by Ellen Mandeville
“Let no one ignorant of geometry enter here.”
– inscription above the gate of Plato’s Academy in Athens
The ancient Greeks believed that the universe was ordered upon logical, discoverable, mathematical theorems; and that discovering mathematical theorems gave humanity a view into the workings of the universe. Mathematics is foundational to all of learning in that it demands clarity of thought, develops logical thinking, inspires self-reliance in thinking, and trains students to think abstractly. (The Educated Child, pp. 279-280, by Bennett, Finn and Cribb)
Mathematical teaching must teach more than just the concrete stage of manipulatives and pictures. A solid mathematics curriculum must also incorporate the abstract nature of mathematics because abstract thinking is vital to living in the real world. Abstract thinking proficiency in mathematics leads to the ability to think abstractly in all of life. “Why should we want our children to work with such abstract notions? Because we want them to be comfortable operating in the world of ideas. Though ideas often have ‘real-world’ consequences, they are in themselves abstract.” (The Educated Child, p 279, by Bennett, Finn and Cribb)
I have been reading The Educated Child: A Parent’s Guide From Preschool Through Eight Grade, by William J. Bennett – former US Secretary of Education; Chester E. Finn, Jr.- professor of education and public policy at Vanderbilt University; and John T.E. Cribb, Jr. – formerly of the US Department of Education. I won’t pretend to be an elementary curriculum expert, because I absolutely am not. I am searching for analysis as to what does constitute excellent curriculum that prepares our children for adulthood realities. I write this post to share with others what I am finding in my research. In the “Mathematics” chapter of The Educated Child, the authors state on page 281 (emphasis in original):
There is an attitude in some schools today that goes something like this: ‘It’s not so important that students know theorems, equations, and definitions. They can always look those up. What’s important is that they understand the concepts behind them.’ All too often, this is just an excuse for failing to teach children fundamentals. Of course we want students to understand the concepts behind the symbols and equations. We want them to grasp how the Pythagorean Theorem works, not just be able to plug numbers into it. But educators who scoff at the notion of requiring children to remember that formula, have yet to explain the conflict between understanding a ‘concept’ and being able to recall the relevant math facts. The two are not mutually exclusive. More important, it has yet to be demonstrated that students can do math consistently, correctly, and comfortably without knowing fundamental terms, axioms, definitions. Doing math takes knowledge of math. It’s that simple.
We at Parents of Blaine County Students agree with these authors that there is no conflict between mathematical concepts and relevant mathematical facts. “The two are not mutually exclusive.” Bravo! to that, we say.
As Patty McLean stated at the Hemingway Elementary Parent Math Meeting, BCSD does not yet have a written Mathematics curriculum that has been approved by the School Board of Trustees. We want to see a comprehensive, integrated Mathematics curriculum that encompasses both mathematical concepts along with the relevant mathematical facts and plenty of practical application. Such a curriculum must be written so as to be accessible to students of all learning styles and must promote fluency of mathematical processes. Let us not consign our children to reference books and computational aids as crutches. Let us expect our children to achieve excellence and fluency in Mathematics, thereby facilitating excellence in their future academics, in life and in their inquiries to the workings of the universe.