Alysia Krafel -- Suki Glenn -- Susan Carpenter
Pattern Press Philsophy on Education
Pattern Press is a company which produces books about elementary mathematics. The authors have had a wide variety of experiences in the field of education. They have taught in public schools, private schools, alternative, tutored children, and one has a charter school for teaching natural science and math, and homeschooled her children.
The three authors were all teachers at the University of California, Irvine Farm Elementqary School during the time Professor Michael Butler was the director. The Farm School , a research and development lab school for over thirty years, has observed how children learn and can learn better. The philosophy of the school is based on the insights, ideas, and teachings of Professor Michael Butler. Many teachers have contributed to the development of a mathematics program which aims to teach children to think like mathematicians, not just memorize some of the things that mathematicians have found out. Children "do" mathematics from the beginning, so there is an emphasis on inquiry and discovery, on invention, and on learning what genuine understanding feels like and how to achieve it. The materials are drawn from an array of published and unpublished sources and have been refined through practice with children.
We want children to learn to "do" mathematics. Related goals include the habit of solving problems several different ways and verifying answers to problems; knowing what it feels like when you understand (which often is accomplished through "Ah-ha" flashes of insight); knowing what it feels like not to understand and what to do then; loving learning; and, enjoying math. Using these techniques will help students learn perseverance and how to push through feelings of uncertainty and frustration.
These goals are accomplished by using many tools. We want children to create their own methods for solving problems. Concrete materials are used for students to build models of their inventions. Additional ways to achieve these goals are to have students make up problems, estimate and predict, look for and discover patterns, develop flexibility in thinking, use different methods to verify answers, learn about and use kinds of relationships, and pursue their own mathematical investigations. And above all else, we want them to have fun learning.
What do mathematicians do? They are good at constructing models, looking for number patterns, and using those patterns to develop reliable procedures for solving problems. The procedures we all use to add, subtract, multiply or divide were created by mathematicians who generalized a physical reality to an abstract mathematical formula. They invent short cuts and easy recording systems (like place value) and then teach them to all of us.
The skills of a mathematician can be developed in children by allowing them to use manipulatives to build models of the physical reality of addition, subtraction, or whatever subject with which they find and use patterns, and then create their own procedures for doing arithmetic operations. If children are given the chance to discover the procedures instead of being told how to do it and then drilling it in, you will find the results superior, the learning more of an adventure. You will have experiences of delight as your young mathematicians surprise you with methods and models you have never seen.