# The Complexities of Graphing

I spend a lot of time thinking (and writing) about incorporating inquiry into my math classes. I often classify inquiry in math class into two different categories: math by inquiry and math for inquiry.

Graphing is a great way for students to use their math skills for inquiry. From Kindergarten students using pictographs to visualize trends in the weather to humanities students analyzing government spending, graphing allows students to visualize relationships, make comparisons and formulate hypothesis in a wide range of fields.

Graphing is also a great way for students to strengthen their math skills. Creating an accurate graph is a very complex task…

• It requires critical thinking. In order to select an appropriate type of graph, students need to know what question they are trying to answer, or what message they are trying to convey.
• It requires estimation and rounding.  In order to draw axes, students need to match the range of their data set with the space available for their graph and select an appropriate scale. To do this, students have to estimate the factor the relates the size of the graph and the range of the data. This can’t be done through division alone – students will probably have to round the range in order to reach a more reasonable scale. For example, if trying to fit a range of 78.3 degrees on a 20 cm axis, it would make sense to extend the axis to 80 degrees, so that each centimeter represents 4 degrees.
• It requires number sense. Students need to be able to place their data points on a number line. This becomes even more complex when data points belong between numbers labelled on the axes.

Creating a persuasive graph is another very complex task, but that’s a post for another time…