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.
I’m not sure I can say too much without knowing some more information. Averages are ok, but what were the distributions? What were the number of students getting each score range in a country? What were the highest and lowest scores in each country? Did everyone in those countries take the test?
Given my questions, I would like to see more of an emphasis on basics, and the application of that basic math knowledge. Maybe we need to focus even more on basic skills in lower income areas so they have a strong foundation to build upon later. I wonder if our scores are lower because we are trying to make the best better. Maybe we should focus a little more on those students who are struggling and raise their knowledge – with a subsequent increase in scores. I think that’s where the real work is for teachers. I see it with IB. They get the smallest classes and some of the best teachers. Wouldn’t it be better to have struggling students in smaller classes with better teachers?
All these Qs and hundreds more are addressed in the reports’ 5 volumes. I’ll post some helpful info at the bottom of the current post. You will want to read Vol II where student self-reports about their experience is provided and analyzed in dozens of ways.
What always strikes me in these international comparisons of cognitive and affective relations with mathematics is how smugly complacent AND ignorant Americans are about math. They seem to have no idea what they don’t know and what many others in the world actually do know. I remember reading somewhere that Koreans attribute their lack of success in math to their inadequate efforts, while Americans shrug it off with, “I lack math ability” or “I just don’t test well”. The irony of the society which claims, historically, to believe in “equality of opportunity” and “self-help”, resigning itself to weak math comprehension because of some missing “gene” for math! I don’t know how to pull it off, but Americans need a massive attitude change about the importance of learning math and the vital importance of personal effort in achieving this. We can play around with the curriculum; I hear Singapore Math is very promising, but real change won’t occur until more Americans take acquiring these skills and knowledges more seriously.
I don’t think it’s arrogance; I think it is ignorance. The same findings occur in NAEP: Asian, White, Black, Hispanic is the rank order of proficiency by group; the self-confidence is the reverse!
Americans aren’t exactly arrogant about math–just dismissive, as if it really doesn’t matter if they don’t get it because, after all, it’s just not that important. Math is only important to “geeks” and other “rejects”. My college student son, who majors in business at OSU, was shocked to learn that he needed to take three semesters of college calculus to APPLY to undergraduate business school! Not being a math wizard–unlike his old man–he blanched. After much struggle and plenty of expensive tutoring, he managed to pass. He says now that he wishes the necessity of studying math seriously had been more clearly communicated to him in high school. Lord knows, I tried, but what does your old man know?
You probably also subscribe, but I see some real possibilities in the complex/applied domain in Eureka Math — the examples are challenging tasks that get to the heart of the mathematics (as opposed to “recipes” that a student memorizes and follows).
Thanks for bringing this to my attention!
It would be nice to see a discussion of how the students who took the tests were chosen in different countries (e.g., with whom did PISA work in selecting these students). Specifically, here are two questions:
1. What were the determining factors for inclusion of the Shanghai-China PISA participants?
2. What were the determining factors for inclusion of the United States PISA participants?
Thanks Grant. Will try this asap.
Modified for the 8th grade mind, feel free to pillage: https://goo.gl/SsT8om
It seems like folly to compare the US education system with 50 states, 14,000+ school boards, competing political agendas, a belief in educating, or at least testing, everyone, with countries that are much smaller, with tracking, with a common curriculum, or programs that focus exclusively on testing ( I have been in Shanghai 6 years). The emphasis on rank is no different than the parents that I see that are more interested in comparisons than in the strengths and needs of their particular child. US education takes a beating in the US, but where do international parents want to send their students? To American curriculum schools.
This a difficult problem because we know at least two things from this (hopefully). We know that other countries “play the system” and this is well documented. Some of the countries are also very homogeneous and quite small in comparison to the USA. And please, don’t try to convince me that Sweden, Norway, Finland, etc are more diverse than the US, Russia, UK, etc.
We also know that we do need to improve. The hard part is not getting too defensive about our own (USA) position. We do have room to grow and should have high expectations and a good debate as to how to reach those expectations. I just think we really need to take the scores in context and make it more of what we in the USA need to do and frankly not worry too much about the other country’s games or how we rank according to them. This reminds me of the old USSR Olympic teams that were amateurs, but their full-time Army job was to play sports. It’s hard to measure apples to oranges.
I don’t put much stock in the rankings, but the failure to perform at the higher levels is the key issue. Many of our kids could not do the sample task I posted – and, note, their comment about alignment of PISA with Common Core.
A problem is doable, and therefore assigned, if the teacher deems it doable. Perhaps our teachers find these problems to be “too hard.”
For sure. That’s why we have to rethink what we mean by curriculum and assessment vs. grading whereby we entice teachers and kids to take on interesting challenges without worrying that initial efforts will be graded very low.
Perhaps the teachers do think the problems are too hard. This can be disappointing though if we consider why mathematicians love mathematics, it is the challenge of solving a difficult problem. According to Stanford Professor, Jo Boaler, “One clear difference between the work of mathematicians and schoolchildren is that mathematicians work on long and complicated problems that involve combining many areas of mathematics.” When we deny children the opportunity to struggle to solve a challenging problem, we are denying them the beauty and art of the subject of mathematics.