I’ve been mulling a story on how K-5 math instruction will change under the Common Core State Standards, which emphasize conceptual understanding over formulas and tricks—and how elementary teachers in most states will need to change their pedagogy to keep up with the new requirements.
It’s particularly interesting because most math teachers are now being asked to instruct students in a way they were neither taught during pre-service training nor learned themselves in the early grades. And while teachers may understand these concepts well, teaching them, as you know, is a different story.
In a recent EdSource piece, Lillian Mongeau got right to this point, saying teachers are “unevenly prepared” to teach in this “dramatically different fashion.”
She writes that in most classrooms previously, “To find the area of a rectangle, for example, students would be given the appropriate formula—multiply the width of the figure by the height—and then expected to practice similar problems on worksheets or homework.” However, with the new standards, “Rather than providing a formula to calculate the area of a shape, students might be given a set of problems or activities that help them discover how to arrive at the formula on their own.”
A 6th grade teacher-friend recently gave me another example. She said that when teaching students algebraic equations with fractions, for instance 1/2x = 8, she no longer uses the flip-and-multiply approach. Instead, she emphasizes the concept that 1/2x is the same as x divided by 2, and lets them figure out the trick on their own. The process can be slow-going, she said, but ultimately it pays off because students can start transferring the concept to more difficult problems on their own.
However, she also mentioned that it’s tough designing problems that allow students to figure out the tricks—something she’s never really had to do before. I imagine it’s also quite challenging not to succumb to the temptation of teaching the short-hand.
Would be great to hear from other math educators below. Does this ring true for you? Have you had professional development to help you adjust to the new type of instruction? If so, what tips/suggestions do you have for other math teachers?