A typical 8th grade math textbook includes just a handful of real-world problems for students to solve, finds a new international study.
And that’s not enough, according to William Schmidt, distinguished professor at Michigan State University. “It’s not enough anymore to just teach the kids the fundamental skills, but to move toward being able to reason with those to solve real-world examples,” he said, “because the textbooks simply do not provide enough opportunities for students to actually practice applying mathematics in real-world applications. And I think that now is a major issue confronting American education in math.”
Schmidt led the analysis of 50,000 math exercises from the 8th grade textbooks of 19 countries, including the United States, by researchers working on behalf of the Organization for Economic Co-operation and Development’s Future of Education and Skills 2030 project. The researchers found less than 150 student tasks in all dealt with higher-order, real-world applications of math. In the United States, such problems accounted for just over half a percent of all problems, or seven.
The Mathematics Curriculum Document Analysis study follows up a similar study in 1995, which looked at the content and coherence of topics covered in grades 1-12 in the math standards of more than 40 countries that participate in the Trends in International Math and Science Study.
Compared to 25 years ago, Schmidt said, U.S. math standards have become more in line with other top-performing industrialized countries. “It’s a much, much more coherent structure and reflects the logical structure of mathematics,” Schmidt said, “but the question is what textbooks are chosen because we have lots of choices—I think at one point we had 20-some different versions of an 8th grade math book—and some of those books have not caught up with the change in the standards.”
The 2022 audit focused on textbooks because prior studies found that while teachers do add their own lessons, the majority are overwhelmingly likely to follow the content of the textbook—and this was particularly true during remote instruction, Schmidt said.
The United States, like other countries, has increased its coverage of statistics, geometric, and algorithmic reasoning, higher-order real-world applications, and 21st century competencies such as communications and creativity in math.
But the study also looked at the kind of exercises that were included: purely computational, either in numbers or standard word problems; higher-order math problems that require identifying a problem and logical progression; and real-world higher-order problems, that situate those higher-order problems in realistic contexts.
Worldwide, 85 percent of textbook exercises were purely computational, checking students’ ability to multiply, divide, and so on. In the United States, just over 68 percent of math exercises were computational, with about 29 percent of them being word problems and fewer than 3 percent involved higher-order math that was not situated in real-world problems, such as a geometric proof in which students must identify relevant information and develop a logical process to solve it.
But the word problems often ended up as “really computational problems with words around [them]” Schmidt said. “So instead of asking what’s 6 plus 2, they say Jill has six apples, Sally has two; how many do they have? And then that’s considered to be an application. When we look across these countries, we only found a little over 100 out of all 50,000 [math exercises] that would actually expect children to take their math and apply it.”
The study, released this spring, comes amid ongoing concerns about U.S. students’ decline in math performance in both national and international assessments. The United States’ use of real-world, higher-order problems has varied more widely than those of other high math-performing countries, even though students perform roughly on par with global averages.
Realistic problems can engage students
More-realistic math problems offer the opportunity for more class involvement, too, Schmidt argued.
For example, one Hungarian exercise set out a family of four who lived within driving distance of a ski resort. Students were asked to help the family decide, based on the travel distance and the price of gas and hotel, whether it was more cost efficient for the family to spend their vacation driving each day to the slopes or staying at the resort. The students then could work through how the costs might change for their own families, he said.
“With this kind of question, the issues are more around the reasoning and the development of the problem, and thinking through how to use that mathematical set of knowledge you have to solve something that’s important,” he said. “Yeah, the end is you have to compute something, but it’s learning to think through, lay out the logic, realize what you need to do to figure out the answer to your question. That’s really what the world is about. That’s what all of us need to be able to use as serious adults.”