This is an example of color coding (highlighting) to help make a calculus problem accessible. You don’t have to know calculus to see that the yellow sections (left and right of the 0) are going up while the green section is going down. Color coding breaks a whole into parts that are easier to see and understand – works in preschool all through calculus!
The graph shown involves derivatives – a calculus level topic. Before getting into this heavier mathy stuff, consider the title of this post and the other content presented on this blog. Making math accessible to all students is not a special ed or a low level math thing. It is a learning thing. This artifact is what I drew to explain the math concept to a student in calculus to help her grasp the concept as well as the steps. The following are strategies used.
- color coding – each of the 4 sections written in different color
- connecting to prior knowledge – the concept of velocity was presented in terms of a car’s speed and direction (forward or backing up)
- chunking – the problem was broken into parts and presented as parts before exploring the whole
- multiple representations – the function was represented with a graph, data (1, 2, 3, 4, 5) and a picture (at the bottom)
As for the mathy stuff, the concept of velocity was address by its two parts: speed (increasing or decreasing) and direction (positive or negative). The graph was broken into the following parts: decreasing positive, decreasing negative, increasing negative and increasing positive. Each part was presented with possible y-values (data) and the sign. The most intuitive part is increasing positive which is a car going forward and speeding up.
I find that when I provide intervention, this approach especially by addressing conceptual understanding is effective as the students respond well.