**Subject Area:** Math

**Course**: Calculus & Vectors (12)

**Topic:** Calculus (Derivatives)

**Task:** Reviewing, learning how to graph, checking work.

**Technology Tool:** Desmos Graphing Calculator

**Description**

Graphing functions and seeing graph behaviors in specific intervals are extremely important in Calculus. Graphing can be used in questions that simply ask for a sketch of a graph or in problems which require students to find intercepts or asymptotes, and etc. However, learning to graph is typically more challenging than performing algebra because of the many steps students must take before they can actually draw a graph.

**Suggested Use of Technology Tool**

Desmos can be used to check over work and ensure that students understand the origin of particular graph characteristics. Desmos also has features that allow students to enter multiple functions and toggle on and off of them to compare characteristics or find intercepts. Furthermore, the user can find the tangent to a curve, which allows them to visualize derivatives. After a while, derivatives become abstract concepts to math students if they do not make the effort to understand its applications. With Desmos, derivatives can represent a more tangible version of a math problem.

**Why and how would the technology tool improve student learning?**

Many students often have a hard time understanding complex mathematical theories, because they do not know what certain solutions to math questions mean. Although they may be able to perfectly solve an equation, they are not able to explain the significance of the values they found. Desmos helps students employ the learning strategy of elaboration, since it causes them to ask *why* their answers are correct or incorrect. Additionally, students must use previous knowledge of more basic math ideas in order to interpret graphs, which helps reinforce previous lessons they have learned as well.