When it comes to introducing elementary students to statistical concepts, less can be more.
That’s the idea behind “slow reveal graphs,” a lesson model in which teachers gradually unveil and discuss information in a complex chart to prompt students to think more deeply about how data are chosen, measured, and analyzed. While data visualizations are one of the most common formats for statistics education, studies find math lessons involving charts can overfocus on the visual aspect without engaging students in how to think about the underlying mathematical meaning.
In the photographs that follow, Jenna Laib, a math specialist at Driscoll School, part of the Brookline, Mass., public schools, walks through a slow-reveal lesson for math and civics. It’s part of a co-teaching residency program in which Laib works with each teacher for a few weeks at a time, helping them find ways to integrate more data-science lessons across different subjects.
Notice and wonder
Laib begins by presenting a mostly unlabeled bar chart to Christine Sevigny’s 3rd graders.
“OK, so think about what you notice and wonder about this,” Laib says. After giving them a few minutes to discuss with their table mates, she asks for their thoughts.
“I think it’s a staircase going up and down,” says Maria “Masha” Borodina, “so if the pattern goes on, it will go up again.”
Hanhee Lee agrees. “If I was going down those steps, I’d probably fall and die there,” she says, pointing to a big gap between two bars as Laib marks the students’ comments and calculations on the chart.
“That is a big step, isn’t it? I’m going to add a word here, because this interval is showing a big change,” Laib notes. “Remember we did that word, ‘interval,’ when we were talking about number lines and fractions?”
As Laib reveals new layers of the chart, including numbers along the y-axis, Oliver Spiers and Amelie Lu begin to calculate the numerical value of each bar in the chart while Aiden Cullen puzzles over what the y-axis title, “Number of Countries,” means for the seven unlabeled bars on the x-axis. “There are seven bars, so maybe each bar represents a continent? So the low one is North America that only has a few countries, and the high ones are places like Africa, where there are a lot of countries,” Aiden reasons.
The picture comes clear
With the reveal of the x-axis, which show the number of colors on each country’s flag, Stella Azrin, another student, wonders why the labels are numbers rather than the typical word labels.
“[Students] want the number to represent the quantity not the category, and it just doesn’t, and that is a really, really key idea that we touch on in 3rd and 4th grade but is really done in middle school, when you are dealing with statistical measures,” Laib explains after class. “So all of this is lightly touching on previewing 6th grade stat stuff.”
The geopolitics of numbers
Once the students see the full chart title showing the number of colors on national flags, students suggest how they would represent the countries they know. “How many colors are on the American flag?” Laib asks. “So where should the United States be on those bars? Or Japan?”
The students, who have connections to a dozen or more countries, calculate how they would represent various nations. Then Laib pulls up a different representation of a similar sample of data, using images of the flags themselves, and the students talk through other issues: why certain countries seem to use the same colors and why one chart holds an empty space for one color (because Libya was the only country with one color, an entirely green flag, before its change of government in 2012).
Students also question why the charts aren’t identical, which leads to a conversation that is half data and half social studies: “It seems like a very [simple] thing—like, what are the number of countries?—but it turns out that is a very complicated question,” Laib explains. “There are some countries that some people recognize and others that people don’t. And there’re some countries that are fighting to be countries and get recognized by others. And so different measures might say there’s different numbers of countries in the world.”
This story is part of Miscalculating Math, a deep examination of math instruction.
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