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A host of recent studies have examined how U.S. students鈥� 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 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 , in Washington, examines the math content of Hong Kong and Massachusetts by comparing the two jurisdictions鈥� standardized tests in 3rd grade math.
Hong Kong鈥檚 test includes a higher percentage of number and measurement concepts than Massachusetts鈥� exam does, the study found. Number skills are essential preparation for algebra, and measurement is important to being able to handle 鈥渞eal world鈥� math, the authors say.
鈥淲hen you ask, 鈥榃here do I do math in real life?鈥� the real world is about measurement,鈥� said Steven Leinwand, a principal research analyst at the AIR and one of the study鈥檚 authors. 鈥淗ow much? How far? How long? How big?鈥�
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鈥檚 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鈥� which tend to be more demanding鈥攃ompared with just 29 percent of Massachusetts鈥� items. Constructed-response questions, however, are generally more costly to develop and score.
In addition, a higher portion of Hong Kong鈥檚 test questions, 55 percent, were deemed to have moderate or high 鈥渃ognitive complexity,鈥� compared with just 34 percent of Massachusetts鈥� questions. Complexity was judged by whether the question required the application of knowledge, rather than simple recall, as well as the use of 鈥渘onroutine鈥� 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鈥攖hough its mark was well below Hong Kong鈥檚. Massachusetts is also a consistent elite-scorer on the primary U.S. domestic test, the National Assessment of Educational Progress.
Hong Kong鈥檚 use of more difficult and complex test items could be connected to a higher proportion of its test-takers, 40 percent, scoring at the 鈥渁dvanced鈥� 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 鈥渟trong correlation鈥� between nations鈥� 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鈥� 3rd grade test is a 鈥渉igh stakes鈥� exam given to gauge student progress, as required by the No Child Left Behind Act. Hong Kong鈥檚 assessment is a 鈥渂asic competency assessment鈥� 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鈥檚 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 鈥渧ery helpful鈥� 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鈥檚 curriculum and its teacher training, not just its tests.
鈥淚 don鈥檛 think assessments alone can tell you the whole picture,鈥� 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鈥檚 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.
鈥淎re we aiming too broadly in our early-grades curriculum, or could we be more focused?鈥� Mr. Chester asked.
Mr. Leinwand said the authors chose to examine test content in Hong Kong and Massachusetts because the two jurisdictions鈥� early-grades math curricula were relatively similar鈥攁nd because state tests in the United States tend to guide math instruction.
American educators 鈥減ay attention to the tests,鈥� he observed. 鈥淚f you change the state tests, it鈥檚 a powerful lever for what goes on in the classroom.鈥�
