The latest international test scores of 15-year-olds are in, and the results are appalling. The Program for International Student Assessment, or PISA, found that the United States — the most affluent country in the world — failed to rank in the top 20 in any category. In math — the subject most critical for careers in high-paying science, technology and engineering fields — slightly more than a quarter of U.S. students scored below baseline proficiency.

But we shouldn't have been surprised. This year's scores were comparable to results over the last decade, leading Education Secretary Arne Duncan to describe a "picture of educational stagnation."

That could change. Forty-five states, including California, are implementing the Common Core learning standards, a high-quality foundation for math and English-language arts instruction developed by the nation's governors and education commissioners. But will the new standards raise student achievement? The answer depends on implementation.

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The keys to implementation are textbooks, teachers and testing. Getting any one of these wrong will leave our young people even further behind.

**Textbooks:** We don't have a national math curriculum, but for a generation there has been so little variation among textbook options that we have had a de facto national math curriculum. A very poor one. Most school math textbooks are badly flawed. They present a bunch of rules and examples without clear, comprehensible explanations that enable kids to understand the material fully. Professor Hung-Hsi Wu of UC Berkeley speaks of "textbook school mathematics" — an often incomprehensible math curriculum that fails to promote true understanding of the underlying principles students need to understand to succeed in math. For Common Core to succeed, we desperately need new textbooks that are fundamentally different.

**Teachers:** Teachers are the heart of the enterprise. But at this point, nearly all were themselves educated in the American system, which means that they probably learned from textbooks with the same flaws as those they now teach from. Many of them need training they don't get, and they struggle to teach concepts they don't fully grasp themselves. So how will these teachers handle Common Core?

Singapore faced the same issue 20 years ago, when the vast majority of its elementary school teachers had not even had four years of university instruction. They addressed the situation by creating math textbooks that had two critical features. First, they were bombproof. Even if a teacher didn't understand the material well, he or she could follow the textbooks and students would learn. Second, the textbooks were so clear that they taught the teachers. Even if teachers didn't understand the concepts when they began teaching, they would learn them from the book. After a few years, they became self-trained and reached higher levels. We need to help our teachers with these kind of books, borrowing from successful models abroad, and then support teachers with professional development focusing on content so that they are prepared to teach Common Core well.

**Testing:** If teachers teach to the test, then the test had better be so good that teachers should be teaching to it. We need tests that measure both procedural fluency and deeper understanding. Such tests can add value, both diagnostically and in terms of benchmarking achievement. But we should also recognize that not all aspects of learning are captured by tests. We should consciously seek the middle ground, valuing good tests but not letting them serve as the sole goal of our education system.

The PISA test results are an important warning that our country's education system is not getting the job done. We need urgent changes. But we need the right changes. With the right textbooks, systematic use of professional development to enhance teacher knowledge and thoughtful testing, we can put in place the improvements that we need to implement the Common Core curriculum successfully and stop our nation's stagnation.

*Solomon Friedberg, a professor of mathematics and chairman of the math department at Boston College, is a graduate of the Los Angeles Unified School District.*