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Why This Math?

A recent, very short post on the NPR Ed blog covers almost 500 years worth of math curriculum.

However, as a Harvard professor explains, the trip doesn’t really require all that many words since not much has changed in that time. After reviewing some very old textbooks, he says, we find “a curriculum that is so similar to the curriculum we have right now it might as well have been written by the good folks who wrote the Common Core”.

That professor is Houman Harouni, who became interested in this topic when his elementary students asked the question all of us who teach math have heard at one point: why do we have to learn this stuff?

But it isn’t just why we teach math that fascinates Harouni. He is particularly interested in why we teach math the way we do: “Why these topics? Why in this order? Why in this way?”

He says history offers the best answer.

Harouni has studied texts dating to ancient Babylonia, ancient Sumer and ancient Egypt, and, he says, he has found three main ways of teaching math, each associated with a different economic group.

The three types of math Harouni identified are “money math”, used by traders and merchants, “artisanal math”, for carpenters, masons and other craftsmen, and “philosophical math”, which was only studied by “elites”. The first two groups arranged for their math to be taught to their children, trainees, and apprentices, solely with the goal of extending their influence and wealth. Relatively few people outside of colleges studied philosophical math until very recently.

Today the math curriculum used in most schools is a mashup of all three, with elementary kids mostly working in money math, because “we live in a world where money matters”, with some artisanal math in the form of Geometry. That’s followed in middle and high schools with most students receiving a heavy dose of that philosophical math in the standard path from Algebra to Calculus.

The bottom line is, the school math we impose on students in most American schools is largely a legacy from centuries long past. Much of it needs to be thrown out (or drastically rewritten) and replaced with concepts and skills that better fit with the way math is applied in the 21st century rather than the 16th.

For most kids in K12 schools, math should be studied as it was 500 years ago, reflecting how it is used in today’s real world: as a tool for solving problems in many different aspects of life. And not as an independent, overemphasized and excessively tested, stand-alone subject.

Making a Good Teacher (1950’s Edition)

An article in The Economist magazine explains How to make a good teacher.

Good for a classroom from sixty years ago.

If this is to change, teachers need to learn how to impart knowledge and prepare young minds to receive and retain it. Good teachers set clear goals, enforce high standards of behaviour and manage their lesson time wisely. They use tried-and-tested instructional techniques to ensure that all the brains are working all of the time, for example asking questions in the classroom with “cold calling” rather than relying on the same eager pupils to put up their hands.

The concept of “imparting knowledge” and “preparing young minds” represents a very traditional vision of learning, one in which students sit in classroom rows waiting to receive the required knowledge. With the teacher “cold calling” all the questions, using “tried-and-tested” techniques to get pupils to produce the “right” answer.

The basic premise of the article – that we need to improve teacher preparation programs and provide better support on the job – is completely valid. However, the writer’s view of the role that should teachers play in student learning is antiquated at best.

Unfortunately, it’s also the foundation of most education reform proposals.

Picture Post #10

During a recent trip to Philadelphia, I spent a few hours at the Eastern State Penitentiary, an eerie place that encapsulates almost 150 years of the American philosophy of how to deal with criminals in our society. Read more about the facility’s history on Wikipedia and see more of my pictures in this Flickr album.

Cellblock 1

Cellblock one from the original building opened in 1827. Benjamin Franklin was part of the committee that designed the unique spoke and wheel layout that was adopted by many other nations in the 19th century. Each cell was designed to house one person in solitary confinement, giving them plenty of time to reflect on their lives.

Cellblock 7

Later additions to the Penitentiary were two story buildings with cells now housing two people in pretty much the same space.

Barber Chair 2

In it’s more recent history, one cell of each block was set up as a barber shop, staffed by prisoners, with all inmates required to get regular haircuts and shaves. The red chair is an interesting contrast to the very brown and gray walls.

Statistics 1

A display in the Penitentiary yard showing the number of people in imprisoned in the US by decade, along with other statistics of how our penal policies compare to other nations. Notice the huge population jumps since 1990, despite a decrease in crime rates.

Some Things Never Change

Don’t underestimate the value of doing nothing, of just going along, listening to all the things you can’t hear, and not bothering. – Winnie the Pooh

Ok, it’s been a week since I became unemployed and, while I haven’t quite been doing nothing, it’s been an interesting experience knowing that I could have done just that with no repercussions.

Along with plenty of reading and reflection, I’ve been cleaning out lots of the cruft, physical and digital, that has accumulated over many years. Including a few bags of stuff brought home from the former cubicle. No matter the origins, it’s a process that’s often quite cathartic.

One of the odder items that came out of the bottom of an office desk drawer was a folder containing magazine and newspaper articles from my college days. Stories featuring headlines like “What’s Wrong With Our Teachers?” and “Saving our Schools”.

The articles behind those inflammatory headlines called the quality of teaching “woefully inadequate”, related how kids didn’t work hard enough (or were not required to work harder), and declared that their learning was lacking compared to students in other countries (Japan being the big baddy at that time). Accompanied by one or two cherry picked examples of where schools are “working” in the US.

These declarations of a failing American education system were based on the now legendary A Nation at Risk report, which in its executive summary made this provocative claim:

If an unfriendly foreign power had attempted to impose on America the mediocre educational performance that exists today, we might well have viewed it as an act of war.

I remember that hyperbolic line being held over the heads of teachers for many years after that.

Anyway, A Nation at Risk was written by a federal commission, largely populated by people in higher education and corporate executives, and based on reports of poor student achievement from colleges and SAT scores.

As opposed to any number of negative reports about our current education system today, written by think tanks funded by billionaires with no education experience and based on a flood of data from largely meaningless standardized test scores.

It’s a little depressing. The impression of public education and the national discussion of school reform hasn’t really changed in thirty years. Except that back then one of the major solutions was to provide better pay and support for teachers. You won’t find many “reformers” supporting that idea today.

One more nostalgically fun item from the publications for edtech fans: the full-page ads by Apple, IBM, and Texas Instruments (complete with Bill Cosby) pushing their machines for home learning.

Bill’s History Class is Not New

So Bill Gates Has This Idea for a History Class…

Anyway, that’s the headline and, considering that Gates already thinks he knows how to fix American education, it’s not a big stretch for him to replace the traditional high school history curriculum.

The story began when Bill had some time on his hands following his retirement as Microsoft CEO and started watching a series of lectures by Australian professor David Christian titled “Big History”. In his classes, Christian wove together topics from history, biology, chemistry, astronomy and other disparate fields “into nothing less than a unifying narrative of life on earth”.1

A lecture on the Big Bang, for instance, offered a complete history of cosmology, starting with the ancient God-centered view of the universe and proceeding through Ptolemy’s Earth-based model, through the heliocentric versions advanced by thinkers from Copernicus to Galileo and eventually arriving at Hubble’s idea of an expanding universe.

In the worldview of “Big History,” a discussion about the formation of stars cannot help including Einstein and the hydrogen bomb; a lesson on the rise of life will find its way to Jane Goodall and Dian Fossey.

Gates thought this approach could be used to replaced the standard chronological approach to teaching history in high school and started working with Christian to adapt his work.

I don’t often agree with Gates, about his ideas for education reform or much else, but in this case he’s on to something. In most high schools, the major curriculums are highly segregated, especially when it comes to math and science. As a result, students get a very unauthentic view of the world.

However, before praising Gates and Christian too highly, it needs to be pointed out that “big history”, the idea of using interdisciplinary approach to understanding history, is not at all unique.

In the 1970’s, science historian James Burke wrote, produced, and hosted a wonderfully entertaining series for the BBC (later shown on PBS) called Connections, an “alternative view of change”. In the series (plus two sequels and a half dozen books) Burke takes a storytelling approach to illustrate the many links between science, philosophy, world events, art and more, all with great humor, a sense of curiosity, and a large dose of caution about our reliance on technology.

The original series is on YouTube, although somewhat difficult to find,2 so if you have 50 minutes or so, watch part 1 to get a good idea of Burke’s pre-“big history” approach to explaining how our current world developed from seemingly unrelated connections in our past.

Anyway, original or not, Gates’ idea to punch holes in the silos in which we keep high school academic subjects is a good one, something that’s long overdue. I’m just not sure he is the person to make it happen.

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