How to organize and represent data
Scientists decide how to work with, organize, and sometimes transform data – both so that they can see patterns and so they can help others understand what they see. Allowing students to experience unorganized data and to make and compare choices about how to represent data allows them to understand important representational tools (scale, consistent spacing, counts) and to apply and extend mathematical competencies in the context of meaningful science work.
A closer look at uncertainty in the classroom
As fifth grade students examine the data they collected to see whether the volume and weight of water change when the water is frozen, they consider how to use their data to make claims. Students experience uncertainty in how to organize and represent data as:
The class tries to use an unorganized data table
Students work in pairs to reorganize the data
Students compare and make sense of different data representations
The class tries to use an unorganized data table
Lindsay first shows the class the data table that compiles their results and asks how they can use that to answer their investigation questions. Students readily suggest that they can see that water level increases, pointing out examples as Lindsay uses arrows to mark the water level going up in all cases. They’re less sure of whether the weight stayed the same, with students pointing out that some of their vials changed weight.
Students begin counting and grouping as they think aloud. Lindsay writes these strategies down, then suggests they work in partners to make a claim and use one of their strategies to organize the data to support their claim.
Unorganized data table with markings showing all water levels increased.
Students work in pairs to reorganize the data
They generate different representations all seeking to make sense of the data and organize it in light of a claim that the weight stays the same because most of the vials did not change in weight.
While students agreed the weight stayed the same, they created different data representations to support their claim.
Students compare and make sense of different data representations
Lindsay chooses two representations that show different strategies. Students present, take questions, and talk about how the representations are different. Lindsay then introduces a histogram and students compare and map this representation to the ones that they developed.
Histogram introduced by Lindsay so students could consider strategies such as a key and scale
Instructional moves to support this form of uncertainty
Make and show public representations of students’ combined data.
Make sure data is in a form that students can work with given their mathematical capabilities so that quantities make sense to them -- keep pictoral representations of relative distance visible in younger grades; avoid decimals if these aren’t yet fully meaningful to students.
Ask students to begin to make claims with less organized data so that they experience difficulty and begin to count and reorganize. Then name those strategies and ask them to try them out.
Ask questions of data representations: “Where is your vial on that chart?” “How does this representation make it easy to see at a glance that most of the weights stayed the same?” “What’s harder to see in this representation?”
