Recently I started working with a new student, a seventh-grader who was in the regular level of math. Although he had been getting solid B’s all year, he complained to his parents that he was having difficulties and he sensed that there were gaps in his knowledge that were not being addressed systematically in the class.

In our initial work together, it was easy to confirm his suspicions. During our first lesson, he brought a sheet from school with 8 problems to work on as part as review in preparation for the annual state math exam. Although he knew something about how to do each problem, he was able to get only one correct without any help.

It’s really no wonder that he did so poorly. He doesn’t know all of his multiplication facts, he didn’t know how to divide fractions, he can’t read decimal fractions with place value (i.e., say that .014 is fourteen thousandths), he doesn’t know how to do any arithmetic with decimals, and he doesn’t understand the relationship between fractions, decimals, and percents. These are all topics that were covered in his 5th and 6th grade math classes, but he had not yet mastered them.

One of the sad lessons we can draw from this situation is that this student’s course grades did not accurately reflect his mathematical abilities. And this student is hardly unique. We can see how common this situation is when we examine the passing rates of students on state exams and international assessments. In New York, for instance, statewide, the 3rd through 8th grade passing rate on the state assessment was about 39%. But we can be sure that relatively few of the 70% of the students who didn’t pass the exam were given failing course grades. (I know that there are many legitimate criticisms of the state tests, but we can find many other evaluations that call into question the validity of the grades students receive in their courses.)

The problem, clearly is that in so many classrooms and so many schools many students do not have the opportunity to master critical tool skills. Moreover, the curriculum, or at least the classroom assessments, compound the problem of these deficits by obscuring or ignoring them.

States have expended tremendous effort to prepare elaborate sets of standards for each grade, especially in the areas of reading and math. There are some problems with many of these standards (the gobbledygook factor is quite high), but even when they are precise and clear, they are of little use if students are moved on to a new set of lessons even when they are not yet able to perform the skills just covered fluently.

I invite you to share your thoughts on this topic.

Happy Teaching!