October 12, 2011
Beware of Bias â Graphing With a Critical Eye

Grades
3–5,
6–8

My students studied graphing during our first math unit this year. Graphing lends itself to get-to-know-you activities — students can survey each other to collect data — and it provides an entry point for students of all math abilities.

Once my students understood how graphs work and how to create accurate graphs, I started to wonder how I could up the ante. How could I promote critical thinking with this relatively straightforward math unit?

One of my students handed me the answer when he brought in a graph that he had clipped from the newspaper to add to our graph collection. As I looked over his graph, I thought, "Hey, wait a sec! This graph is downright misleading." As I pointed out the graph’s flaws to my students, their eyes widened at the idea that a newspaper might seek to mislead with a graph.

In this post I'll describe how our "misleading graph" study developed from that first lesson. **You'll find a SMART Notebook lesson about misleading graphs, student worksheets, and samples of my students’ work.**

The concept of bias is relatively new for my 3rd graders. Developmentally, many of them still see the world without much gray. To introduce the idea of bias, I showed my students several television commercials for children’s toys. We discussed how the advertisers seek to persuade consumers to buy their products, and how they are sometimes less than scrupulous in how they present their products.

After this introduction to the concept of healthy skepticism, I showed my students many samples of misleading graphs. To see the seven graphs that we analyzed as a class, download my SMART Notebook **Misleading Graphs **file. I also created a **PDF version** to use without the SMART Notebook software.

As I displayed each graph, my students would first turn and talk about what the graph showed. Then I would pose the important question, “What is wrong with this graph?” My students were so excited to prove that they could “outsmart” the misleading graphs. Hands waved wildly as my students triumphantly explained how each graph was “tricky.”

As my students analyzed each graph for bias, we compiled a chart of misleading features, shown at right. Download the **"Beware of Bias" **worksheet.

After we analyzed misleading graphs as a class, I sent my students off to work with partners analyzing misleading graphs. As I circulated around the room, I got a sense of which students were ready for the second lesson about misleading graphs and who needed some additional support.

I noticed that a few of my students wanted to defend the misleading graphs rather than analyze the bias. I pulled these students together for a small group discussion about how a graph can display correct data, but still be misleading in its presentation of that data. For these students, I found that it helped when I prefaced each graph we looked at by emphasizing, “This graph presents true data. The numbers in the graph are not lies. However, the graph maker is being tricky about how he is displaying this true data. Can you figure out how he is being tricky?” Emphasizing that the graph rather than the data is misleading helped to clarify this concept.

For homework, I asked each of my students to bring in an empty cereal box. We began our second lesson sitting in a circle with each student holding a cereal box. I led a discussion about the nutrition information displayed on the box. The students discussed calories, cholesterol, serving size, and vitamins and minerals. I sent the students off to work on a “**Breakfast Cereal Nutrition Facts Warm Up**” page so I could make sure that they all understood how to read the nutrition information on their cereal boxes.

After my students had time to complete the warm-up worksheet, I gathered them close to share a fictitious scenario. “How many of you are experts on breakfast cereal?” I asked the class. The students all eagerly nodded their heads, so I explained the project: “Several breakfast cereal companies have asked you cereal experts to help them with their advertising campaigns. They need graphs to include in brochures promoting their cereals — and since they want to sell as much cereal as possible, they need graphs that make their cereals look healthier compared to the competition. Are you ready to take on this challenge?”

First, I had my students each pick a cereal brand to “represent,” and pick one or two nutrition facts to focus on. I suggested that students choose three to five other cereal brands to compare to their chosen brand.

I let my students decide to work independently or with a partner. I provided a stack of graph paper and colored pencils, and my students were off and running. When students got stuck, I pointed them to the chart from the previous lesson about biased graphs. “Which of those elements are you going to use to make your misleading cereal graph?” I prompted. With this support, all of my students were able to create their own biased graphs. After students finished their first graph, I gave them the option of creating a second graph that presented the same data without bias or that was biased in a different manner.

Many students asked to hang their finished graphs in the hallway to help teach their peers to look out for misleading graphs. Other students were more interested in trying to trick people with their graphs. Here is a photo of one of their misleading graphs and our misleading graph bulletin board display:

By the end of this series of lessons, my students had become bias hounds. They now carefully comb over every graph, sniffing out the slightest hint of spin. “Skepticism is a virtue,” Napoleon Bonaparte said. I hope that you find these lessons useful in cultivating informed skepticism among your mathematicians, too!

My students studied graphing during our first math unit this year. Graphing lends itself to get-to-know-you activities — students can survey each other to collect data — and it provides an entry point for students of all math abilities.

Once my students understood how graphs work and how to create accurate graphs, I started to wonder how I could up the ante. How could I promote critical thinking with this relatively straightforward math unit?

One of my students handed me the answer when he brought in a graph that he had clipped from the newspaper to add to our graph collection. As I looked over his graph, I thought, "Hey, wait a sec! This graph is downright misleading." As I pointed out the graph’s flaws to my students, their eyes widened at the idea that a newspaper might seek to mislead with a graph.

In this post I'll describe how our "misleading graph" study developed from that first lesson. **You'll find a SMART Notebook lesson about misleading graphs, student worksheets, and samples of my students’ work.**

The concept of bias is relatively new for my 3rd graders. Developmentally, many of them still see the world without much gray. To introduce the idea of bias, I showed my students several television commercials for children’s toys. We discussed how the advertisers seek to persuade consumers to buy their products, and how they are sometimes less than scrupulous in how they present their products.

After this introduction to the concept of healthy skepticism, I showed my students many samples of misleading graphs. To see the seven graphs that we analyzed as a class, download my SMART Notebook **Misleading Graphs **file. I also created a **PDF version** to use without the SMART Notebook software.

As I displayed each graph, my students would first turn and talk about what the graph showed. Then I would pose the important question, “What is wrong with this graph?” My students were so excited to prove that they could “outsmart” the misleading graphs. Hands waved wildly as my students triumphantly explained how each graph was “tricky.”

As my students analyzed each graph for bias, we compiled a chart of misleading features, shown at right. Download the **"Beware of Bias" **worksheet.

After we analyzed misleading graphs as a class, I sent my students off to work with partners analyzing misleading graphs. As I circulated around the room, I got a sense of which students were ready for the second lesson about misleading graphs and who needed some additional support.

I noticed that a few of my students wanted to defend the misleading graphs rather than analyze the bias. I pulled these students together for a small group discussion about how a graph can display correct data, but still be misleading in its presentation of that data. For these students, I found that it helped when I prefaced each graph we looked at by emphasizing, “This graph presents true data. The numbers in the graph are not lies. However, the graph maker is being tricky about how he is displaying this true data. Can you figure out how he is being tricky?” Emphasizing that the graph rather than the data is misleading helped to clarify this concept.

For homework, I asked each of my students to bring in an empty cereal box. We began our second lesson sitting in a circle with each student holding a cereal box. I led a discussion about the nutrition information displayed on the box. The students discussed calories, cholesterol, serving size, and vitamins and minerals. I sent the students off to work on a “**Breakfast Cereal Nutrition Facts Warm Up**” page so I could make sure that they all understood how to read the nutrition information on their cereal boxes.

After my students had time to complete the warm-up worksheet, I gathered them close to share a fictitious scenario. “How many of you are experts on breakfast cereal?” I asked the class. The students all eagerly nodded their heads, so I explained the project: “Several breakfast cereal companies have asked you cereal experts to help them with their advertising campaigns. They need graphs to include in brochures promoting their cereals — and since they want to sell as much cereal as possible, they need graphs that make their cereals look healthier compared to the competition. Are you ready to take on this challenge?”

First, I had my students each pick a cereal brand to “represent,” and pick one or two nutrition facts to focus on. I suggested that students choose three to five other cereal brands to compare to their chosen brand.

I let my students decide to work independently or with a partner. I provided a stack of graph paper and colored pencils, and my students were off and running. When students got stuck, I pointed them to the chart from the previous lesson about biased graphs. “Which of those elements are you going to use to make your misleading cereal graph?” I prompted. With this support, all of my students were able to create their own biased graphs. After students finished their first graph, I gave them the option of creating a second graph that presented the same data without bias or that was biased in a different manner.

Many students asked to hang their finished graphs in the hallway to help teach their peers to look out for misleading graphs. Other students were more interested in trying to trick people with their graphs. Here is a photo of one of their misleading graphs and our misleading graph bulletin board display:

By the end of this series of lessons, my students had become bias hounds. They now carefully comb over every graph, sniffing out the slightest hint of spin. “Skepticism is a virtue,” Napoleon Bonaparte said. I hope that you find these lessons useful in cultivating informed skepticism among your mathematicians, too!