So why should you accept my opinion about where the bar should be? I’m not a specialist in child development, or in much of anything really. I guess you could say that elementary school teachers specialize in being generalists. Really, during the school year I’m so busy planning and teaching that I hardly get a chance to pick up a book for fun, much less to keep up with the journals or read about the latest in brain research. I have never been an expert in developmental psychology. I don’t even have an advanced degree in education.
What I do have is fifteen years of experience working with a range of kids in public and private schools. Most of my exposure to the standards is with those here in California, though from what I understand they’re fairly representative of the rest of the country. My best point of reference is fifth grade, since that is what I am teaching this year. It’s also the grade level that I have taught the most since I started my first substitute teaching job fifteen years ago. Since then I have been the lead teacher for ten different classes made up, at least in part, of fifth graders. The bottom line is that I have more than a passing familiarity with this age level.
Fifth graders are knowledgeable, inquisitive, surprisingly independent, and generally a lot of fun to be around. Intellectually they are, on average, smack dab in the concrete operational stage of cognitive development. That means many of them are not ready for serious abstract thinking, at least not without a lot of support to help connect abstract concepts with the concrete. Here lies a major problem. The fifth grade standards, at least in California, are a minefield for the concrete operational thinker. Take a look at the released STAR test questions to see what they are expected to master by the end (if the end of the year comes in May) of the fifth grade.
Every question ties directly in with one of the fifth grade standards, which are tightly bunched around a fairly narrow group of main concepts. There are barely any whole numbers here at all. A mystifying proportion of the questions are about prime factorization. There are several questions involving graphing on a coordinate plane and other beginning level algebra problems involving positive and negative integers. These topics involve some serious abstract thinking, and many fifth graders are simply not ready to understand them in any kind of deep way, at least not in the context of these sorts of problems. It doesn’t have anything to do with how intelligent these kids are. It’s just that ten year olds tend to think like…well, ten year olds.
There is also a huge leap in some areas between fourth grade and fifth. After having no questions at all on the addition and subtraction of fractions on the fourth grade test, fifth graders are suddenly expected to add and subtract mixed numbers with different denominators. In order to that successfully, students need to master several discreet sub-skills. They need to be able to find like denominators, add and subtract fractions with like denominators, convert improper fractions into mixed numbers and put fractions into simplest form. Not one of these skills is measured independently, so a student who has mastered most of them but can’t pull them all together won’t be able to demonstrate what they’ve learned at all.
By overshooting the developmental level of the age group and failing to measure incremental growth, the developers of the standards and the tests that go with them have created an almost meaningless assessment tool. Combine that with the No Child Left Behind mandate that all students must eventually meet or exceed state standards as measured by those tests, and you start to see the impossible situation that our public school teachers are facing.
There is intense pressure to do what cannot be done, and actually teaching your kids what you know they need to learn to move ahead can get you fired. Teachers can either take that risk or do their best to cram in the skills that their kids need for the test. Some, like me, will try to do both. At any rate, the summative effect seems to be that our high school graduates have missed out on a meaningful mathematics education. By pushing them too far, too fast, we’ve turned math into a set of hoops to jump through rather than a lens through which to view the world in a meaningful way. It affects our global competitiveness and the quality of our democracy in profound ways, not to mention the individual toll taken on all those kids who repeatedly experience frustration and failure.
So I say the bar is too high, and I don’t need research to prove it. Unfortunately, these days everything has to be “research-based”, so you would at least assume that the standards people have good data (the standards movement prizes data over all else) to back up the decisions they’ve made. Well, they looked at all the research they could find (8,727 published studies) in the process of putting together the California math standards. 956 of those were actual experimental studies and 110 of those met their criteria for design and validity. They wanted to know what should be taught and when it should be taught. This, in their own words, is how it went:
The principal goal of the study was to locate high-quality research about achievement in mathematics, review that research, and synthesize the findings to provide the basis for informed decisions about mathematics frameworks, content standards, and mathematics textbook adoptions. Although a goal of the study was to find experimental support for the scope of instruction and the sequence of instructional topics, none of the high-quality experimental research studies addressed these important aspects of mathematics instruction. Mathematics Framework for California Public Schools, pg. 205
So how do they know that this is what we should teach our kids and when we should teach it?