Ways to teach the concept of line of best fit
By: Kristin Hunter-Thomson
Being able to look at the overall pattern in data can be challenging for novices, especially in scatterplots. But here is a strategy to consider using...
Before diving into teaching students the mechanics how how to calculate a line of best fit (or trend line, because that isn't necessarily what you want to be teaching when you are teaching content)...
Before having them select the Add Trend Line feature in Excel, Google Sheets, or whatever graphing program you are using (because really that just makes a line appear on the page)...
Consider having them draw the general gist by hand! Let's explore...
For example, let's say we are working with our students to explore predator-prey relationships and are using a dataset of the number of Black Sea Bass (predator) and Crabs (prey) found in the same locations. We could give our students these data and ask them to interpret the pattern:
As experts, we see a great example of predator-prey interaction in these data. As the number of predators (Black Sea Bass) increase the number of prey (Crabs) decrease. Conversely, as the number of predators (Black Sea Bass) decrease the number of prey (Crabs) increase.
However, there are many things fighting against our students' abilities to interpret these data the same way as we do:
-
In general, human brains are much worse at recognizing negative than positive patterns (Berinato, 2016). When you are less familiar with working with data this is more pronounced.
-
The farther data points are away from a linear relationship line the harder it is for human brains to see the patterns (put forward by Ernst Heinrich Weber in 1834). These data do not line up along one clear line.
-
And finally, novices focus on single attributes rather than overall patterns, and scatterplots are all about single attributes as our eyes naturally focus on the individual dots rather than overall what they communicate.
OK, that is a lot of things fighting against us as we are trying to help our students make sense of these data and see the pattern in the data to aid their understanding of the content (remember, predator-prey relationships). But fear not, we can use an easy technique to help students to how to start seeing the patterns more easily and quickly.
First, have the students draw an oval around the majority of the data points...
The key here is to get as many data points included within the circular shape, and to decrease as much space between the outside data points and the shape.
Then have your students draw a line that equally separates the data points in two. They should draw the line along the longest part of the circular shape (aka along the widest part of the oval...in other words along the trend of the data)...
They should try to make it so roughly half of the data points are above the line, and roughly half of the data points are below the line. However, the emphasis should be on generally where should the line go, rather than on exactly making the line bisect the data.
Very quickly we have provided students with a visual cue for the overall pattern in the data. Meaning we have visually made it easier for them to make sense of the data. By seeing the pattern in the data more quickly, they can analyze the data as it relates to your content focus (predator-prey relationships).
Is this the line of best fit? NO!
But that can be a lesson for another day, subject area, or grade level.
Is there benefit in providing visual scaffolds for helping students make sense of the data for why you are using it to teach content? YES!
Think about what you can provide to your students that helps them make sense of the data, in meaningful and authentic ways, without confusing them with more procedures to replicate.
You will be amazed at what your students can make sense of! Have fun...
