Tuesday, August 20, 2013
  How math doesn't work

It appears that 'conservatives' are mounting a campaign against the Common Core curriculum. Seems to pop up often among the columnists and second-string radio yakkers, though it's not nearly as frequent as BENGHAZI.

Unlike most political themes, this one runs deeper than labels and insults. For many decades, in both US and UK, conservatives have pushed rote memorization with a strong focus on theory. Back to the basics is their constant slogan. Currently in UK, Education Minister Gove is advocating for rote memorizing of lists in history classes.

Dammit, this is frustrating. Their ultimate purpose is good and appropriate, but their approach is backwards!

An article in the latest American Thinker shows this contradiction in math:
In my 20 years in the high school classroom (in Georgia), I've often told my students that studying mathematics is not so much (or at least not only) about mastering some specific "objective" or "standard" (as we now call them), nor is it about making some future use of every little concept that they learn. I point out that these are good things, but the study of mathematics is more. It is also about growing and developing that logical part of their brains that mathematics, in particular, serves. What's more, "mathematical training," as the math department of the University of Arizona puts it, "is training in general problem solving." Or, as Thomas Aquinas College declares, mathematics "prepares the mind to think clearly and cogently, expanding the ability to know."
Proper goal. No problem. But then:
The beauty of Elements lies in Euclid's axiomatic approach... One must, initially, establish and accept some finite set of statements (axioms) without proof. All other conclusions are logically deduced from these initially accepted axioms (or postulates).

Sadly, this approach is almost completely abandoned with the integrated mathematics curriculum adopted by the state of Georgia five years ago. Although Georgia recently gave systems the option of returning to a more traditional (Euclidean) approach to mathematics, most stayed with the integrated math.

For example, currently, most freshmen in Georgia take coordinate algebra. This course consists of six units. The first three units are algebraic. They involve things like writing and solving linear equations and inequalities, solving systems of linear equations, graphing linear and exponential functions, using function notation and language, calculating rate of change (slope), and working with arithmetic and geometric sequences...
This integrated curriculum doesn't sound 'sadly' to me. It sounds like an excellent approach and a conservative approach. Begin with something visual and concrete (graphing), then work through all the aspects of math you're likely to need in a modern job and modern life.

Seeing things in graphic form gives you the best possible tool to detect official lies. Euclid gives you nothing at all. Graphing is dynamic, Euclid is static.

Most official lies, whether in Global Warming or Die-Versity or Economics, involve a reverse causation or a false causation. The authorities want to convince us that CO2 causes warming; or that affirmative action removes racial problems; or that quantitative easing improves the economy.

If you habitually think in terms of curves on a graph, you can mentally examine phase relationships. You can see that CO2 has always followed warming; you can see that affirmative action accentuates racial strife; you can see that QE does nothing at all to the economy.

Euclid doesn't help you examine any of those things. Euclid teaches you to accept the axiomatic statements of authorities, which is PRECISELY WHAT THE FUCKING COMMIES WANT YOU TO DO.

= = = = =

Ideally (and conservatively!) we shouldn't even have subject classes in school.

What is the deepest distinction between conservative and liberal? Right-wing thinking starts with the accurate understanding that PEOPLE ARE DIFFERENT. Left-wing thinking starts with the genocidal lie that PEOPLE ARE IDENTICAL.

How do we educate based on the accurate view? Job training.

You have to begin with three or four years of mainly identical rote practice in reading and writing. No way to avoid it. After that, at age 8 or 9, each person shows and knows his proper talents and tendencies. So we should take those distinct passions and use them to the max. Put each kid in a broad training program to develop his own proper skill set, which he understands and likes. Take care of all the necessary subjects within the job-oriented training, in context, at times when they can be used and appreciated.

Example: We find that your talents and passions are aimed at cooking. We give you constant practice in the essential skills of food preparation and restaurant/bakery/grocery work, adding more complexity and subtlety each year. Along the road, we take every available opportunity to discuss those other 'subjects' within the context of your passion. History: We have records and recipes from every culture and nation starting with the Babylonians, and we have riots and revolutions caused by inadequate food supplies. Math: Ratios and proportions, metrology a la Fanny Farmer, rate of change in the oven, pricing and taxes on the menu. Economics: Bread gave us the first written economic observations in 300 AD, and wheat is still part of Goldman's evil manipulations. English: There's plenty of good writing about food, and lots of opportunities to watch and produce Youtube howto videos. Chemistry: Cooking IS chemistry. Acids and bases, oxidation and combustion, alteration of proteins and vitamins. Physics: Elasticity of gluten, thermodynamics of burners, viscosity in stirring, friction in non-stick pans.

Here's how it was done at Iowa State in 1906:

Exactly right, but it needs to start at age 10, not in college.

Every major skill field has its own set of connections to each of those supposed 'basic subjects'. Presenting 'basic subjects' on their own is utterly pointless, a total waste of money, time and human capital. Kids learn things vastly better when they understand relevance and connections, when every lesson is a branch of one broad stream always flowing toward the same goal.

= = = = =

Later footnote: I've always wondered why this form of learning was completely rejected by American schools after it demonstrably succeeded 100 years ago. I've especially wondered why manual training is so fiercely hated by 'conservatives' who should be its main advocates. I suspected that experiential methods had an association with Progressivism, but didn't know how that happened. This explains it. Comrade John Dewey adopted manual training wholeheartedly and infused it with Marxist toxins, stating that the goal of manual training was a classless society. Academics have always pushed Dewey because he's a Party Hero, but they're only interested in the Marxist toxins, not the actual training.

Labels: , ,


<< Home

blogger hit counter
My Photo
Location: Spokane

Polistra was named after the original townsite of Manhattan (the one in Kansas). When I was growing up in Manhattan, I spent a lot of time exploring by foot, bike, and car. I discovered the ruins of an old mill along Wildcat Creek, and decided (inaccurately) that it was the remains of the original site of Polistra. Accurate or not, I've always liked the name, with its echoes of Poland (an under-appreciated friend of freedom) and stars. ==== The title icon is explained here. ==== Switchover: This 2007 entry marks a sharp change in worldview from neocon to pure populist. ===== The long illustrated story of Polistra's Dream is a time-travel fable, attempting to answer the dangerous revision of New Deal history propagated by Amity Shlaes. The Dream has 8 episodes, linked in a chain from the first. This entry explains the Shlaes connection.

My graphics products:

Free stuff at ShareCG

And some leftovers here.

March 2005 / April 2005 / May 2005 / June 2005 / July 2005 / August 2005 / September 2005 / October 2005 / November 2005 / December 2005 / January 2006 / February 2006 / March 2006 / April 2006 / May 2006 / June 2006 / July 2006 / August 2006 / September 2006 / October 2006 / November 2006 / December 2006 / January 2007 / February 2007 / March 2007 / April 2007 / May 2007 / June 2007 / July 2007 / August 2007 / September 2007 / October 2007 / November 2007 / December 2007 / January 2008 / February 2008 / March 2008 / April 2008 / May 2008 / June 2008 / July 2008 / August 2008 / September 2008 / October 2008 / November 2008 / December 2008 / January 2009 / February 2009 / March 2009 / April 2009 / May 2009 / June 2009 / July 2009 / August 2009 / September 2009 / October 2009 / November 2009 / December 2009 / January 2010 / February 2010 / March 2010 / April 2010 / May 2010 / June 2010 / July 2010 / August 2010 / September 2010 / October 2010 / November 2010 / December 2010 / January 2011 / February 2011 / March 2011 / April 2011 / May 2011 / June 2011 / July 2011 / August 2011 / September 2011 / October 2011 / November 2011 / December 2011 / January 2012 / February 2012 / March 2012 / April 2012 / May 2012 / June 2012 / July 2012 / August 2012 / September 2012 / October 2012 / November 2012 / December 2012 / January 2013 / February 2013 / March 2013 / April 2013 / May 2013 / June 2013 / July 2013 / August 2013 / September 2013 / October 2013 / November 2013 / December 2013 / January 2014 / February 2014 / March 2014 / April 2014 / May 2014 / June 2014 / July 2014 / August 2014 / September 2014 / October 2014 / November 2014 / December 2014 / January 2015 / February 2015 / March 2015 / April 2015 / May 2015 / June 2015 / July 2015 / August 2015 / September 2015 / October 2015 / November 2015 / December 2015 / January 2016 / February 2016 / March 2016 / April 2016 / May 2016 / June 2016 / July 2016 / August 2016 / September 2016 / October 2016 / November 2016 / December 2016 / January 2017 / February 2017 / March 2017 / April 2017 / May 2017 / June 2017 / July 2017 / August 2017 / September 2017 / October 2017 / November 2017 / December 2017 / January 2018 / February 2018 / March 2018 / April 2018 / May 2018 /

Major tags or subjects:

Carbon Cult
Constants and variables
Defensible spaces
Experiential education
From rights to duties
Grand Blueprint
Language updates
Natural law = Sharia law
Patient things

Powered by Blogger