Most people probably have been thinking about Christmas preparations and not so much the Common Core Standards. I’ve actually been thinking about these standards a lot lately. The more I think about them, the less comfortable I feel.
Let me explain, first of all, that the common core standards are an effort to get states to agree that they will have the same things they are trying to teach at each grade. They also start with a good idea, addressing the common complaint that U.S. mathematics education K-12 is a “mile wide and an inch deep”. There are so many different topics kids are supposed to learn, they touch on each one before skipping off to learn about calendars or measurement of volume.
The problem is that statistics doesn’t come up AT ALL until the sixth grade. Now, prior to this, in some states, at least, kids in elementary school would learn some basic ideas of probability – like to differentiate between outcomes that are certain, probable, unlikely and impossible. I think most kids could understand this concept before the seventh grade – which is the first mention of probability.
I suspect if I asked my four-year-old granddaughter whether she thought she got any presents in red wrapping paper, and showed her a picture of this tree, she would guess that she did, which shows an intuitive sense of probability. If I asked her if she thought she got any presents in yellow wrapping paper, I’m pretty sure she would get a puzzled look and tell me, “No.”
I’m not suggesting one, non-random, non-representative child is the basis for national standards. I AM agreeing completely with the American Statistical Association post that stated,
“Instead of the K–12 standards document clarifying and providing a pathway to the statistics standards in the college and career readiness document, much of the statistics content that should be in elementary school and middle school has been pushed to high school.”
As someone who has been teaching statistics since 1985, it is hard for me to accept that knowledge is going to emerge full-blown, like Athena from the head of Zeus.
Now maybe people who came up with these standards went along the Piagetian route and said that children were concrete thinkers and they weren’t going to be able to understand abstract concepts until they were teenagers.
The curriculum seems disjointed to me. Kids learn about bar graphs in second and third grades and then pick it up again in sixth grade with a discussion of distributions. I understand the argument that the old standards often had kids doing the same thing year after year. I understand the desire to have children learn fewer things and learn them well, to attain “deep understanding”. What is still troubling me, though, is the thought that if they are going to get that deep understanding, then I surely hope they are going to have a LOT of time spent on statistics in sixth and seventh grades to present those topics that students have never seen before and don’t see again for years. Probability is covered in seventh grade and then eighth grade picks up bivariate relationships with no discussion of probability.
To be fair, I don’t recall hearing about the Central Limit Theorem until I was in college. Yes, my high school days pre-dated AP Statistics by a good two decades. I took Calculus, Analytic Geometry and Matrix Algebra in high school because those were the courses offered (it was small school). I don’t know that I learned them all that well, but I think that had a whole lot more to do with the fact that I was more interested in skipping school and hanging out at the local fast food joint after doing various illegal things in the parking lot than inappropriateness in the standards or teacher quality. *
The standards are not all bad. I do like very much, for example, the concept of integrating what students learn in mathematics with other subjects, like in this example:
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
You can take a gander at the common core standards here. Tell me what you think.
* True story: My math teacher was a conscientious objector to the Vietnam War and teaching in my urban high school for “troubled youth” was his alternative service. I’m not sure there were not days he would rather have been in the jungle, but that was our fault, not his.