Since Real Change recently presented the views of UW Atmospheric Scientist Cliff Mass on mathematics education ["Storm Front," May 20-26], I would like to take the occasion to present some contrasting views held by a number of mathematicians in the UW Mathematics, Applied Mathematics and Statistics departments, as well as among education researchers in the UW College of Education.
For a start, the interview references Seattle Public Schools' recent selection of a new standard math text on the basis of a recommendation made by a committee of teachers, parents and community members who had put in many hours of study and discussion.
The one selected has plenty of solid mathematical content in a format that is quite different from textbooks written a generation ago. The most telling argument presented in its favor was that teachers from the full range of teaching philosophies felt they could teach from those texts, whereas the alternative supported only traditional teaching. Teachers need and deserve every kind of support we can give them; the more we avoid asking them to teach from a textbook they are actively at odds with, the better off we'll be. No textbook can make all teachers happy, but it sounds as if this one comes close for many.
Closer to home for me and a number of colleagues in the Mathematical Sciences and Education Dept. is the statement by Mass that "The basic tenet of [Constructivist Math] -- and it's completely unproven -- was that the only way kids can learn a math principle is by discovering it themselves." This description of our "basic tenet" is far enough from the truth to be barely recognizable. And while his statement that it is "completely unproven" may well apply to what he claims we believe. Several decades of highly respected research support the actual beliefs that many of us share.
Mass is not alone in misinterpreting the constructivism that underlies a lot of what we do. It does indeed have to do with viewing knowledge as something personally constructed rather than externally imposed, but how that construction can be induced varies widely with the knowledge and the constructor. I did some heavy-duty and very effective constructing of complex variables while making sense of the notes I had taken in a warp-speed lecture. My granddaughter is constructing the concept of orientation as she works with her wooden puzzle pieces.
The corresponding view of the job of a teacher is that it is to set up a situation where the student is motivated to take his or her existing knowledge and use it to develop specific new knowledge -- which is a lot tougher proposition than working an example and telling students to imitate it with minor variations 15 times over.
There are few things more intellectually exciting than actively engaging with an idea. Babies do that full-time (except when sleeping!) -- and look at the amount they learn in their first few years. And there are few things deadlier than being told to park your brain outside the door and do what the teacher tells you to do. This is what became the model of mathematics teaching in the U.S. over many years, which in turn is a major cause of the self-perpetuating societal rejection of mathematics.
How do you fix it? Not instantly, and not in one prescribed and flawless way. But fix it we must. That's what many of us have been trying to do since the '90s, and where we will continue to invest our time and energy and talent.
It is good to see mathematics education being taken seriously and discussed. My hope is that the discussion will extend to