Visualizing Math

Math is very abstract by nature and requires significant visualization to solidify ideas in student minds. As examples of how I visualize math for my students, I included two diagrams and a Geogebra interactive tool that I designed.

Geogebra is an interactive math tool that allows students to drag elements around the screen and actually interact with the mathematical function or shape on-screen. The software is very flexible, allowing the creator of a widget to add many elements to a single sheet. In this example, I created a widget for parabolas. When students adjust the slider for "a", the parabola gets wider or narrower and flips direction when you go from negative to positive. Students can also drag the vertex to any point on the screen. As they change these values, the table on the left and the many forms of the equation on the right get updated with the correct values. This is very helpful for teaching students how to decide which form of a parabola to use in which situation. Below is a screenshot of the tool in action (click for full size). To play with the full version online, click here.

In this same unit, I wanted students to understand how all of the topics we were learning elegantly connected to each other. To do this, I created the graphic below (click for full size). In my first semester using it, I simply gave the diagram to students. This was effective for only a few students. In the second iteration, I gave students a partially-filled-in graphic and had students fill it in as we went through the unit in short bursts, reinforcing the relationships between the topics as we went. With this approach, more students understood the diagram and referenced it often when doing their homework.

In Statistics, students had trouble remembering when to use different calculator functions when working with normal curves. To help alleviate the confusion, I created the diagram below. First, I asked students to draw their own version so they would understand the components and how they fit together. Later, I gave them a neatly printed version that they could keep and use as a reference sheet. The diagram shifted the focus from computation and memorization to conceptual understanding of area and standardized scores.