Carolyn Balch

# Graphing Data without Using Numbers.

Do your students struggle with graphing?

Here we'll look at a Distance vs. Time graph and we won't use any numbers or rulers or graph paper.

I developed this process with my students while we were in our motion unit. Learning to interpret graphs is a skill no budding scientist should be without, and yet the process can be so painstaking that we often don’t do it enough for the skill to solidify. Figuring out how to make graphs quickly and simply enabled kids to become competent, confident graph-makers.

I’ll refer to one of Galileo's ramp experiments to demonstrate this process, but I think you’ll be able to see how it might work with other experiments and data sets as well. In this experiment, students track a ball as it rolls down a gentle incline and mark its position every half second.

Students use a metronome timer and mark the position of the ball at each tick: 0, 1, 2, 3, etc. They can clearly see that the distance between each mark is getting greater and greater which makes sense since the ball is speeding up or accelerating. Most students can do this fairly easily, but then, when we ask them to turn this data into a graph, things get complicated.

Traditionally we ask them to use a ruler to measure the distances; a step which turns the concrete measure of length into a number, which is abstract. We then ask them to take those numbers and to plot them onto a piece of graph paper, which tends to require a scaling dimension (another level of abstraction). Provided that they follow directions, students will end up with a graphical representation of their data, which for most of them means nothing and makes little sense.

Kind of by accident I came up with a strategy that bypasses the numbers and the graph paper and still allows students to create a graph, a picture of their data, directly from their results.

You’ll need a roll of tape (masking or painters tape works well), a pair of scissors, and a large blank space such as a wall or door. Rather than use a ruler, students cut lengths of tape to match the distances covered by the rolling ball. As kids cut these lengths, they stick them to the wall, and the graph emerges. When they’re done, they can use a sticky note to add labels to the axes.

These graphs can be quite large, up to 8 feet, which is part of their charm. Kids use the wall, the whiteboard, the door, any clear, flat place that’s available. You could also use the floor or ceiling. I like leaving them up so we can refer to them as we continue through the unit. There are only about four important motion graphs they need to learn to interpret, and I like to be able to revisit them again and again.

Once they’ve made a few full-sized graphs, they can scale them down, or use numbers to plot them onto graph paper. Now the transfer from the large full-sized graph to smaller ones in their journals begins to make more sense. Since these graphs are relatively quick and easy, you can make them again and again. I can’t overstate the importance of repetition for being able to internalize an understanding of interpreting graphs.

Graphing is difficult for a lot of students and, I think we do them a disservice when we forget how difficult it is. We take this very concrete exercise that they did, and then we ask them to turn that into a number by measuring and to plot that number on a piece of graph paper and so it's many steps removed from what they did.

My goal is to keep it as closely aligned to what we did as possible—to be able to see the graph emerge from the exercise that we did. Later we can learn that the curve that appears in the distance vs time graph is a parabola. Later we can label axes and add units. But in the beginning, we focus on the shape of the graph and how it connects to the data we collected.

Once students have made their large graphs they can take a picture of them, scale them down, make a sketch of them for their journals.

To see the instructions for the referenced __Galileo’s Ramp Experiment, click here__.

What’s your experience with graphing with your students? Have you tried something like this or something else that helped them grapple with this process? I'd love to hear if you do and I'd also love to hear about any graphing strategies you use with your students. Chime in, don’t be shy.