Some not surprising but still depressing excerpts from the PISA Math Results, US results:
Students in the United States have particular weaknesses in performing mathematics tasks with higher cognitive demands, such as taking real-world situations, translating them into mathematical terms, and interpreting mathematical aspects in real-world problems. An alignment study between the Common Core State Standards for Mathematics and PISA suggests that a successful implementation of the Common Core Standards would yield significant performance gains also in PISA.
- U.S. students have particular problems with mathematical literacy tasks where the students have to use the mathematics they have learned in a well-founded manner. Given that even in more demanding tasks some basic skills are nevertheless needed, an implication of the findings is that much more focus is needed on higher-order activities, such as those involving mathematical modeling (understanding real world situations, translating them into mathematical models, and interpreting mathematical results), without neglecting the basic skills needed for these activities.
- It may be that U.S. students seldom work on well-crafted tasks that situate algebra, proportional relationships and rational numbers within authentic contexts. More generally, perhaps the application problems that most students encounter today are the worst of all worlds: fake applications that strive to make the mathematics curriculum more palatable, yet do no justice either to modeling or to the pure mathematics involved. Providing students with the necessary “opportunity to learn” will therefore be necessary in order to develop the skills in students that allow them to make frequent and productive use of mathematics in their work and life.
- Despite their below-average performance in mathematics, U.S. students feel relatively confident in their own abilities in mathematics compared with their counterparts in other countries. For example, 69% reported that they felt confident in a mathematical task such as calculating the petrol- consumption rate of a car, compared with the OECD average of 56%.
- OECD countries with greater equity in education outcomes, as measured by the strength of the relationship between performance and socio-economic status, show smaller performance differences between students from different socioeconomic groups, as measured by the slope of the socio-economic gradient. The correlation between the slope and the strength of the socio-economic gradient is 0.62 across OECD countries and 0.58 across all participating countries and economies. Canada, Estonia, Finland, Hong Kong-China and Macao-China combine high performance, a weak relationship between performance and socio-economic status, and relatively narrow performance differences across socio-economic groups.
- Among high-performing countries, Belgium, New Zealand and Chinese Taipei are the only two school systems where performance differences are above average and so is the strength of the relationship between socio-economic status and performance. Among countries that perform at or below the OECD average, the same pattern is observed in France, Hungary and the Slovak Republic. Chile, Costa Rica, Peru and Portugal are the only countries with relatively narrow performance gaps, despite a strong relationship between socio-economic status and performance (Figure II.2.2).
Here is a sample task:
Overall Results by Proficiency Band:
Rubrics describing the 6 levels:
Implications? Please comment.