The Math We Need to Know and Do in Grades PreK-5: Concepts, Skills, Standards, and Assessments Book

Mighton proposes an unusual practice in the current how-to-teach-math climate: teach kids (who have fallen behind) how to get the right answer first, then let the confidence and intuitive math ability in them make conceptual leaps. I would be skeptical, but his method is the product of day-in-day-out teaching math to failing kids in his tutoring program, JUMP. This program has brought over a thousand under-achieving math students up to or ahead of grade level. And he is absolutely right in his main tenet: break math down into SMALL steps. His book provides familiar examples of ways a certain math problem is typically taught, in which several steps are combined into one step--and in which each sub-step goes unexplored, unacknowledged, even. In such cases, the student gets lost but has no map to point to where exactly she got off the train. In this aspect, I think Mighton is ON THE MONEY.

This book is not a general criticism, though. It has outlines of very specific teaching techniques and ways to organize worksheets, etc. This is particularly useful advice for teaching a room of 25 kids at different levels the same material, a challenge inherent to classroom teaching.

His other great PRACTICAL points include teaching concepts with numbers low enough to be manipulated comfortably. If your student is okay with times tables for 2, 3 and 5, but not 6 or 7, don't teach multiplying and dividing fractions with numerators and denominators other than 2, 3, and 5. His recommendation is to have worksheets A, B, and C. Sheet A only uses 2, 3, and 5. Sheet B has 4, 6, and 7. Sheet C has 7, 8, 9, etc. And if your student is still struggling with the higher numbers, but DOES have the arithmetic to do the fraction operation, get him going on Sheet A. Mighton believes that when a kid starts to be successful at math (for the first time in his life!), he'll get the confidence to master the higher numbers. This will lead to the work effort that catches him up with his peers on worksheet C. I don't think this is liberal wishful thinking because the man has done his time in the classroom, and as idealistic as this book sounds, it also reads like someone who earned his stripes in the trenches of the classroom. His techniques AND observations about student behavior do coincide with my own experience as a teacher of kids who have fallen behind.

Another major point of his, which I have felt deeply but rarely heard expressed -- is WHY TEACH EVERYONE MATH. He criticizes the notion that math opens up certain fields of study or other practical uses, and therefore, this is why it's important to study. He compares facility with numbers to appreciating a sunset or the view from a mountain, or the delight of painting. We wouldn't take paint brushes away from half the 6 years olds in Kindergarten because they just didn't have the ability to fully appreciate the joy of paint. We wouldn't discourage a kid with no apparent "sunset talent" from admiring a sunset. But by assuming that math is for some and not others, we cut many children off from a major source of beauty in the universe: math. For this point alone I think the book should be required reading for all educators and parents.

I'm on board.