Category Archives: Teaching data literacy

Strategies for building students’ data literacy (in the context of learning disciplinary content).

Line plot and dot plot: What’s the difference?

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.

Visualizing data in line plots and dot plots is the backbone of learning to describe and compare groups of things and reason statistically about real phenomena that are naturally variable. It makes sense to introduce line/dot plots to very young learners and to use them frequently throughout the grade bands. They have only one axis, are simple to make by hand, are easy to read, and they tell much about the nature of a group. They are wonderful for a first look at data to get a sense of what’s there.

Line plots are introduced in Grade 2, and they (or dot plots) are mentioned specifically in all grade bands in the Common Core Math Standards, except Grade 8. That does not mean eighth graders should not use them as frequently as others when analyzing and interpreting data! As Bobby Robson, British footballer and former National Team manager put it, “Practice makes permanent!”

Dot plots and Line plots through the grade bands (CCSSM)

Grade 2: Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

Grade 3: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

Grade 4: Make a line plot to display a data set of measurements in fractions of a unit (½, ¼, ⅛). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Grade 5: Same scale resolution as grade 4 (to ⅛ inch). Use operations on fractions (½, ¼, ⅛) to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers shown in a line plot, add up the total amount of liquid in all the beakers. Calculate the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Grade 6: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Example: What are typical maximum wind speeds for Atlantic hurricanes? Sixth grade is when students start to think statistically about properties of distributions, and what range, shape, and center mean in the context of the data.

Grade 7: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. Example: Do male marathon runners have faster times than females?

High School: High School students continue to represent distributions of data with dot plots, histograms, and box plots. They use quantitative statistical reasoning to compare groups, and interpret differences in shape, center, and spread in the context of the data, accounting for possible effects (and meaning) of extreme data points (outliers). They use interquartile range, standard deviation and use appropriate statistics to fit it to a normal distribution and to estimate population percentages, when warranted. They use calculators, spreadsheets, tables, and other tools to estimate areas under a normal curve and interpret what the area means in the context of the data.

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Working with line plots and dot plots gives students much information to use when describing and reasoning about a group of data points.  Consider this: If they just added up all the points and graphed the total or the average in a single, what is left for them to to reason about other than the height of the bar? 

Look for the next blog about differences between bar graphs, bar charts, and histograms — and when each is useful.

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Reference: National Governors Association (NGA) Center for Best Practices and Council of Chief State School Officers (CCSSO) (2010). Common Core State Standards for Mathematics. NGA Center and CCSO, Washington D.C.



Why bother graphing by hand?

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.

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Link graph choice to a question

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

You have data, now what?

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?

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