Identifying independent and dependent variables only matters when the two variables concerned have a causal relationship — a change in one variable causes the other to change, but not the other way around. For example, more turns of a wind-up band causes a model cart to travel farther. The inverse relationship, the idea that the distance a cart travels determines the number of wind-up turns, makes no sense because the wind-up turns already happened. The relationship is causal. Other relationships aren’t causal at all, for example arm span and height. Neither variable is independent or dependent, but they are correlated.
When do students need to recognize the difference between independent and dependent variables? Why is distinguishing between independent and dependent variables important?
They are the same thing!
Line plots and dot plots show how data values are distributed along a number line:
For some reason, the Common Core Math Standards call them line plots in the standards for grades 2 through 5, and dot plots in grade 6 onward. Don’t confuse line plot with a line graph, which has two numeric values on X and Y axes, with the points connected by lines.
Sometimes we forget that a pencil is technology, an idea easily lost in this age of electronics constantly at our fingertips, and computers in every classroom. But a good pencil or pen, with its tactile connection to our brain, can be a useful tool for learning to informally assemble information from small datasets, picture relationships, and glean ideas without the constraints of pre-programmed graphing applications.
Graphing by hand is a powerful strategy for learning, and for teaching. Students gain several skills when they first learn to draw a graph by hand.
You many be familiar with the Graph Choice Chart, a classroom tool we developed when we realized that many students did not have a logical basis for deciding how to graph data when given a choice. The Graph Choice Chart provides a decision tree that leads students to a variety of graph types that support the kind of question they are investigating. It provides one more way for students to be decisionmakers in analysis, and “own” their outcomes. Continue reading
When students encounter variability in data, they often assume they (or someone) has made a mistake, or that the dataset is too hard because the data are scattered and don’t tell a nice, neat story. They are used to working with values that fall neatly on a line or function, or that have an unambiguous pattern. Continue reading
Students can be great at collecting data. But once they have a table of data, many are not sure how to proceed.
As teachers, we often toss students data in different forms to analyze and interpret: pre-made graphs, data collected during labs, small tables of data to graph by hand, or tables of data to graph in Excel or Google sheets. We hope they will “analyze” the data and come up with meaningful insights and explanations of the data as evidence. But we are often discouraged by what students hand in.
What does one actually do when analyzing data? More precisely, what are some of the decisions that students can wrestle with and come to own as they turn a table of data into evidence and useful information?