Some districts around the U.S. have begun to experiment with blending math courses like Algebra 1 and geometry, versus the more traditional model of teaching the two subjects separately.
While the National Council of Teachers of Mathematics doesn’t take an official position on whether educators should do so, NCTM President Latrenda Knighten sees advantages and disadvantages to the blended approach. Blending two or more math topics, for instance, helps reinforce “coherence” and connections across mathematics through an integrated lens that could be helpful in college and beyond, Knighten said.
“You’re going to help students with connections across mathematics topics. We do feel an integrated type of approach would support more modeling, more real-world problem-solving, and that math is an integrated discipline,” she said.
But the blended approach must be done extremely carefully and with fidelity across curriculum design, teacher preparation, instructional quality and with an equity lens, or such integrated pathways can easily go sideways, Knighten said.
“Don’t just take something someone threw together and think, ‘Here it is,’” she said. “It should be obvious to that math instructor that those pieces are there. … Math is not a bunch of disconnected courses. People think only Algebra 1 and Algebra 2 are connected.”
Supports for a blended approach
Ensuring success of the blended approach starts with a well-designed curriculum, Knighten said.
“It has to have all of those pieces built in that show the coherence and the connections,” she said. “We would not want a student to not get the best out of that experience because [a district] either didn’t have the people to create this or didn’t have a vetting process for someone to provide feedback on what they’ve created.”
Professional development is key — especially at the secondary level, where math teachers sometimes have siloed visions of themselves as “I’m an algebra teacher, or I’m a geometry teacher,” Knighten said.
“Blending doesn’t mean four weeks of algebra and then four weeks of geometry,” She said. “It’s about understanding courses well enough to know that content, to know which themes you can blend together, and to show how I can apply this in the real world — that relevance students need.”
And professional development can’t just be delivered at the outset and then “let them loose,” she added. “You need support to guide them throughout the year so that implementation is at its highest level at all times. … It has to be ongoing to support this.”
Given sometimes-siloed mentalities, school leaders should tap those who seem most open to expanding their teaching horizons, Knighten said.
“So many people say to me, ‘Latrenda, I’ve never taught geometry before.’ I applaud people who do that,” she said. “But that may not be everybody. People who are seasoned administrators, who carefully think about things, that might be their fear: ‘Do I have enough people who know this well enough to do this well?’”
If they don’t, a school or district will end up with poor implementation, which can weaken the coherence among subject matter and inadequately serve students, Knighten said.
“How successful your students are going to be will depend on that instructional quality,” she said. “We’re talking about making sure people are providing instruction to students that plays on the relevance piece, that is big on making connections and applications to the real world, [and] making sure we see elements of statistical reasoning and problem-solving.”
Finally, school leaders should think about blended instruction through an equity lens, ensuring that students entering high school who are not quite ready for Algebra 1 have the opportunity to gain blended instruction in a way that’s not “watered down,” Knighten said.
“They should still have opportunities for the same high-quality experiences,” she said. “We want [courses] blended for coherence and connectiveness, not ‘They can do a little of this and a little of that, get them through both, and get them out of their math requirement.’”
