On Sep 1, 2012, at 5:41 AM, Clyde Greeno @ MALEI <firstname.lastname@example.org> wrote:
> From the time a child leaves the crib, there are many humanly natural paths of personal growth ... depending on the child's environmental experiences. Curricular educators traditionally presume that most children, as they enter kindergarten, are mathematically "about equal" ... (absurd, of course). Curriculum developers do so because of the tradition of trying to educate "classes" of students.
You have seen me speak out before about social promotion. I don't know why it is so pervasive. We have test scores galore now. It is obvious that the range of student's ability to get things ranges from very good to very poor. That would tell you that the amount of subject matter the students got that year also ranges from very much to very little. They do have grade retention, but that is the extreme case and I am not sure that putting a student right back through what they just failed is the right course of action. Also, what if their reading skills were ok, but just not their math? I hate to say it, because I generally think elementary school should not be tracked, but considering the range of test results, the only right way (if success is your motive) would be place the students having difficulty into more of tutorial setting that can focus individually on their difficulties. If it were your own kid you would do exactly that, but you won't see that happen in public schools. People will claim that by not putting them in the same class you are denying them the same opportunity. Why do you think we have AP classes now where the entire class fails. Probably even the teacher. Another reason we don't see this is that the schools don't want to take the responsibility. Can't blame them really, they are being thrown under the bus as it is.
> That brings me back to your time table. Similar "scope and sequence charts" have long been used by authors and publishers of school-mathematics curricula, for designing/describing their respective works. But yours appears to represent the presently "norm" curriculum ... what it actually is, rather than what it "should"/could become. I suspect that some publishers have used such global summaries as basis for composing their own works ... and that the same is true of authors of the "Common Core Standards" in mathematics. But their cross-curricula analyses are not being widely shared.
Norm curriculum? Actually I will admit that the timeline at the top (grade 1, 2, 3, ..., 6) is "norm" but the order of the topics is not "norm". I am not saying that the order I represent here is perfect but it is generally correct pedagogically speaking. I arrived at this order by looking at all of the pieces and arranging them in order of prerequisite necessity, the core at least. The rest I placed with respect to sophistication and in relevance to that core. Yes, it will look like many other curriculums, but that is because they went through the same process. It doesn't look like all curriculums. I don't think it is fair to suggest that these curriculums are "copied" as long as I can supply the reasoning behind the order. Is there something extra in my timeline that shouldn't be there or is there something missing that should? Or are you saying that you would skip around more?
> So, I cannot propose a progress-path that "should" be used, but it is obvious that the present prescriptions are badly failing. What I can proffer, instead, is a growing compendium of Mathematics As Common Sense ^TM improvements over prevailing curricula, some of which might startle conservatives. [For example, normal kindergartners can easily begin to learn about fractions or algebra ... but not the kinds of "fractions" or "algebra" that presently are taught in American schools.]
The push for conceptualization has done a lot of what you suggest (learning about fractions and algebra in kindergarten). What is missing is that no one really went back and checked to see if that does anything, and at this point no one will ever be able to gauge the effectiveness of planting concepts in kindergartner heads. You know why? Because for some lame reason, the educationalists conceptualized all the grades, not just the early ones. We cannot tell if planting algebra concepts in kindergartners help them tackle algebra later because algebra also was conceptualized. They will never get to real algebra later and we will never see if this was an effective strategy.