On Sun, Jun 2, 2013 at 10:47 AM, Robert Hansen <email@example.com> wrote:
> > Longer Answer... > > Consider the doctor that treats those things that can be successfully > treated, like broken bones, infections, etc. The general practitioner. For > every 100 patients they treat, 95 are cured and fully recover. Now consider > the doctor that treats those things that cannot be successfully treated, > like many cancers. For every 100 patients they treat, 95 die. You can't > call both of these scenarios "doctoring" and leave it at that. At best, you > can say that they doctors in the second case are trying to treat. > > Likewise, when a teacher who is teaching students that are interested, > prepared and able to take algebra, the process of teaching algebra is as > well defined as is the process of mending a broken bone. Remove the > preparedness, interest and ability and now teaching algebra becomes just > "trying to teach algebra". > > Then we have my contingent, off to the side, who think "teaching algebra" at leastmeans mentioning Al Jabber (yes, jokes OK too) and the Wisdom School of Al Khwarizmi. Investigate about how that lineage (OK: vector) percolated through Pisa, Fibonacci (Liber Abaci etc.), and how this helped fuel the European Renaissances (more than one) that followed. Write some papers, draw some comics, trace the math. How did they learn long division in 1492, who did, for what reasons?
In some textbooks, that's there, as a sidebar, as the teacher whizzes through some factoring polynomials section, with nary a glance nor mention (that's why it's called a sidebar). To really dive into the history of mathematics and ideas at this point would be considered a travesty -- this is *ALGEBRA!* (a sense of ownership) -- by the "teach to the test" death-to-the-mind squads patrolling today's prison-schools.
The age of navigation required increasing mastery of spherical trig. 'Divided Spheres', a primer, re-introduces navigation instruments and terms like "rhumb line" (loxodrome). Given geodesy and GIS/GPS concerns have a big footprint in STEM, we're not planning to be stingy when it comes to learning about the ecliptic, geostationary orbits and what not.
Friends of Outdoor School gathered at the local theater the other day. Kids need more time under night skies without light pollution, not less, and individual families going car camping is not fuel efficient, even with the growing Prius / Leaf / Volt fleet.
> > And this is what has occurred with algebra and education in general. We > went from an industry of teaching to an industry of trying. In the > beginning the effort to teach algebra to more students was genuine. They > started with the traditional principles that worked with traditional > students, but success was elusive and over time the standards of success > that define algebra were lost. Even the purpose of teaching algebra was > lost. Algebra's simple mathematical certainty of reasoning was replaced > with notions like creativity, diversity or equality. In the worse cases, > such as with Richard, Dan and his little cult, they have not only abandoned > the principles of algebra, they have abandoned their own students. What I > mean by that is that you realize quickly that their blogs are not about the > success of math, they are about its failure. They have abandoned the > teaching of mathematics and have become more interested in studying its > failure. Even if their original urge was to devise a cure, that is long > past. They have invented another purpose for their time and their students > be damned. >
I think it's devastatingly irresponsible to suppose the education you received some decades ago should be replicated now, or maybe that's not your thinking. The vista has changed. We do record keeping on computers now, that's just how it's done, so lots of focus on paper-based double entry ledgers makes less sense than accounting in terms of SQL tables. Spreadsheets are generally too changeable for real accounting, much better for "what if" planning -- but not saying what actually happened (that's where databases shine).
So we'll teach SQL now, a lot more (if at all competent), where maybe you were doing something else in 4th grade. But that means learning more typing which wasn't imposed until college in the old days, but is now more of a basic skill (with alternatives, with voice recog etc.). Kids are learning typing earlier and earlier, even displacing cursive, making that a "learn it on your own" endeavor, a "trivial" skill acquisition schools no longer have time to get into that much...
> > My chief problem with this is that algebra as a skill ranks pretty damn > low in importance unless you are a quant. And I don't mean just the quants > in finance, I mean the quants in all professions where mathematical > reasoning and analysis is fundamental to the profession. These students > could have been studying something else. Something more akin to their likes > and aspirations. There was no real reason to create an industry of trying > and fill it with non-teachers who for lack of anything better to do, spend > their time discussing the failure of mathematics. These students will > eventually become adults and have to provide a life for themselves. In > place of every site like dan's there should be a site geared to students of > construction, nursing, home finance, fashion, beauty, etc. etc. etc. > > There are these other sites you mention, although lets remember a lot of schools cannot afford to just sit around dumping content on the Internet for free. They need paying customers.
I think trying to freeze STEM standards, in separate sections (AP Comp Sci vs. Maths vs. Physics etc.) is doomed at this point because the standards-writers no longer have up to date information themselves, the "information explosion" we were warned about ('Future Shock' etc.) having occurred, with many of the predicted effects. People need to spend more time upgrading skills and knowledge even while on the job, even as teachers. But are we ready as a culture? You have offices packed with record keeping administrators who don't have much if any background in SQL. Universities get by on dinosaur software when it comes to course creation. The situation just doesn't look that stable to me.
> If education's purpose was the student then that is how it would be. > Education's purpose should have never been algebra. It damn sure should > have never been to give a bunch of failed algebra teachers something to > talk about. > > Bob Hansen > > There should be no teaching of algebra as it was taught in say 1964. They had no decent way to program personal computers back then, no Google Earth, no GPS. They did what they could with what they had. That was then, this is now.
Here's what I taught over a decade ago at our Portland Public, Winterhaven, a magnet for geeks:
But so many schools have frozen in time and we have less and less reason to think their failings are recoverable. Fighting back with a teaching-to-the-test crazed reflex is more evidence of the infrastructure just getting too far out of date to have bounce back ability.
But I'm really not sounding an alarm here, as I don't think change is a bad thing. We have many advantages, great tools, with more in the pipeline. Change is happening, like it or not, and education helps people guide and plan for (anticipate) versus just getting dragged along with greater helplessness. Education is about expanding possibilities, from wherever you're starting, could be with cancer, but then life is terminal so lets not pretend 95% of patients are spared the same outcome eventually, when the true number is 0%.