In last week’s EdSurge, Jeremy Kun pointed to a very real problem—the quality of mathematics to which an average American K-12 student is exposed. He is hardly the first to notice this problem. He is following in the footsteps of mathematicians such as Paul Lockhart, Hung-Hsi Wu and Keith Devlin. The basic observation that the intellectual challenge in secondary American classrooms is substandard is borne out by the research work in the TIMSS video study, published in The Teaching Gap by James Stigler and James Hiebert.
So Mr. Kun has identified an important and real problem. Unfortunately he seems to think the solution to this problem is quite simple:
“[I]f you give me an hour with a group of disillusioned but otherwise motivated high school students, I can teach them more mathematics than they have ever done in their entire lives. I can give them a dose of critical thinking and problem solving like no algebra problem can.”
But a one-hour lesson is not a real solution to this problem.
I am delighted to know that Mr. Kun engages in the service work of K-12 outreach, and I hope that he is as open to learning from his K-12 collaborators at least as much as he hopes they will learn from him.
Having agreed that there is a problem, I propose some ways to work on this problem, and invite Mr. Kun to join the conversation as a humble and valued participant. Those of us working hard on improving U.S. mathematics education are doing so in the following ways.
By educating ourselves on the existing work of others
Mr. Kun would likely be surprised at the intellectual demands placed on K-12 students in classrooms where quality curriculum is in place, and where experienced teachers expect understanding and careful thought from their students. Whether these are comprehensive packaged materials—such as Connected Mathematics at the middle school level, or The CME Project at high school—or supplementary materials such as Mathalicious, there do exist excellent materials to support deep and rich mathematics learning.
There is also excellent research on the kinds of teacher practice that support this kind of mathematics learning. The ongoing TIMSS video study mentioned above is but one source. Jo Boaler has been doing excellent work on supporting real mathematics learning. The research results of the Cognitively Guided Instruction project at the University of Wisconsin are foundational for understanding the relationship between how children think and how to design instruction at the elementary level. Robert Moses insists that we settle for nothing less than rich, connected mathematics knowledge for all students.
To characterize high school mathematics education as “a farce” (as Mr. Kun does in a blog post where he describes an excellent lesson he has done with high schoolers) seems dismissive of the dedicated work of many who have gone before. If we are going to participate in solving a systemic problem, we have a responsibility to learn about its origins, and about solutions that are currently proposed.
By understanding the unique offerings we each bring
Mr. Kun brings mathematical expertise to this conversation; I encourage him to share this and I assure him it is necessary and valued in schools. But he does not seem to grasp the constraints of the system in which this problem resides. He would do well to ask the teachers in whose classrooms he works what they know about engaging those who are not “otherwise motivated”, and about how they deal with the challenge presented by a student who is a computational whiz but does not want to be asked to think.
Examples of teachers working through these kinds of questions as a community abound on the Internet. The #MTBoS hashtag on Twitter, together with the various education chats there (e.g. #msmathchat, #alg1chat, etc.) are examples of place where we can learn about the challenges and rewards of public school teaching. In these conversations, and on the blogs of teachers who participate in them, questions of content and pedagogy are hashed out daily as individual teachers create professional learning networks and seek to improve their work. Participants welcome people with diverse expertise.
But Twitter can be time consuming and distracting, of course. Closer to home, spending a day with a practicing teacher can be remarkably educative, and it can go a long way towards building a professional, reciprocal relationship.
When we acknowledge our strengths, we implicitly acknowledge our weaknesses as well. This opens us to the idea that we may learn from those whom we initially sought only to teach.
By questioning our assumptions
There are two important assumptions in Mr. Kun’s piece that deserve questioning. First is that the relationship between disciplinary knowledge and school subjects is uncomplicated. Mr. Kun claims that his Calculus students have done virtually no math, despite having been enrolled in “math” courses for many years. Should we only teach graph theory—and not fraction computation—in courses titled “math”? What exactly is the right content for K-12 math courses? Or should we just use a different title for these courses, since we are not teaching “anything close to math” in them?
A second assumption worth questioning in Mr. Kun’s piece is that the responsibility for the problem he identifies lies mainly with the K-12 math teaching community. A brief examination of the placement tests that form the gateway to entry into Mr. Kun’s (and my own) Calculus courses will reveal that the very things he decries are what students need to master to be deemed college ready. Indeed, my own institution (and we are not alone) has experimented with offering a placement-test preparation course. In such a course, high school seniors work on the algebra skills—and only the algebra skills—that will prepare them to score well on the placement test. In short, colleges are complicit in the curriculum and instruction problem we are talking about.
When we seek to solve a problem, we need to keep an open mind about its causes, and about potential solutions. We need to question our assumptions in order to be sure that we (to quote George Polya) understand the problem.
I sincerely hope that Mr. Kun will take me up on the offer of deeper engagement with improvement efforts in K—12 mathematics learning. Judging from the lessons he has written up on his blog, he has plenty to offer, and the connections between K-12 and college badly need strengthening. I hope, too, that he can become a leader among his mathematician colleagues—a champion for spreading the research and curricular insights in the field of mathematics education. I hope these things because the problem he identifies is real, and because the work of solving this problem is extremely difficult.