# Guiding students through approximating trendsAn instructor's guide to Best-fit Lines

Many exercises in introductory geoscience courses require the construction of a best-fit line (or approximating linear trends in data). Many students struggle with this, particularly because they often want to just "connect the dots". The Best-Fit Line module is designed to give students the tools to construct (approximate) best-fit lines through data points plotted on X-Y graphs.

## What should the student get out of the page?

By the time the student has worked through the page, he or she should be able to:

• recognize trends in plotted data that are appropriate for a best fit line
• use one of two procedures for approximating a best fit line
• construct a best fit line for plotted data (see plotting points for a tutorial on constructing plots from data)
• demonstrate their newly acquired procedure by solving sample problems

## Why is it hard for students?

For whatever reason, many students do not understand the concept of fitting a line to a set of data. Perhaps it is because, in many mathematics courses, the process is reversed - students construct a table of data from a line. Most students arriving in their first geoscience class will be familiar with the equation for a line (many can recite "y = mx + b" if you ask) but most of them cannot conceptualize what that means.

The most common mistake that students make is to connect the lines; however, in the geosciences, we are most often describing a natural, somewhat chaotic system and we are not interested in the absolute value of the data, we are interested in the general trend of the data. Instead of needing to know all the values in a data set, geoscientists often want to be able to describe a set of data with an equation that approximates a natural phenomenon - a concept with which many introductory geoscience students will be unfamiliar. Students are also often unfamiliar with the "messy data" of natural systems and try to make sure the line goes through all the points by connecting the dots. Try to get students to understand that the trend is more important than the actual data set - we plot the data to help us visualize the trend.

For more help on teaching about trends in data, please see Understanding Trends in the Teaching Quantitative Literacy section of SERC.