Using The Maple Technology to Connect Mathematics and Art Dr. Lina Wu lwu@bmcc.cuny.edu Department of Mathematics Borough of Manhattan Community College -The City University of New York @2017 MAA MathFest Themed Contributed Paper Session on Encouraging Effective Teaching Innovation July 26-29, 2017 Chicago, IL

Area of a Triangle

Sequence and series

Pedagogy of Project-Based Learning Design of Maple Projects with Calculus Graphs of Equations The presenter is interested in sharing her research experience on how to use an educational technology of Maple Software as a bridge to connect mathematics and art in her Project-Based Learning (PBL) pedagogy. Visualizing beauty of math-related artwork created by computer-generated diagrams of using Maple Software has ignited students’ passion to learn. Demonstrating animated graphic images with simplified symbolic calculation in the use of Maple Software has enhanced students’ conceptual understanding ability. Practicing on Maple projects in Math Labs has increased students’ problem-solving skill, communication skill, teamwork, creative thinking and other multiple skills.

Advantages of PBL Method Characteristics of Successful Calculus -Notices of The AMS (Vol. 62 # 2) by David Bressoud and Chris Rasmussen Construction of challenging and engaging courses “Challenging intellectual and creative work is central to student learning and collegiate quality.” Use of student-centered pedagogies and active- learning strategies “Students learn more when they are intensively involved in their education and have opportunities to think about and apply what they are learning.” Passive Learning Role to Active Learning Role

Summary of Calculus Art-Related Maple Projects Mathematical subjects taught in art-related context can be meaningful and memorable to facilitate students' learning. During a sequence of pilot summer Calculus courses from 2013 to 2017 at BMCC, the presenter has designed a sequence of art-related maple projects in Calculus. Projects of "Polar Art“(2013), “Cartoon Art-Funny Face"(2014), "Geometric Abstract Art"(2015), “Culture Art”(2016), and “Sport Art-Olympian Figures”(2017) attached with students' artwork will be presented. The sequence of pilot courses were supported by NSF Grant from Minority Science Engineering Improvement Program through US Department of Education and also supported from Enhanced Classroom Teaching Funds at Borough of Manhattan Community College.

Teaching Experience & Students’ Feedback In this talk, I will illustrate how to design group projects based on Maple Software to enhance student’s learning for the Calculus fundamental concepts. Feedback from students’ success and frustration in the pilot Calculus courses will be analyzed based on students’ laboratory exercises under the lab instructor’s assistance. Students’ successful projects will be presented at the end. As students said, they became artistic in mathematical minds. They considered these experimental projects as a life-time experience. Working on projects brings knowledge, technology, challenges and excitement in their life.

Project Description -Geometric Abstract Art The project of “Geometric Abstract Art” was to teach students how to use Calculus graphic knowledge of surfaces in space to create different 3-dimensional shapes. Students were expected to use various surface equations, revolution or rotation to create irregular or regular shapes with or without symmetry. Textbook Resource: a list of quadric surfaces on Page 815 (Section 14.4) in the textbook of “Calculus “ (alternate 6th edition) by Larson, Hostetler, and Edwards.

Project Description -Polar Art This project of “Polar Art” was to ask students to use Calculus graphing knowledge in Polar coordinates and Polar graph equations to create 2-dimensional flat diagrams. Students were required to combine different polar graph equations to create different geometric patterns, shapes, compositions, colors, and sizes. Textbook Resource: a list of special polar graphs on Page 705 (Section 12.4) in the textbook of “Calculus “ (alternate 6th edition) by Larson, Hostetler, and Edwards. Website: http://www.maplesoft.com/applications/view.aspx?SID= 4087&view=html

Project Description Cartoon Art-Funny Face The project of “Funny Face-Transformation and Distortion of Images" was to teach students to apply their knowledge in Calculus, Algebra and Trigonometry by transforming or distorting images. Students were expected to use the basic types including transformations of graphs, combinations of graphs, and composition of graphs for piece-wise functions to create or distort images. Textbook Resource: a list of basic types of transformations of graphs and composition of functions on Page 41-44 (Section 1.5) in the textbook of “Calculus “ (alternate 6th edition) by Larson, Hostetler, and Edwards.

Project Description -Culture Art Students will be expected to apply their Calculus graphic knowledge to create their geometric designs that depict the national symbols of their favorite countries. For example, if a student selects United States, he/she may want to create a geometric design of the Statue of Liberty. If Canada is selected, he/she may want to create a geometric design of a maple leave. If China is selected, he/she may want to create a geometric design of a panda bear. This calculus project will show how diverse the student body is at BMCC. Textbook Resource: exponential and logarithmic functions (Chapter 7), trigonometric functions (Chapter 8), polar graphic equations (chapter 12), quadric surfaces (Chapter 14) in the textbook of “Calculus “ (alternate 6th edition) by Larson, Hostetler, and Edwards.

Project Description Sport Art-Olympian Figures The project "Olympian Figures Poster Created with Calculus Graphs of Equations” requires students to use Calculus graphs of equations and Maple Software to create different sports figures. The class was divided into small groups to work on this project. Students combined all the sports figures together to create a poster design. At the end of this course study, students were required to submit a written report to explain what Calculus graphic knowledge they have used to create the sports figures. Furthermore, students were required to make a PowerPoint presentation to demonstrate the various Maple Software commands to create their computer- generated sports images. Textbook Resource: Algebra & Trigonometry &Calculus exponential and logarithmic functions (Chapter 7), trigonometric functions (Chapter 8), polar graphic equations (chapter 12), quadric surfaces (Chapter 14) in the textbook of “Calculus “ (alternate 6th edition) by Larson, Hostetler, and Edwards.

Example of Christmas Flower Diagram in Maple