Not everything that can be counted counts, and not everything that counts can be counted.

What do you do when you call out the number three hundred and five and a child in the third grade writes 3005? Of course, the first time one sees it, one prays that it is a simple mechanical error so one tries again and again. Eventually it becomes clear that this is a conceptual error and the child has no understanding whatsoever of place value.

Observing a class on place value in some schools is a dreary prospect and I don't blame the children for not getting very much out of it. Essentially, in the very first class of the unit, the teacher walks in, writes U, T, H on the blackboard from right to left and begins to call out numbers. In most situations, she will probably call out the number very slowly three or four times, hoping that a child who is unable to properly arrange the number the first three times will somehow be able to do it the fourth time. Explanations are inadequate and the use of probing questions to elicit logical reasoning is an unheard of technique. Concept building does not occur at all early on which makes for a pretty unsteady foundation on which to explore more complex topics.

But, from a teacher's perspective, what do you do when you are made to teach mathematics when you are most comfortable teaching English? What do you do when you are overwhelmed with the inordinate pressure of getting first and second grade students to score high marks on tests when you barely understand the material yourself, never mind understanding how best to assess students. How do you prepare a lesson plan or teaching aids when you barely have the equivalent of one class period a day to plan for your seven classes the next day? And, given all of these other constraints, how can you teach when you do not understand that problems involving arithmetic operations are not the concept, they are merely a tool to exemplify and reinforce a concept?

I wish I could say that this situation is rare and is rectified as soon as it is noticed but it is not. I struggle with this everyday because instinctively, my first thought is for the children. It is heartbreaking to walk into a classroom and watch these kids who are so desperately hungry to learn being numbed into silent boredom. However, it is equally if not more painful to watch a grown woman fumbling while teaching place value to a class of six year olds, despite having a detailed lesson plan and elaborate, albeit misused, teaching aids which took all night to prepare.