Cathy Seeley on achievement differences and the math curriculum

In "Doing the Critical Things First," Sharon Griffin describes critical elements in the development of mathematical proficiency in young children, and she identifies issues central to the education of every citizen beginning before kindergarten. However, I might respectfully suggest that this article addresses only part of the challenge of educating every child in mathematics. One of the greatest challenges society faces is the unequal education of children and resulting achievement differences. As Dr. Griffin notes, affluent children are more likely to bring experience with games and language that give them a head start in school. This problem needs to be addressed early by educators, but also by society. Providing strategies for making up differences may be helpful. But even if a student can make up a deficiency, it is difficult to judge the lasting impact on a student’s attitudes and confidence when the student has missed important informal experiences.

I strongly agree with the observation that in the United States, we try to address too many topics at each grade level. Because of different state standards and tests, textbooks may be packed with material not relevant to a cohesive approach to mathematics. Dr. Griffin appropriately (in my biased view) identifies the National Council of Teachers of Mathematics’ (NCTM’s) recently released Curriculum Focal Points for Prekindergarten Through Grade 8 Mathematics as a major step toward resolving this problem.

As Dr. Griffin points out, teachers need adequate time and expertise to develop fewer topics in far greater depth than we see in many classrooms. NCTM’s position statement, "Math Takes Time," calls for schools at all levels to allocate 60 minutes a day for mathematics. While simply allocating more time is not enough, it is difficult to provide the kind of rich development of number that Dr. Griffin describes without both allocating more time and using that time in more focused ways.

Finally, in addition to number, young children also need to develop notions of space, shape and size, as described in NCTM’s Curriculum Focal Points. For some time, American students have not performed well in geometry and measurement compared to their international counterparts. Recent efforts to improve instruction in these areas are beginning to pay off. We can now find evidence in some American classrooms of effective teaching that not only develops number sense, but also geometry and measurement, while still focusing on teaching fewer topics in greater depth for better understanding and proficiency.

Schools indeed need a cohesive, coordinated approach to teaching mathematics from preK-12. This is not likely to occur until school systems tackle issues of coherence and depth, until they make hard choices about what to teach and what to leave out, and until they redesign testing systems so that they do not encourage superficial coverage of too many isolated bits of knowledge.

Cathy Seeley is the immediate past president of the National Council of Teachers of Mathematics and a senior fellow at the Charles A. Dana Center of The University of Texas at Austin. She is a mathematics educator with over 35 years of experience working with students, teachers and future teachers at the elementary, middle and high school levels.