I asked John Mighton about his latest thinking on math teaching. JUMP (a non-profit math curriculum producer based in Canada) has been getting some traction in the USA. This is not a response to the NYT Magazine piece, just a general view as he watches discussions about Common Core re-trigger debates from the past few decades. Here's a 2011 NYT article about John's work.
So here's what John emailed to me:
There has been a great deal of debate in the media lately about which approaches to teaching math are most effective. The charity JUMP Math has gathered a great deal of evidence that a balanced approach, called “guided discovery,” can close the gap between students and help every student realise their full potential. In guided discovery, students are given many opportunities to explore and derive concepts on their own, but the teacher provides enough rigorous guidance to make sure everyone succeeds. (See JUMP's page about their research in Scientific American).
New research in education and cognitive science suggests that discovery based approaches are only effective when lessons are well scaffolded (for instance, when complex problems are broken into more manageable challenges), and when the teacher provides continuous feedback and frequent practice, and helps students with elicited explanations.
Teachers can only lead students to make discoveries if they have a deep knowledge of the material they are teaching. This means not only understanding the math itself, but knowing how to break challenges into steps, how to assess what students know, and how to take a different approach when a student is stuck. One way to help teachers develop this knowledge is to give them more professional development. However, with tight budgets and full schedules for teachers, school districts may not have the resources they need to help all of their teachers become experts in mathematical instruction. In a survey cited in the New York Times, teachers said they were concerned about delivering the new (and extremely promising) Common Core State Standards because they had only had four days of training.
Fortunately, there may be another way to help teachers become experts in math. Studies of the JUMP Math program suggest that teachers can develop a deep knowledge of math as they teach it, if they are given clear, detailed and mathematically rigorous lesson plans that embody the knowledge of expert teachers. (Emphasis MG).
In a randomized controlled study, teachers who followed the JUMP Math lesson plans were able to produce striking results after only two days of training: over a five month period their students progressed at twice the rate of students in the control group. (See the Scientific American articles mentioned above.)
In the future, teachers should certainly be given more opportunities to learn math at teachers college and through professional development. But teachers who would like to begin the process of learning the math they must teach now can find a complete series of evidence-based lesson plans for the Common Core at jumpmath.org. (To download the lessons for grades 1 to 6, just register on the website.)
The takeaway here is two things.
1. "Guided discovery" tries to find a useful middle ground in pedagogy. Kids are not totally lost with some fuzzy faux "figure it out" lesson, with cognitive overload. But nor is the teaching entirely "I'll show you a couple of find-the-hypotenuse problems, now you bang out 20 of them."
2. Instead of creating a utopian public policy ideal where we attract teachers with unusually high math aptitude, and then train them really effectively, so they can invent their own clever lessons -- utopian because none of the 3 things typically happens now in real life -- put the teachers we have now in a position to succeed through very prescribed curriculum. Does this approach reduce teacher autonomy to create whatever math lessons they feel like? Yes. But it creates a much higher "floor" for the kid experience. Often it creates more satisfied teachers, too. Less time to prep, more time to help kids.