So why have a child study algebra as early as 3rd grade? – or as early as 1st grade in a longer program of study (as I did in the 1993-94 school year)? There are several sound educational and mathematical reasons.
First, arithmetic too often gets focused on the many different individual procedures. This detail-oriented emphasis on the myriad of different arithmetic procedures reinforces the notion that arithmetic is merely and only a collection of a whole lot of particular procedures. Too often, all these procedures seem to be just a collection of disconnected, unrelated rules to memorize. With year after year of elementary math focusing on arithmetic procedures, too many students have trouble seeing the wider forest of mathematics because all the trees (of individual arithmetic procedures) are in the way. What is needed here? Precisely the very thing in SAI that ties directly to the second reason for studying algebra at an early age.
This second reason is this: it is so helpful to also study what unifies and connects all those different arithmetic procedures. This is precisely what algebra reveals – especially if taught in the way we teach algebra in SAI.
In arithmetic, the focus is on individual facts like 8+1, 9+7, 5+3, 2+10, and 4×6, 3×9, 6×5, etc. In algebra, the focus is on the general case of x + y and a•b. What’s needed for math mastery is both the individual particulars of arithmetic as well as the broad generalities of algebra.
This unity between arithmetic and algebra is especially revealed by how we teach algebra in SAI. One very exciting aspect of SAI is that we have identified a handful of broad, practical principles that are kid-tested and adult-friendly. These principles – these “grand ideas” of math – turn out to be extremely helpful in assisting kids from an early age to see and experience the unity between arithmetic and algebra. Experiencing this unity at an earlier age will help your child have a smoother transition from arithmetic in grade school to algebra in middle school – and higher math in high school.
This is why we make a point of saying that SAI is not just for the gifted and talented. Learning the connectedness between arithmetic and algebra is helpful for students of a wide range of abilities.
We hope to see you and your child at SAI this summer!