica to produce some images, at the same time that they learn some basic commands. I have used this activity in calculus or linear algebra classes (first or second year level). The problems that I pose are simple: Draw the Mitsubishi logo, the Texaco logo, and a tetrahedron. These problems are easy to state, very visual, and yet, very challenging for students at this level. The activity is well received by the students, who normally are fully engaged in solving the problems, brainstorming, and sharing their thoughts.
1077-D5-1554	Taking Instruction with Numerical Computations to the Next Octave.	Talitha M Washington talitha.washington@howard.edu	Often times in a typical numerical analysis course, a computer program is used to implement the numerical schemes. GNU Octave is a freely redistributable software that provides a way to numerically solve problems through command-oriented programming, quite similar to Matlab. This talk will present ways to implement programming with GNU Octave for a typical numerical analysis course, discuss its similarities and differences to Matlab, analyze challenges that students may encounter, and offer ways it may be used in other courses such as calculus and linear algebra.
1077-D5-2556	Teaching Transformations of Function.	Susan L Schmoyer sschmoyer@worcester.edu	Graphing functions using transformations (like vertical and horizontal shifts) is a skill usually introduced in college algebra and used in precalculus, calculus, and mathematical modelling. In this talk I will demonstrate a Sage worksheet that helps students to make the connection between an algebraic transformation of a function and its respective graph. Sage is a free, open source alternative to Maple, Matlab, and Mathematica. Part of the Sage worksheet is a “Transformations Guessing Game” that creates a random graph of a function and asks the student to find the formula of the function. This knowledge of transformations is then applied to create some basic mathematical models.
1077-D5-1357	Mystery Plots: Motivating Algebraic Function Models using Dynamic Mathematics Software.	Michael Todd Edwards* edwardm2@muohio.edu, Robert M Klein, Steve Phelps	Functions are central to the study of mathematics. As Froelich, Bartkovich, and Foerster (1993) note, “the concept of function is probably the most important idea in mathematics” (p. 1). Although students in introductory courses spend significant time working with functions, much of this time is spent transforming familiar functions - for instance, stretching, reflecting, and translating exponential, quadratic, square root, and sinusoidal functions - rather than creating original functions. The tendency to modify and “borrow” rather than create impacts students' attitudes regarding mathematics. Functions become “gifts” from teachers rather than objects of discovery in their own right. Mathematics is not construed as a creative area of study. In this talk, we explore the use of dynamic mathematics software (DMS) as a medium for constructing algebraic function models that extend student knowledge of function. We share a strategy for developing original function sketches, the three-step MTA process (Measure - Trace - Algebratize). The MTA approach provides students with opportunities to explore and construct remarkably non-standard functions - often beautiful, unexpected, and thoroughly original. We share several examples of such functions in our talk.
1077-D5-2589	The Power of Symbolic Spreadsheets.	Rejoice Mudzimiri mudzimir@math.montana.edu	Researchers have suggested that spreadsheets in general can support students in developing an understanding of variables. The availability of symbolic spreadsheets (spreadsheet that allow for the manipulation of variables) has the capacity to enhance explorations, visualization, pattern recognition and ultimately conceptual understanding. In this presentation I will use the TI-Nspire symbolic spreadsheet to demonstrate three pedagogical principles: 'wastefulness', variation or parameterization, and generalization using a 'simple' word problem. The activity is adapted from a senior capstone course for high school mathematics teachers.
1077-D5-1952	Visualizing Lagrange Multiplier Optimization using CalcPlot3D.	Paul E Seeburger pseeburger@monroecc.edu	In multivariable calculus, we teach our students the method of Lagrange multipliers to solve constrained optimization problems. As we introduce this topic, many of us use some form of visual presentation to help students understand how we develop the Lagrange multiplier equation, i.e., ∇ f (x, y) = ∇ g(x, y). Using a freely available online multivariable calculus applet named CalcPlot3D, instructors can give a dynamic demonstration of the visual nature of Lagrange multiplier optimization during class. After class, students can complete a guided exploration of this topic using the same applet. As part of this activity, students complete a pre-test, answer exploration questions, and then complete a post-test. The pre- and post-tests measure what improvement occurs in their conceptual understanding of the geometric nature of Lagrange multiplier optimization by completing the visual exploration. Student responses to this online activity can be sent to instructors for grading. CalcPlot3D is part of an NSF-funded grant project titled Dynamic Visualization Tools for Multivariable Calculus (DUE- CCLI #0736968). See http://web.monroecc.edu/calcNSF/.
1077-D5-1700	Using Geometer's Sketch Pad to examine whether the SSA condition in Euclidean geometry is always ambiguous.	Jennifer Bergner jabergner@salisbury.edu	In this presentation I will share a Geometer's Sketch Pad activity that uses the dynamic capabilities of the software to explore the situation in which two triangles have two sides of one congruent to two sides of the other, and a non-included angle of one congruent to a corresponding angle of the other (the ”ambiguous” SSA condition). The students use GSP to examine and conjecture when this is not an ambiguous condition and why. This activity uses several nice features of GSP such as tables, sliders, and the calculator and can also be extended to explore some of the other standard congruence theorems from Euclidean geometry