Everyone's an expert, it seems, not so much on the math necessarily, but on the best remedy. (Ontario students didn't do so well.)
This article from the Globe and Mail discusses the problematic "new math", often painted as less formal in structure...
"The OECD report noted that the top performers had more exposure to formal mathematics, algebra and geometry than the word problems used in “discovery learning,” which advocates that children can learn math more effectively when they are given opportunities to investigate ideas through problem-solving and open-ended investigations."
As someone keenly interested math education, especially at the elementary level, I am troubled by comments like the one above because it implies that a problem-based approach to teaching math is inherently inneffective in providing a rigourous mathematical education.
I would argue that the problem isn't so much the pedagogical approach itself, but rather the way in which it is manifested in a classroom. Many teachers know the words "constructivist" and "problem based", but -- in addition to lacking confidence with the math itself -- they may lack a firm understanding of the theory behind these terms and practical experience in implementing these approaches effectively.
This doesn't necessarily mean that problem based learning is a bad thing in and of itself, but rather perhaps suggests that teachers need to develop strengths and confidence in this area in order to teach math more effectively, incorporating both the mathematical skills and the broader learning skills into a rich, holistic program.
After exploring a quote from John Van de Walle, on how we teachers cannot "think for our students", one teacher commented that "if we can provide opportunities for our students to discover math truths, that will be more valuable and far reaching for them" than the skill and drill and kill model.
Of course, in order to provide said opportunities, teachers must be both masterful facilitators and knowledgeable math teachers.
The truth is that teaching is complex! And the average teacher -- even a very committed "average" teacher who takes the odd PD workshop -- has a wee bit (or more) of math phobia. This was confirmed in tonight's session, where several teachers "blanked out" and "shut down" (their words, not mine) when confronted with fairly typical math word problems incolving proportional reasoning and unit rate at about the Grade 4 level.
More rigorous mathematical instruction for pre-service teacher candidates is perhaps a critical componant. (I shudder to think how little I understood about even basic mathematical concepts when I graduated from Teacher's College nearly two decades ago!)
Still, being "good at math" is not enough.
If we don't equip our students with the tools for critical thinking and encourage them to develop a growth mindset (Carol Dweck), then those who struggle with math may give up rather than persevere with mathematical challenges. Taking the time to teach students "stick with-it-ness" as well as specific mathematical tools (how to draw an effective picture to model mathematical thinking, for example, or, how to ascertain when something "makes sense") will help those students who are not rote learners to stay "checked in" in the math classroom.
(Of course a reasonable depth of mathematical understanding on the part of the teacher is vital in order to be able to do this effectively.)
If we want students to fluently rattle off facts they have memorized but with minimal understanding or ability to apply, then we should "return to the basics" as some in the article mentioned above insist, and focus on traditional skill-based, rote-only teaching. But if we want our students to "learn to think and think to learn", then we had better inform ourselves about the math, AND ALSO nurture thoughtful communities, frame critical challenges, teach intellectual tools, and assess thinking and performance.
The recipe for solving the disappointing PISA results problem includes two main ingredients: A more solid foundational understanding of mathematics for teachers, and a deep comprehension of how to effectively teach critical thinking in the classroom.
Both are needed if we are to effectively educate students for success in the 21 century.