My doctoral research focused on effective strategies for helping students learn calculus. My dissertation was entitled An Investigation of Calculus Students Working Collaboratively in an Interactive Software Environment (advisors Dr. Dan Kalman and Dr. Lyn Stallings, American University), and in this work I designed and programmed interactive computer screens (software Mathwright) that pairs of students used to solve problems involving the relationship between the graph of a function and the graph of its derivative. I investigated two research questions: "How does working collaboratively help or hinder students' understanding of the concept?" and "In what way does an interactive software tool help/hinder student learning?" To answer these questions, I videotaped pairs of students as they worked and analyzed their conversation and their written work. My most surprising and significant conclusion was that talking with a partner seems to be very helpful in resolving misconceptions and moving toward a right answer, but not because the partner necessarily provides correct or useful information. Communication seems to be promote effective learning primarily because it forces a student to organize her own thoughts and not because the partners learn from each other. I also found that the students used the interactive software to confirm their ideas, and the presence of the software often prevented a student from adopting an incorrect idea or faulty method from their partner.
At Messiah College, I continue to work on developing materials that help students learn calculus effectively, with the goal of emphasizing connections among mathematical topics in calculus, algebra, trigonometry, and geometry, so that students who complete Calculus I, II, and III at Messiah College are well-prepared for subsequent courses in math and science.
I am also interested in helping mathematics majors think about how their growing mathematical maturity during the college years informs and strengthens their Christian faith and understanding of Scripture. In 2006, colleague Dr. Doug Phillippy and I coauthored a draft of a text, "The Study of Mathematics: Developing a mature understanding of mathematical thought, with consideration of Christian faith and vocation." This is the primary text for MAT 194: First Year Mathematics Seminar.
In January 2006, I traveled with a Dokimoi Ergatai team to the country of Burkina Faso in West Africa, where I observed math classes at the 'Handicapes En Avant’ Center operated by SIM Missions in the village of Mahadaga. In this remote village, children with multiple handicaps struggle to learn mathematics and to think abstractly in a highly illiterate country. I am working now with Messiah College students in mathematics, education, and engineering to investigate how issues of language and culture are connected to education, and how we might develop materials that help these children learn mathematical literacy.
August 2004: " Building Mathematical Maturity in the Calculus: Teaching Implicit Differentiation through a Review of Functions”, with Doug Phillippy, published in Mathematics Teacher, p. 6.
December 1999: "Climbing Around on the Branches of Mathematics", The Bridge, Messiah College
March 1997: "Software Review: Mathwright 2.0"; The College Math Journal, Mathematical Association of America
Spring 1997: "Exam Drafts and Earned Partial Credit: Involving Students in the Exam Process", College Teaching