THE MATHEMATICS CURRICULUM
The following sections give you an idea of what a good mathematics curriculum looks like from kindergarten through eighth grade. Your school should lay a solid foundation in arithmetic, geometry, and algebra, as well as related topics such as measurement, probability, and statistics. The knowledge and skills to be learned in these years do not come automatically to most children. They require frequent practice and sustained effort. If you do not see your child consistently practicing the rudiments outlined here-working sets of challenging problems on a daily basis-then do not expect her to be a particularly good math student.
As children learn about numbers and equations, they should gradually develop certain habits of mind. Above all, they should learn to think logically. Children should learn to scrutinize problems carefully; separate relevant from irrelevant information; and break large problems into smaller parts. They practice choosing the best approaches to solve a problem. They get in the habit of making precise calculations and expressing answers clearly in mathematical notation. In good schools, attention is paid not only to getting the right answer, but also to how you got it. That is, the aim is to make sure students understand (and can explain) exactly how they arrived at a solution. All of these lessons should be solidly embedded in your school’s math program.
Mathematics is a precisely structured field and its teaching should reflect this. Lesson plans should be carefully ordered so that students gradually build a base of knowledge and skills, beginning with the simplest and then moving step by step, topic by topic, to more complex ideas. It’s a bit like building a tower. Each new floor rests squarely on what has been constructed before. If the walls in the lower floors are weak, the building can’t rise very far. Consequently, math is not a subject that treats students kindly when they fail to master the early lessons.
It is important, therefore, that your school be able to show you a curriculum that indicates goals for each grade and proceeds toward them in orderly fashion. The goals should be specific, spelling out what your child should learn and do at each level. If your school presents only vague objectives such as “formulate and solve a variety of meaningful problems,” then you have reason to suspect that there is no coherent plan of study. What you may have, instead, are large gaps in the curriculum and a fair amount of needless repetition. That adds up to trouble.
The curriculum outlined here is excerpted from the estimable Core Knowledge Sequence (see page 100). Your own school’s curriculum may not look exactly like it on a grade by grade basis. No single “best” sequence fits all circumstances. In one school, students may begin adding and subtracting simple fractions in fifth grade. In another, it might be the sixth. The important thing is to satisfy yourself that your school’s curriculum is coherent, demanding, and covers the basic ground indicated here in a systematic way over the course of study.
One more word of advice, in case you are one of those people with “math anxiety.” Take a deep breath. Sit back and relax. It’s okay that you may not understand all of the terms and concepts that follow. Perhaps you did once but have forgotten some of them. (We’re with you.) You need not grasp every word to make use of these grade by grade summaries. Even if some of it goes over your head, these lists can still help you determine whether your child’s school is offering a quality math curriculum. You can look at her textbooks, tests, and homework assignments to see if topics, lessons, and problems resemble the listings here. You can ask your child questions about some of the terms she’s studying and observe whether she responds with confidence or just scratches her head. You can talk to the teacher and simply ask, “Will my child learn to solve basic algebraic equations this year?” even if you’re not sure how to do that yourself. Be honest with the teacher. Let her know that even if your own math skills are rusty, you still want to do your best to gauge the quality of your school’s program and to help your child succeed with it. She should welcome your efforts.