Thoughts of a traditional math classroom may bring to mind images of students sitting silently at desks while a teacher works through a math problem on the board. There could be more to this scene though. Perhaps one student is using her fingers to keep track of numbers while another quietly taps his pencil along to key points of the equation. These are both small examples of embodied cognition, the idea that features of thought are shaped by aspects of the body other than the brain.

Counting with fingers and tapping along to certain points on a number line can help with basic mathematical concepts, but what happens when it comes to understanding something a bit more complex?

For instance, it can be difficult to help students understand slope. Sybilla Beckmann and Andrew Izsák, both professors of mathematics, describe this particular struggle in their article, “Why is Slope Hard to Teach?”

“Consider the ideas surrounding slope and rate of change, which are well known to be difficult for students… even students who appear to be proficient—because they can calculate a slope and use it to find an equation for a line—may be missing some crucial connections.”

Typical approaches to teach slope involve memorizing the formula and applying it to a static graph. Straight memorization, however, can prevent students from exploring what slope really means and gain a deeper understanding. Today, educators can leverage technology to apply research on embodied cognition and manipulatives in the classroom.

## Experience Slope As Rate Over Time

One example of this is the ST Math game, Graph Path, also known as Tap Tempo.

Graph Path allows students to experience different slopes through physical tapping on the screen, providing an embodied understanding of slope as a literal rate over time.

Tap faster in a vertical direction, and the line becomes steeper.

By having physical control of this mathematical process, students can more easily internalize that slope is about a vertical change over a specific horizontal distance.

Experience the power of learning through embodied cognition in this video demonstration of Graph Path:

Tapping and Graph Path are just one example of how embodied cognition and technology can help students better understand math. When educators leverage the right technology, students can gain access to comprehending complicated mathematical concepts like slope.

## See the Math and Grow

ST Math is a visual instructional program that builds a deep conceptual understanding of math through rigorous learning and creative problem solving to deeply engage, motivate, and challenge Pre-K-8 students toward higher achievement. Digital manipulatives like those found in ST Math allow students to experience mathematical concepts in a tangible way.