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Somewhere between third and fourth grade, most students learn that area is calculated by multiplying length and width. It's a formula that's easy enough to memorize ... but it's also a formula that many students don't fully understand.
"Many students know the area formula length times width, but don't know that a square unit is the unit of measure for area," says Jennifer Kobrin, a senior research scientist at Pearson. "A full conceptual understanding of area involves knowledge that the area formula yields a count of the square units that cover a shape."
"Students gain this understanding by first learning to count individual units, then progressing to more sophisticated strategies that involve multiplication of rows and columns. Putting it all together requires moving through these stages one step at a time."
Jennifer and her colleagues are mapping out these steps of learning.
They're working to understand HOW children learn the concepts associated with complex topics like area, from basic concepts to more abstract concepts:
"These 'learning progressions' are based on research on student learning," Jennifer says. "They can be used to develop map that gives teachers new insight about how students think about problems."
Classroom Pilot Programs
More than a dozen classrooms around the U.S. and Australia participated in research about learning progressions. Teachers participated in professional development on the learning progressions and used progression-related classroom activities, performance tasks, and even a digital game called Alice in Arealand to gain a better understanding about the stages their students had mastered on the concept of area measurement—and the stages that still needed work.
"It's an integrated learning system," Jennifer says. "And the main takeaway is that we can assess students without explicitly testing them."
"Our thinking goes like this: if you have a learning system built around learning progressions," Jennifer says, "students will learn better."
"Traditional assessments show whether students know a standard," Jennifer says. "Teaching with learning progressions helps us understand and enrich what students are thinking."
Alice in Arealand
For nearly two years, Jennifer and her colleagues have been using a game to help understand students' thinking with regard to the learning progression on area measurement. It's part of an integrated learning system that involves classroom activities, performance tasks, and professional development.
The game is called 'Alice in Arealand'—and you can play it online here. Early levels challenge learners with basic concepts about area. Later levels get more difficult.
Kids love it. And teachers can know, in real time, what students are learning and where students need help.
"Teachers may not always know why a student is having a difficult time with a concept in class," Jennifer says. "This kind of approach gives teachers new clarity about what kids are thinking and how to help them get to the next stage in their learning."