When it comes to introducing elementary students to statistical concepts, less can be more.
That鈥檚 the idea behind 鈥�,鈥� 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 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鈥檚 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鈥檚 3rd graders.
鈥淥K, so think about what you notice and wonder about this,鈥� Laib says. After giving them a few minutes to discuss with their table mates, she asks for their thoughts.
鈥淚 think it鈥檚 a staircase going up and down,鈥� says Maria 鈥淢asha鈥� Borodina, 鈥渟o if the pattern goes on, it will go up again.鈥�
Hanhee Lee agrees. 鈥淚f I was going down those steps, I鈥檇 probably fall and die there,鈥� she says, pointing to a big gap between two bars as Laib marks the students鈥� comments and calculations on the chart.
鈥淭hat is a big step, isn鈥檛 it? I鈥檓 going to add a word here, because this interval is showing a big change,鈥� Laib notes. 鈥淩emember we did that word, 鈥榠nterval,鈥� when we were talking about number lines and fractions?鈥�
Questioning labels
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, 鈥淣umber of Countries,鈥� means for the seven unlabeled bars on the x-axis. 鈥淭here 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,鈥� Aiden reasons.
The picture comes clear
With the reveal of the x-axis, which show the number of colors on each country鈥檚 flag, Stella Azrin, another student, wonders why the labels are numbers rather than the typical word labels.
鈥淸69传媒] want the number to represent the quantity not the category, and it just doesn鈥檛, 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,鈥� Laib explains after class. 鈥淪o all of this is lightly touching on previewing 6th grade stat stuff.鈥�
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. 鈥淗ow many colors are on the American flag?鈥� Laib asks. 鈥淪o where should the United States be on those bars? Or Japan?鈥�
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).
69传媒 also question why the charts aren鈥檛 identical, which leads to a conversation that is half data and half social studies: 鈥淚t seems like a very [simple] thing鈥攍ike, what are the number of countries?鈥攂ut it turns out that is a very complicated question,鈥� Laib explains. 鈥淭here are some countries that some people recognize and others that people don鈥檛. And there鈥檙e some countries that are fighting to be countries and get recognized by others. And so different measures might say there鈥檚 different numbers of countries in the world.鈥�
This story is part of Miscalculating Math, a deep examination of math instruction.
Overview and key data: Advocates say reforms in math teaching are pushing out statistics and geometry and driving a drop in students鈥� math scores. Here鈥檚 what you need to know.
Q&As: Hear three professionals talk about how they use statistics and geometry in their careers.
Handy guide: Find tips, lesson ideas, and free resources for beefing up instruction in statistics and geometry.
Quiz: Test your knowledge of math concepts, and then see how U.S. students fared.
Complete Coverage: There鈥檚 even more to explore on this topic. Check out the complete collection, Miscalculating Math.
