From: Robert Hansen Sent: Saturday, September 01, 2012 1:47 PM To: Clyde Greeno @ MALEI Cc: email@example.com Math-Teach ; kirby urner ; Richard Hake Subject: Re: Martin Bickman On The Needless War Between Traditionalists And Progressives
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. # Because the alternative would make the instruction of "classes" too cumbersome. How do you think the enrollment numbers would look if students were "promoted" only if they were mathematically ready for the next level? In curricular mathematics, the whole idea of "promotion" is contra-productive and unhealthy for students, schools, and the nation.
>We have test scores galore now. # We have score-numbers, galore ... but very few genuine tests of personal mathematical achievement or growth. Most "tests" actually test only for how well students have been trained to perform as directed. Its like testing the condition of your automobile by seeing how fast it will go.
>It is obvious that the range of student's ability to get things ranges from very good to very poor. # True, but the prevailing systems of "testing" and "grading" and "crediting" do not manifest how well students "get" mathematics ... only how well they play the scholastic game. Millions who have strong *abilities* to "get" mathematics, as such, simply cannot (or will not) "get it" from scholastic curricula that make little mathematical sense.
>That would tell you that the amount of subject matter the students got that year also ranges from very much to very little. # The test scores would that? Unfortunately, not the kind of "tests" that are commonly used. But there are much more reliable indicators that support your claim.
>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. # Alternatively, "putting a student right back through ..." what *failed them* earlier has a very low rate of success. The American curricular myth is that the students could not handle the math. The truth is that *that* kind of math curriculum (the non-common-sensible kind) progressively undermines personal mathematical development.
>Also, what if their reading skills were ok, but just not their math? # Its called "the gull wing profile" everything else is "level", but the profile dips at math. The dip might be visible (through inadequate performance) or hidden (when undue diligence supports performance). Both conditions are strongly correlated with MLD (Mathematics-Learning Distress).
>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. # You're close! "the only right way" is to nurture independent progress all the way up the K-calculus ladder. Curricular educators have badly failed to develop the instructional systems for doing so. That is why "Khan-math" is so popular. (Its shabbiness is because it merely represents "the normal curriculum", but his does facilitate independent progress in at least that sense.)
>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. # OK same "classroom" ... but not the same instructive experiences!
>Why do you think we have AP classes now where the entire class fails. Probably even the teacher. # How many teachers can make calculus common-sensible to students? ... how many own it as common sense?
> 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. # You are presuming that the schools have the know-how necessary for taking that responsibility. So, where do you think they would get it? ... from Khan or Saxon? >>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? # None of the above. I just misinterpreted your table. On first glance, it looks rather norm-ish to me. There surely is nothing wrong with your doing something like what others have done... including the CCSS-math authors. My hat is off for your efforts. I am sure that you have a rationale to support your "map." But, unless you have derived it from serious research into the psychomathematics, I have no more reason to attend yours in detail than I have for attending CCSS-math. Too bad ... I was hoping that you could help show the world what the problem is. But now I gather that you, like many others, are trying to solve a problem without fully knowing what the problem is. >> 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. # The MALEI Clinic does so, frequently.
>You know why? Because for some lame reason, the educationalists conceptualized all the grades, not just the early ones. # I have yet to discern that "the educationalists conceptualized ...." much of any curricular mathematics! Despite their glib dialog, it seems that very few know enough about psychomathematics to be able to do so. I have spent many years of research in that area, and have only begun to scratch the surface.
> 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. # Surprise! "... planting algebra concepts in kindergartners help them tackle ..." borrowing and carrying, place value, operations with Arabic numerals, fractions decimals, percent, and even algebra. The MALEI Clinic is presently developing the video documents. But don't hold your breath. Video-production is a costly, lengthy process.