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!
Students often struggle with the jump from 1 variable situations to 2 variable situations, i.e. functions. Visuals are an effective way to present concepts which may be abstract, e.g. functions. Graphs and visuals in general are designed to allow a big picture view of a concept. The photo above shows mileage and price for Honda Odyssess vans collected in January 2012. The work is from a student who has a non-verbal learning disablity (basically a mild version of asperger’s). Students are first asked to identify the van with 66,000 miles and that costs $21,000. This ensures they understand what is presented. Then they are asked a leading question about mileage and price (#3). Finally, in question 4 they are asked to use the graph to draw a conclusion – choose the best van (based on mileage and price). This leads into a discussion about the relationship between mileage and price (you can see notes I wrote on the graph to facilitate this).
The photo below shows four scenarios and one of four graphs students are to use for matching. For the first graph students were to determine that the graph best models the US economy (problem given in 2013). Over the past few years the economy dropped rapidly but has been improving since. This student (same as the one identified above) identified one aspect of the graph – the recent rise. Breaking a graph down into parts and comparing the parts is an example of Bloom’s analyze level. By justifying his choice of C this student was evaluating.