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Textbooks require more real math exercises, research findings

Textbooks require more real math exercises, research findings

A typical math textbook for 8th grade includes just a few real-world problems that students have to solve, finding a new international study.

And that’s not enough, according to Honorary Professor of Michigan State University William Schmidt. “It’s no longer enough to just teach children fundamental skills, but move on to thinking about them, to unraveling real-world examples,” he said, “because textbooks just don’t give enough opportunities for students to actually practice the application of math in real applications. And I think that’s the main problem that American math education is facing right now. “

Schmidt led the analysis of 50,000 mathematical exercises from 8th grade textbooks in 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. Researchers found fewer than 150 student assignments related to high-order real-world mathematics applications. In the U.S., such problems accounted for just over half a percent of all problems, or seven.

The Analysis of mathematics curriculum documents continues a similar study in 1995, which examined the content and consistency of topics covered in grades 1-12 in the mathematical standards of more than 40 countries involved in trends in international mathematics and science research.

Compared to 25 years ago, Schmidt said, U.S. mathematical standards have become more in line with other most successful industrialized nations. “It’s a much, much more consistent structure and reflects the logical structure of math,” Schmidt said, “but the question is which textbooks to choose because we have a lot of options – I think at some point we had 20 different versions of the textbook in math for 8th grade – and some of these books haven’t caught up with the change in standards. ”

The 2022 audit focused on textbooks because previous research has shown that while teachers do add their lessons, most are likely to follow the content of the textbook – and this was especially true during distance learning, Schmidt said.

The United States, like other countries, has expanded its coverage of statistics, geometric and algorithmic reasoning, higher real-world examples, and 21st century competencies such as communication and creativity in mathematics.

But the study also looked at the types of exercises that were included: purely computational, either in numbers or in standard word problems; higher-order mathematical problems that require problem identification and logical progress; and real higher-order problems that place these higher-order problems in realistic contexts.

Worldwide, 85 percent of the exercises in the textbooks were purely computational, testing 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 less than 3 percent involving higher-order math that was not placed in real-world problems such as geometric proof in which students must determine appropriate information and develop a logical process to solve it.

But word-tasks often ended up as “really computational problems with words around [them]”So, instead of asking what 6 plus 2 will be, they say Jill has six apples and Sally has two; how many do they have? And then it’s considered an application. If we look at these countries , we found just over 100 of the 50,000 [math exercises] it actually expects kids to do math and apply it. ”

The study, published this spring, comes amid continuing concerns about the declining performance of American math students on both national and international scores. The United States ’use of real high-order problems differs more than other countries with high math scores, even if students keep up at about the same level as world averages.

Realistic problems may interest students

More realistic math problems allow for more active class participation, Schmidt argued.

For example, in one of the Hungarian exercises a family of four lived a short drive from a ski resort. Students were asked to help the family decide based on the distance traveled and the cost of gas and hotel, whether it would be more economical for the family vacation to spend every day on the slopes or stay at the resort. Students could then think about how costs for their own families could change, he said.

“With such questions, the problem is more related to reasoning and developing the problem, as well as thinking about how to use this mathematical set of knowledge that you need to solve something important,” he said. “Yes, the end is that you need to calculate something, but it is to learn to think, to teach logic, to understand what needs to be done to find the answer to your question. This is really what the world is about. That’s what we all need to be able to use as serious adults. “

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