Okay. I don’t hate the standards so much.

I hate the way that they’re written^{1}.

For example, from the California 7th grade standards:

Number Sense 1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.

Number Sense 2.3 Multiply, divide, and simplify rational numbers by using exponent rules.

Algebra & Functions 2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.

These three standards are from completely different sections, yet they all address the same concept of powers and exponents. (It doesn’t stop there – there are more standards that address fractional exponents, and graphs and equations with exponents. This is just the very basic concept, spread around to 3 different places.)

What I really want to see is a concept list. Like this (thanks dan):

Or, better yet, the same list but drawn as a directed graph indicating dependencies between the concepts. The next problem is how to chunk those concepts: Too fine, and you’ve got a million things to asses. Too coarsely, and you can’t tell what you’re assessing anymore. It seems to me that the chunks should be for about a weeks worth of material – some a bit more, some a bit less, but on average a week. Say 35-40 for a year. Certainly some students will learn more quickly than others, and be able to cover more concepts, but even that, I think, is a good thing.

The advantage of the directed graph version? It would work vertically, across grade levels. Not only would it simplify the process of evaluating understanding of prerequisites, it would help lower grade teachers really identify the key standards, the cornerstones on which everything else rested.

Here then is my attempt to do just that for the 7th grade standards. I’m quite sure that, in trying to implement it, some of the concepts will need to be condensed and others expanded to get balance (for one, the geometry section in red seems a bit heavy compared to the algebra section in green.) Heavy boxes indicate starting points that are either introduction of completely new material, or concepts that should be established from previous years.

I’m not sure that, at first glance, this is any more comprehensible, and that perhaps it would work better as just a text list. On the other hand, It indicates some of the complex connections that we as teachers have to try to make, and as such may help (after the initial confusion) develop into a guide for how the instruction should be laid out over the course of a year.

^{1} I also hate the way that they are interpreted on the standardized tests, but that’s a pretty dead horse at this point.

## { 1 } Comments

CA History-Social Science is a little better, and it doesn’t help that lawyers wrote the bulk of the standards.

Personally, I’d rather they be organized thematically. Apparently, that’s too hard.

If you create a version of that chart with relevant standards under each point, you’ll help out anyone trying to adopt that to their school.