A witty Frenchman once said, “All generaliza tions are fa lse, including this one.” What follows is a discussion of a generalized model of mathematics teaching and its relation to problem solving. I find this model useful because it supplies a framework for problem solving in a regular classroom setting
Mathematics education suffers from a condition that resembles schizophrenia. One of its personalities is exhibited in the day-to-day realities of classroom learning; another is evident in journal articles, in-service presentations, and other such forums where educators present alternative realities of learning. For the purposes of this article, these personalities will be labeled, respectively, as the practice and theory of mathematics education. This article focuses on the latest form of the theoretical personality of mathematics education, constructivism, by asking what is constructivist learning theory and what does it imply for the practice of learning mathematics?
George Gadanidis and Janette M. Hughes
Children's literature and the dramatic arts can aid students in communicating mathematical understanding.
George Gadanidis, Janette M. Gadanidis, and Alyssa Y. Huang
Sometimes Missing in Mathematics classrooms is mathematical humor, which might alleviate the tension that many students experience. Also needed are opportunities for mathematical insight, through which students might sense the pleasure of doing mathematics. Humor and insight have many similarities. Both are creative acts. Both emerge from our predisposition to explore and take pleasure in novel ways of seeing and understanding our world. We are drawn to apparent dissonance, to seek to understand complexity, and to make ourselves more complex; these elements often produce positive feelings and all can be a part of both humor and insight.
George Gadanidis, Janette Hughes, and Marcelo C. Borba
What if we take the view, as an elementary school teacher once noted, that mathematics “can be discussed with your family and friends just like you would a favorite book or new movie”? (Gadanidis, forthcoming).