Teaching Hour

Teaching Hour Presentations

Saturday 1:00 - 3:00 PM

Moderator: Heiko Todt

1:00-1:20 Modeling Geometric Problems with GeoGebra

Jose Contreras, Ball State University

In this presentation I will illustrate how learners can use GeoGebra as a tool to facilitate solving geometric problems. In particular, I will explore the picnic problem (a version of Viviani's problem): Three towns are the vertices of an equilateral triangle. The sides of the triangle are the roads that connect the towns. A picnic area will be constructed such that the sum of its distances to the roads is as small as possible.

1. What are all the possible locations for the picnic area?

2. For practical reasons, what is the best location for the picnic area? Justify your response.

1:20-1:40 How I Learned to Stop Worrying and Love Online Exams

Jeff Suzuki, Brooklyn College

The shift to distance learning formats caused an existential crisis among mathematicians: How can we give valid online examinations? Online proctoring software and webcam monitoring are the usual answer, but they are too easily circumvented by motivated students. Instead, we relied on a combination of innovative questions and fingerprinted exams. We present an overview of our strategies and their implications beyond the return to campus.

1:40-2:00 Innovative Assessment Methods in Advanced Undergraduate Mathematics

Andrew B. Perry, Springfield College

In this brief presentation I will discuss grading strategies designed to accomplish pedagogical goals in my classes using incentives that behavioral economics suggests are necessary to change student behavior. I've employed grading strategies in recent years that border on the unconventional, including high weighting of class participation. This semester I'm dividing my advanced math classes into five modules and students will receive a letter grade in each, with their final grade being the average of their highest four module grades.

2:00-2:20 Using GeoGebra to gain insight to solve converse geometric problems

Jose Contreras, Ball State University

In this presentation, I illustrate how my students and I use GeoGebra to explore geometric converse problems. In particular, we use GeoGebra to gain insight into the solution to the following three problems:

1) Let ABCD be a quadrilateral with medial quadrilateral EFGH. If EFGH is a rectangle, what type of quadrilateral is ABCD?

2) Let E, F, G, and H be the midpoints of the consecutive sides of a quadrilateral ABCD. If EFGH is a rhombus, characterize quadrilateral ABCD.

3) E, F, G, and H are the midpoints of the consecutive sides of a quadrilateral ABCD. Name quadrilateral ABCD when EFGH is a square.

2:20-2:40 Developing First-Year College Students' Problem Solving Abilities through Game-Based Learning

Adam Case, Drake University

In this talk, I present an overview of a first-year seminar aimed at developing the creative problem solving abilities of first-year college students. To accomplish this, the seminar makes use of digital game-based learning by having students solve puzzles from the computer game called The Witness (Thekla, Inc. 2016). This game challenges the player/student to explore an island filled with "line puzzles," which must be solved in order to make progress. An interesting aspect of these puzzles is that their rules are never explicitly stated. Instead, students must first discover these rules through experimentation and then master them. The game provides an engaging environment for non-mathematics majors to get a taste for what it is like to develop their own techniques for solving complex problems. Various teaching strategies used for fostering students' problem solving abilities will also be discussed.

2:40-3:00 Designing Calculus Tasks to Foster Creative Mathematical Thinking

Houssein El Turkey, University of New Haven

Fostering students' mathematical creativity necessitates certain instructional actions such as designing and implementing tasks that foster creativity. Literature indicates that most Calculus textbook exercises only require imitative or algorithmic reasoning, thus there is a need for tasks that have the potential of fostering mathematical creativity, particularly in Calculus 1 courses. I will share our task design framework incorporating research-based task features and aligning them with the Creativity in Progress Reflection (CPR) formative assessment instrument. I will also provide some examples of utilization of this framework through instructor-designed tasks and transformation of routine exercises.