A host of recent studies have examined how U.S. students’ mathematics skills compare against those of their foreign peers. Now, a new analysis probes a more precise question: How does the math covered in the highest-ranking American state stack up against that of a top-scoring international performer?
A study released last week finds that elementary students in Hong Kong are exposed to more difficult and complex math than pupils in Massachusetts, an elite scorer on national and international exams.
The analysis, published by the American Institutes for Research, in Washington, examines the math content of Hong Kong and Massachusetts by comparing the two jurisdictions’ standardized tests in 3rd grade math.
Hong Kong’s test includes a higher percentage of number and measurement concepts than Massachusetts’ exam does, the study found. Number skills are essential preparation for algebra, and measurement is important to being able to handle “real world” math, the authors say.
“When you ask, ‘Where do I do math in real life?’ the real world is about measurement,” said Steven Leinwand, a principal research analyst at the AIR and one of the study’s authors. “How much? How far? How long? How big?”
A study compares the content and difficulty of a top-performing state against a top-performing East Asian jurisdiction.
SOURCE: American Institutes for Research
One of the most striking differences between the two tests was Hong Kong’s much broader use of questions requiring students to construct responses to math questions, rather than simply check boxes through multiple choice.
The authors found that 86 percent of the Hong Kong questions required a constructed response— which tend to be more demanding—compared with just 29 percent of Massachusetts’ items. Constructed-response questions, however, are generally more costly to develop and score.
In addition, a higher portion of Hong Kong’s test questions, 55 percent, were deemed to have moderate or high “cognitive complexity,” compared with just 34 percent of Massachusetts’ questions. Complexity was judged by whether the question required the application of knowledge, rather than simple recall, as well as the use of “nonroutine” and multistep problem-solving, which are relevant to everyday tasks, Mr. Leinwand said.
Hong Kong was chosen for the study because its 4th graders ranked first among all participating jurisdictions on the 2007 Trends in International Mathematics and Science Study, a widely scrutinized international exam. Massachusetts, which along with Minnesota was one of two U.S. states to take part in the test, also fared well, scoring fourth in that category—though its mark was well below Hong Kong’s. Massachusetts is also a consistent elite-scorer on the primary U.S. domestic test, the National Assessment of Educational Progress.
Hong Kong’s use of more difficult and complex test items could be connected to a higher proportion of its test-takers, 40 percent, scoring at the “advanced” TIMSS level, than Massachusetts, at 22 percent. Just 10 percent of American students, on the whole, reached that level, the authors argue. In addition, research shows a “strong correlation” between nations’ math performance in early and later grades, they say.
The co-author of the study was Alan Ginsburg, the director of the policy and program studies service at the U.S. Department of Education, which underwrote the study. The two researchers have worked together on a number of studies of foreign curriculum in recent years.
Tests and Levers
Massachusetts’ 3rd grade test is a “high stakes” exam given to gauge student progress, as required by the No Child Left Behind Act. Hong Kong’s assessment is a “basic competency assessment” used to help schools judge student performance and shape lessons, the authors say.
Hong Kong, a special administrative region of China, is a densely populated island of 7 million residents located off that country’s south coast. Its schools follow a curriculum crafted by the central Hong Kong government, according to the 2007 TIMSS report.
Mitchell D. Chester, the Massachusetts commissioner of education, called the study “very helpful” and said state officials would weigh it when reviewing test content. But he also said that when evaluating what is taught in elementary math in his state, it is important to consider the state’s curriculum and its teacher training, not just its tests.
“I don’t think assessments alone can tell you the whole picture,” Mr. Chester said.
While adding more constructed-response items to the tests is generally desirable, those changes increase costs, Mr. Chester said. He was particularly interested in the study’s finding that Massachusetts perhaps goes too far in introducing students to a range of basic algebra concepts, while it does less than Hong Kong in promoting foundational skills such as number sense and measurement.
“Are we aiming too broadly in our early-grades curriculum, or could we be more focused?” Mr. Chester asked.
Mr. Leinwand said the authors chose to examine test content in Hong Kong and Massachusetts because the two jurisdictions’ early-grades math curricula were relatively similar—and because state tests in the United States tend to guide math instruction.
American educators “pay attention to the tests,” he observed. “If you change the state tests, it’s a powerful lever for what goes on in the classroom.”
A version of this article appeared in the May 20, 2009 edition of Education Week