Doug McKenzie Upper School Math Teacher and Department Chair E-mail:
Telephone: (805) 969-7732 ext. 317 I came to Crane in 1989 as a science and math teacher, but I eventually dropped the science and became math full time. Crane has shaped me over many years, and I am grateful to the colleagues who, in addition to helping me grow as a teacher and advisor, also encouraged me as I learned to ride a unicycle and play bass guitar. I love doing mathematics and I love teaching mathematics. I am dedicated to making the subject accessible to as many students as I can, and I really enjoy refining a lesson so that the students can discover relationships and rules for themselves. I have been a California resident all my life, except for a fall and spring in Boston. I received a B.S. in Geology from Stanford University and a single-subject teaching credential in the physical sciences from UC Berkeley. Before Crane, I taught environmental education in Massachusetts and California. I attended and led workshops at the CA Math Project at UCSB, and regularly attend conferences and curriculum training in mathematics.
Looking for a puzzle? Here are some great sites. Be sure to support the ones you like that take donations. Some are run by hobbyists.
Sudoku, Bridges and others - Logic puzzles in the Japanese style that you can play on line. Look at the bottom of the page for the different puzzle types.
Meffert's - A great source for the moving puzzles we have in my classroom
Columbus State University Problem of the Week - We use this site as a source for problems of the week... these are challenging, worth thinking about for a while. If you are working on one, come tell me about it!
More about Hypercubes and the 4th dimension
Hypercube at Wikipedia - Some great pictures and links to other sites. Look at the animation near the bottom.
Hypercube: a 4d game - Give it a try... my best so far on the 3d version is -30!
7 Pre-Algebra 6 Mathematics
Geotiles People sometimes say that math builds on itself, and each skill is like a brick in the wall. Every brick has to be in place for the wall to be strong. I look at my set of math skills more like a toolbox, and I think of the training to use them like an apprenticeship. There are often more ways than one to solve a problem, and the choice of tools will vary from problem to problem, and person to person. Of course we do need to teach specific skills and techniques, but real mathematics outside the classroom is rarely pre-structured under chapter headings, or solvable with a recipe-like approach. We have to give students many, many opportunities to make sense of problems on their own, and to make their own choices about how to solve those problems. Without those opportunities, we perpetuate what we have now: millions of adults who, despite years of math education, say they can’t or don’t use math outside a math classroom. I encourage each student to think and reason about mathematics for him or herself. I believe that the students should be active participants in the study of mathematics, not just the recipients of rules and procedures. I want to encourage their growth as independent learners, and as explorers in the field of mathematics. 6th Grade: The students develop essential computational skills and practice them daily throughout the year. They use models and examples to deepen their understanding of the mathematical relationships among fractions, decimals and percents, especially involving the operations of multiplication and division. The students extend their knowledge of geometry and statistics. Most importantly, they develop algebraic habits of thinking, and familiarity with the symbols of algebra. There is an emphasis on mental math, and encouraging the students to develop a broader set of tools to handle computation. We play games together, and explore number patterns and topics like topology and number theory. I want students to learn mathematics, and I also want them to learn to think for themselves. Math is as much a field of invention and discovery as it is a collection of rote procedures. It may be a rare occurrence or a frequent one, but I want all students to have a chance, more than once, to say “Look what I figured out.” My hidden agenda is to encourage them to develop their own questions.
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