4 ms·

The common core Mathematics standards are available for anyone to read here: http://www.corestandards.org/Math/ http://www.corestandards.org/Math/ I would enc

The common core Mathematics standards are available for anyone to read here: http://www.corestandards.org/Math/ http://www.corestandards.org/Math/ I would encourage anyone who is really interested in this issue to spend some time reading, or even skimming just a few sections. I find the standard is generally quite readable (conceding that it's a non-trivial commitment to read more than 1 grade level, but then again, there's a lot to know about math...) and I also tend to agree with many of the ideas in it. I've been disappointed, but in hindsight not very surprised by the anti-intellectualism in the public response to the common core. I'm more surprised to see similar anti-intellectualism here. I expect better from you, HN! It's true that the common core places more emphasis on critical, analytical, and sometimes even abstract thinking than the "traditional" math curriculum (whatever that is...). But as people who read hacker news, doesn't that sound good to you? It's also important to know that the Common Core standards are a set of expectations, and that's actually all they are. They are not worksheets or standardized tests. If you see a bad "Common Core" worksheet, it is a bad response to the Common Core, but it isn't actually the Common Core itself. If you want to criticize the Common Core itself, choose a part of the document above and criticize it. Or failing that, criticize the process that led to its creation and dissemination. But criticizing a few oddball problems is not a powerful argument. My own criticism-in-hindsight is that the Common Core is trying to do two things at once. Maybe it would be succeeding better if it only tried to do one of them at a time. The first is to provide a nationally standardized set of grade level expectations. Many people have an interest in this goal because it makes it easier to prepare teaching materials for a large group of students, and to compare education effectiveness across regions. In an alternate world, this could have been done descriptively instead of prescriptively. The standards could have simply described what was happening in the largest fraction of the country's classrooms. The second goal is to improve math pedagogy in the U.S. and bring it up to the best international standards, including tying math more strongly to critical, analytical, and abstract thinking skills. This is a prescriptive goal. If the standard was a process, we could have started with 1, and moved to 2 incrementally. But I suggest this only half-heartedly, because I think 2 is a great goal, and I think the Common Core (as a document) does a pretty good job of it. Now to be clear about my own biases: I don't have any children (school age or otherwise). If my first exposure to the Common Core was seeing my child assigned problems that looked unfamiliar, unimportant, or even that I didn't know how to do, I'll concede that I might have reacted negatively too. I do have a physics Ph.D. (i.e. math background), I do think and care a lot about how people understand math, and I do work on a software tool that tries to help children think about (part of) math more powerfully.

zaroth 12y ago
The issues with Common Core as I've read are a lot bigger than a few oddball problems, or under-developed worksheets or testing. The problem is apparently instead of taking these core and mostly trivial concepts and finding ways to actually make them intuitive, in the name of "critical thinking" we've created this theater-of-the-absurd approach like what you see discussed above. I don't have much personal exposure to "Common Core", but I've found when all the implementations turn out as shit, the blame usually lies with the specification. My personal opinion is that a lot of this overloading on processes and bizarre approaches to presenting problems (and don't get me started on the form of homework assignments and tests) is because we're out-pacing the natural cognitive developmental process. For example, take the sample chapters that were on the front page a couple days ago from "Math from [Age] 3 to 7" [1] you can see a very interesting approach to building math skills. But even in that case, the author is rushing developmentally advanced tasks which are more likely to result in frustration and giving-up than engagement and learning. Fundamentally, most learning does not occur while a teacher is speaking. The more absurd lengths the teacher goes to "explain" some concept, the less likely any child is to actually learn it. The more foreign the concept is by the time the kids get home, the less likely it is to be mastered. I have a daughter in Kindergarten, but fortunately not one that follows CC. I just spent some time reading through /Math/Content/K/ on corestandards.org. Most of it is, IMO, complete trash and not at all aligned with how kids in kindergarten actually learn this shit. As a "spec" it's writing is sloppy, poorly defined, and highly ambiguous. If this is the starting point, I'm not at all surprised the resulting lesson plans are worse than nothing. I also spent some time reading /Math/Practice and it struck me how all these things that CC is presenting as "Standards for Mathematical Practice" are not at all how children conceptualize mathematics, or cognitively approach the task of solving a math problem. Many of the stated practices are directly contrary to how children will naturally want to approach and solve a given problem, and I can imagine exactly how teachers faced with "instilling" these practices would get to exactly where we find ourselves. [1] - http://www.ams.org/bookstore/pspdf/mcl-5-prev.pdf http://www.ams.org/bookstore/pspdf/mcl-5-prev.pdf
- jwmerrill 12y ago
  > I just spent some time reading through /Math/Content/K/ on corestandards.org. Most of it is, IMO, complete trash and not at all aligned with how kids in kindergarten actually learn this shit. As a "spec" it's writing is sloppy, poorly defined, and highly ambiguous. I respect that you took the time to read the document, but your criticism isn't very specific. Are you bothered by the fact that it uses words that aren't appropriate for Kindergartners to describe what they should know? Or that it says what they should know, but not always how to teach it? I think the "spec" analogy is a good one. The goal of a spec is to lay out requirements, not implementation. Same idea here, which strikes me as the right choice. The actual expectations are to know a few things about counting, numbers, and shapes. That seems developmentally appropriate to me (admitting that I don't have much recent experience with kids this age). What do you think Kindergartners should know? Re: the practices part, these same practices are mentioned at every grade level through high school. I agree that the practices sound way too advanced for Kindergarteners, but the goal is to get students to do them well by the end of high school, not by the end of Kindergarten.

zaroth 12y ago

The issues with Common Core as I've read are a lot bigger than a few oddball problems, or under-developed worksheets or testing. The problem is apparently instead of taking these core and mostly trivial concepts and finding ways to actually make them intuitive, in the name of "critical thinking" we've created this theater-of-the-absurd approach like what you see discussed above. I don't have much personal exposure to "Common Core", but I've found when all the implementations turn out as shit, the blame usually lies with the specification. My personal opinion is that a lot of this overloading on processes and bizarre approaches to presenting problems (and don't get me started on the form of homework assignments and tests) is because we're out-pacing the natural cognitive developmental process. For example, take the sample chapters that were on the front page a couple days ago from "Math from [Age] 3 to 7" [1] you can see a very interesting approach to building math skills. But even in that case, the author is rushing developmentally advanced tasks which are more likely to result in frustration and giving-up than engagement and learning. Fundamentally, most learning does not occur while a teacher is speaking. The more absurd lengths the teacher goes to "explain" some concept, the less likely any child is to actually learn it. The more foreign the concept is by the time the kids get home, the less likely it is to be mastered. I have a daughter in Kindergarten, but fortunately not one that follows CC. I just spent some time reading through /Math/Content/K/ on corestandards.org. Most of it is, IMO, complete trash and not at all aligned with how kids in kindergarten actually learn this shit. As a "spec" it's writing is sloppy, poorly defined, and highly ambiguous. If this is the starting point, I'm not at all surprised the resulting lesson plans are worse than nothing. I also spent some time reading /Math/Practice and it struck me how all these things that CC is presenting as "Standards for Mathematical Practice" are not at all how children conceptualize mathematics, or cognitively approach the task of solving a math problem. Many of the stated practices are directly contrary to how children will naturally want to approach and solve a given problem, and I can imagine exactly how teachers faced with "instilling" these practices would get to exactly where we find ourselves. [1] - http://www.ams.org/bookstore/pspdf/mcl-5-prev.pdf http://www.ams.org/bookstore/pspdf/mcl-5-prev.pdf

jwmerrill 12y ago
> I just spent some time reading through /Math/Content/K/ on corestandards.org. Most of it is, IMO, complete trash and not at all aligned with how kids in kindergarten actually learn this shit. As a "spec" it's writing is sloppy, poorly defined, and highly ambiguous. I respect that you took the time to read the document, but your criticism isn't very specific. Are you bothered by the fact that it uses words that aren't appropriate for Kindergartners to describe what they should know? Or that it says what they should know, but not always how to teach it? I think the "spec" analogy is a good one. The goal of a spec is to lay out requirements, not implementation. Same idea here, which strikes me as the right choice. The actual expectations are to know a few things about counting, numbers, and shapes. That seems developmentally appropriate to me (admitting that I don't have much recent experience with kids this age). What do you think Kindergartners should know? Re: the practices part, these same practices are mentioned at every grade level through high school. I agree that the practices sound way too advanced for Kindergarteners, but the goal is to get students to do them well by the end of high school, not by the end of Kindergarten.