The Architecture of the Mind
By Peter W. Cookson, Jr.

Most of us know that there is a math crisis in American education. In elementary school our students seem to do as well as other students around the globe, but by middle school there's a very sharp decline in math achievement for too many American students. This crisis is not simply academic, it's also cultural and economic. In a world where mathematics is applied to problem-solving in fields as diverse as computer science, medicine and architecture, a high school graduate who is not numerically literate will find him or herself increasingly marginalized, particularly in the workplace.

The minds of babes
Mathematics is far more than arithmetic; it's part of the architecture of the mind. For over a century, cognitive psychologists have tried to unpack how children and infants think. There was a time when psychologists thought of the mind as a "blank slate," but we know from research that the mind is far from being a blank slate at - and most likely before - birth. The brain from which the mind springs is a highly sophisticated and discriminating instrument of sense, thought and feeling. Contrary to psychologist William James, who nearly a century ago described a baby's mind as a "blooming, buzzing confusion," today's developmental psychologists, such as Elizabeth Spekle at Harvard University's Laboratory for Developmental Studies, now believe that mathematical reasoning is part of the architecture of the mind from the very beginning of life. In her work, Spekle and her colleagues found that babies as young as six months can reliably distinguish between displays of eight and 16 dots and can do a kind of addition and subtraction when objects are added or taken away. Babies understand that the world is a real place and they are able to make predictions about the world at a surprisingly early age.

Math phobia
Math phobia is something that we have socially constructed by teaching math in destructive ways. Most math courses tell students that there is such a thing as "mathematics" and their job is to understand it more or less without question. For many students this is an overwhelming experience; when students feel overwhelmed they resist and reject learning.

If Spekle and her colleagues are right, all of us are capable of mathematical reasoning even if we can't grasp the finer points of advanced mathematical strategies such as calculus and trigonometry. What this should tell us as new teachers is that we may be looking at our math lessons through the wrong end of the pedagogic telescope. Rather than starting with a defined content, we should utilize an inquiry method that allows students to utilize their innate abilities. I know that many poor math students are outstanding students in shop. Carpentry is the application of math to physical objects; why can't a student who makes a beautifully proportional chair not also grasp algebra? Where have we failed?

Making math real
As a new teacher you have the opportunity to give your students the freedom to exercise their natural mathematical abilities. The best step in making math real is to use actual materials for students to work with: different-sized blocks for young children, different shapes for emerging mathematicians, etc. As they develop, students can build complex mathematical relations by using physical objects to represent different quantitative values.

Learning logic
One of the key reasons to master mathematical thinking is that math teaches us to think simply and eloquently about relationships and to think probabilistically. We live in a time when too many people define social reality in absolute terms, when the real world is constructed on probabilities. The physical and non-physical world is best thought of in terms of infinite shades of gray, rather than black and white. Mathematics helps us to understand that the law of numbers actually works, but the law of numbers is not like the Ten Commandments. It requires a tolerance of ambiguity and a willingness to admit error.

So, as you think about math in your class, I hope you'll help students understand that mathematics is about relationships, probabilistic thinking and clarity. If a student can understand the logic behind an equation, she or he is prepared to think in quantitative and logical terms for the rest of her or his life and to apply that thinking to a whole variety of analytical challenges that require critical thinking based on logic and probability.

Our greatest educational hope
All this may seem a little theoretical for teaching students in elementary and middle school. This approach, however, is very practical because our current way of teaching mathematics intellectually disenfranchises hundreds of thousands of students every year. This waste of talent is a personal tragedy for students, but it's also a social crisis because the twenty-first century will require more, not less, mathematical literacy. Those who are illiterate in math will find themselves increasingly on the margins of the economy and society at large. Mathematical thinking is one building block of the open, adaptive mind - the creation and cultivation of which should be our greatest educational hope.

Peter W. Cookson, Jr. is the founder of TCinnovations and the Dean of the Graduate School of Education of Lewis & Clark College. He is also founder of the Center for Educational Outreach & Innovation at Teachers College at Columbia University.

January, 2007, Vol.37, No.4