Focus: Mathematics

Upon entering a room of 18 high school students with heads buried in Tablet PCs, completely engaged and engrossed, one might assume that they are watching the latest YouTube sensation or checking out the latest Facebook update. 

Not so at Mount Notre Dame. 

These students are actually manipulating a free-moving point on the graph of a polynomial - this is the scene during Ms. Paula Schute’s pre-calculus class.  Ms. Schute leads as the students follow, noting on their tablets how the zeros, extrema and intercepts are affected as well as how the equations of the function changed.  Questions and answers fly about the room, the students responding to Ms. Schute with an enthusiasm that shouts of complete understanding.   

Ms. Schute utilizes an innovative software program called Geometer’s Sketchpad, which allows students to interact with visual representations such as graphs and geometric figures. By dragging points on the mathematical image and objects on-screen in Sketchpad, students overcome the limitations of static textbook images and the misconceptions they can develop from seeing only a few generic samples. Dragging and shifting the geometric points immediately shows what works and what doesn’t, a feedback process that encourages imagination and error correction.

Senior Jackie Kremer loves that the class is so interactive.  “Ms. Schute does so much to help us understand.  The programs we use on the tablets give us a visual of what is happening with the graphs.  If you are ever confused about something, you have the ability to enter a formula into Sketchpad and actually see how the numbers change the graph.”

This kind of digital access has changed the way MND students learn.  Ms. Schute uses the program to interact with her students in an unprecedented manner that wouldn’t be possible without this technology.  “Implementing this program gives students the ability to interact with the visual representations of mathematics.  They can manipulate different properties of one representation and see how the properties in the other representation are affected.  I think it’s important for my students to be able to experience the mathematics on their own,” Ms. Schute observes.

Through Sketchpad activities, the processes and questions of arithmetic and algebra themselves become structural objects.  This process is vital for visual learners, but it also provides other cues that students need to experience if they are to expand their mathematical and problem-solving ability.  Using this type of technology also encourages and requires communication, reasoning and proof of concept and answer by consensus. Answers can be derived by both solo work and group discussion, theoretical processes that can be constructed visually instead of simply disproportional sketching on college-ruled homework sheets.

“The true beauty of mathematics is in the patterns and connections between the numeric, geometric, graphical and algebraic representations of relationships.  Geometer’s Sketchpad has allowed my students to observe and discover some of these connections and patterns,” shares Ms. Schute.