Students would be better off if algebra teachers began their lessons with word problems, according to a recent study covered by my colleague Sarah Sparks, rather than waiting to present them until students have mastered equations.
Starting with symbols can impede learning, Mitchell J. Nathan, an educational psychology professor at the University of Wisconsin-Madison, said in the article. “Language itself provides an entry point to mathematical reasoning that is highly superior to the algebraic equation.” The researchers, who presented at the International Mind, Brain, and Education Society conference in Washington last month, found that students more accurately solved word problems than they did equation problems in both arithmetic and algebra. Students were also more likely to try solving word problems than equations.
The study’s recommendations reflect, in some ways, the type of teaching that math educator Dan Meyer has been advocating for many years. As I wrote in 2011, Meyer, whose TED Talk “Math Class Needs a Makeover” has garnered nearly 2 million views, asks teachers to start class with a real-world question and allow them to inquire their way to the answer. He disdains the traditional textbook presentation of a problem, which is to offer all the information and then ask several questions—usually equation-based—leading up to the narrative problem.
But as the researchers on the word-problem study note, students who learning English, and those who have other language challenges, tend to have difficulty with word problems.
Math teachers across the country using the Common Core State Standards in mathematics, which have heightened language demands, are grappling with just this issue. How do you give students who struggle with language access to a language-heavy math lesson? As my colleague Anthony Rebora wrote recently, some math teachers are working more closely with English-as-a-second-language teachers to support their students’ language skills. Others are using strategies such as sentence starters and pairing linguistic prompts with diagrams and sketches.
Meyer advocates starting class with an image or a video to present a problem, rather than relying on on text-based language. From my 2011 story:
For example, when teaching high schoolers, Meyer uses the digital projector to display a photo of himself shooting a basketball. Meyer has doctored the photo so that it shows the ball at several different points along the trajectory, stopping at the apex. “When I put that up on the board, the premise of that problem is obvious to every student. I don’t even have to say it. ‘Will the ball go in?’ That’s what we’re all wondering,” he says.
So my question is this: Rather than starting class with text-based word problems, would it be more effective to start class with word problems that rely heavily on visuals? Could this make the content more accessible to all students? Food for thought for the next research study, perhaps.
A version of this news article first appeared in the Curriculum Matters blog.