Ten Resolutions for Mathematics Teachers Dan Kennedy Baylor School Chattanooga, TN Dkennedy@chattanooga.net "Despite the dramatically increased role of mathematics in our society, mathematics classrooms in the United States today too often resemble their counterparts of a century ago." Helping Children Learn Mathematics National Research Council "Many of us can remember when a firm tradition decreed that college mathematics should consist of the sequence: College Algebra, Trigonometry, Analytic Geometry, Differential Calculus, Integral Calculus, Differential Equations, Theory of Equations, Advanced Calculus... ...That old structure, which comfortably regulated college mathematics, has fallen apart." A General Curriculum in Mathematics for College MAA Committee on the Undergraduate Program in Mathematics, 1965 "Currently, the greatest growth in the high school curriculum is in courses that have traditionally been taught in colleges. The greatest growth in the college curriculum is in courses that have traditionally been taught in high schools. It is not clear that either institution is serving its clients very well." Dr. Bernard Madison, Chair of the MAA Task Force on Articulation, 2002 "My Ph.D. is in mathematics; by most standards, I was very 'well trained.' Nonetheless, the mathematics education that I received was in many ways impoverished." -- Dr. Alan Schoenfeld, Reflections on an Impoverished Education, from Mathematics and Democracy: The Case for Quantitative Literacy, NCED 2001 "The problem is, this is such an unusual country." -- Jan de Lange, Director, Freudenthal Institute for Teaching and Learning, Utrecht, The  Netherlands Resolution 1: We must find ways to teach real mathematics to all our students. We must not send the message that some students can not succeed in mathematics. We should not allow, let alone encourage, students to walk away from  mathematics. Success in my course should not depend on success in other courses. Resolution 2: We must assess what we value and value what we assess. Resolution 3: If our students can succeed, we must not fail them. Assess students often. Use a variety of assessments. Scale grades to keep all students "in the game." Ignore those comments about "self-esteem." This is about teaching students. Resolution 4: We must avoid doing all the mathematics in our own mathematics classrooms. Watch students solve problems. Let students see students solving problems. See how much the students can figure out without us! The Dangerous Instinct: "They don't understand this. How can I explain it more clearly?" A Better Instinct: "They can figure this out. I just need to ask the right question." Resolution 5: We must encourage healthy collaboration among students. Collaboration is good for business. Collaboration can homogenize a classroom. Collaboration lets the teacher share the responsibility for student learning. Collaboration overcomes the nerd syndrome. Resolution 6: We must make peace with technology. Technology is here to stay. Technology does most computations more quickly and reliably. If we understand the first two points, it will affect the way we teach. If students understand the first two points, it will affect the way they learn. Resolution 7: We must succeed despite our textbooks. This is such an unusual country. There is too much in your textbook for your students to learn. If you understand every problem in your textbook, it probably isn't much of a textbook. Resolution 8: We must succeed despite our politicians. This is such an unusual country. Resolution 9: We must make students show all their work all the time. We must value correct mathematics more than we value correct answers. We must let our students know it. What we don't see can hurt our students. Good math: Bad math: Good algebra: Bad algebra: Bad higher mathematics: Resolution 9 Corollary: We must not tolerate sloppy mathematics. Ever. As calculators are used more, students are writing mathematics less. Multiple-choice tests are too forgiving of sloppy mathematics. Assess what we value... Resolution 10: Have fun. Learning is enjoyable. So is teaching. Any other philosophy of teaching and learning is counterproductive. Even in mathematics.