If you lower your expectations, people will meet them

Occupy Math has been teaching mathematics at the University level since the age of 17 (they let him teach one section of a remedial algebra-trig class at the University of Kansas when he was a first-year student). He has also done volunteer teaching in both middle and high schools and has been a faculty member in a teacher-training program. This experience spans 35 years with regular contact with recent high-school graduates. This parade of credentials is intended to support the following opinion: the amount of math taught to North American high school students has been going down steadily over a period of at least three decades.

Why, as we cross into the 21st century, deal with climate change, and reach for the stars, why are we crippling our children?

There are a number of things happening that interfere with sensible, effective teaching of math.

  • We are skipping foundations like geometry and neglecting other important pre-requisites like algebra and trigonometry to get to calculus as fast as we can. This means we are teaching that calculus to people that do not have the tools to learn or understand it.
  • We are entrusting basic math instruction to people that do not have full subject mastery and some of whom are terrified of mathematics. This creates self-perpetuating incompetence and fear.
  • We are abusing standardized testing in a manner that interferes with learning and education. This is getting so bad that protest movements are forming.

Over the last few decades, we have reduced the number of topics taught in math classes and reduced the total time in math class. Worse, in Ontario and other places, math classes have become repetitive in order to make really, really sure that students do well on standardized tests. In theory, standardized tests ensure that teaching is effective. As we use them, standardized tests are a menace to teaching. When a teacher’s performance review and a school district’s funding depend on the performance of students on standardized tests, it turns out that standardized testing narrows the curriculum and so decreases what students learn. All of these factors contribute substantially, but there is another pervasive factor in play.

The most pernicious contribution to declining math skills is lowered expectations.

A question that anyone who teaches ends up asking is: “what is the appropriate level of expectations I should have of my students?” A pervasive societal belief that normal people cannot do math has led to a steady erosion of our expectation of how much math people can learn. Two universities that Occupy Math has worked at have created ways to excuse entering students from meeting the minimum math requisites needed for admission. It was disguised as permitting students missing one of several requisites to still be admitted – but the common missing requisite was math.

If we expect that students will not learn math, that belief saps our will and energy to teach students effectively. These lowered expectations are exacerbated by micro-management of math teaching, largely by innumerate administrators who are themselves far more concerned with standardized test averages than student achievement. These administrators talk a good game about student achievement, but their every action says that they expect the students to fail unless they, themselves, rig the game. This cheating varies from teaching to the test (while ignoring the topic) to outright theft of the test answers by teachers. In more than 40 states.

Occupy Math feels this conduct is a betrayal of a sacred duty.

The teachers and administrators that did this deserve, at a minimum, to be fired and blacklisted. Thousands of hours of unpaid community service would not be unreasonable. Having said that, the guilty parties felt they needed to steal, cheat, and lie in order to meet educational goals. They were so sure that their students could not learn that they slipped them the answers instead. This conduct encompasses reprehensible dishonesty, but it is also is a form of despair. Teaching, as a profession, has a very high turnover rate – especially among younger teachers. This suggests that new teachers encounter situations they cannot endure and then go do something else.

These issues hit Occupy Math at the core of his job and his passion. He teaches students, from first-year to the doctoral level. Graduate students are usually close friends with a relationship that lasts for years. Across the board, Occupy Math needs the people that taught these students before they became his responsibility to do their job. Every month I must spend tutoring students in basics they are supposed to already know is lost to teaching them what they are supposed to be learning. Students without a need for remedial instruction have become rare, and the problem is not at all limited to math.

An article that speaks to fuzzy Muppet coding instruction is entitled “American schools are teaching our kids how to code all wrong”. Instead of teaching programming languages and development environments that might lead to achievement or even jobs, they create kiddie instruction platforms with drag-and-drop coding and very little actual room for learning or achievement. Occupy Math knows that students can learn Java, Python, or C++; I’ve met students that learned these tools in exceptional high-schools or who taught themselves to program. This is all too rare!

There is a serious problem with teaching valuable subjects as if the students cannot learn them.

Another problem is dumbed down math education in many places – and attempts at reform are also opposed vigorously by people that do not understand the issues. The common core initiative in the United States is controversial. After an afternoon of surfing the objections Occupy Math has found that there are objections that occur over and over:

  • The standards are Federal, not local.
  • The standards are sponsored by Bill Gates.
  • The standards are not on topics parents are familiar with.
  • The name of the standards has the word “core” in it (lots of pictures of
    rotten apples or apple cores with evil worms here).
  • The name of the standards contains the word “common”. The most memorable objection was several parents holding signs reading “My children are not common”.

What was blindingly conspicuous by its rarity was objections or discussion based on the content of the standards!

A common core is a statement of what common subjects should be learned by everyone. Objecting that you children “are not common” represents ignorance of even the meaning of the name of the standards. The University of Chicago – an institution replete with Nobel Prize Winners and distinguished graduates, prides itself on its extensive and complex “common core” of topics taught to all students. Occupy Math’s wife benefited from this education and there is nothing plebeian (“common”) about it.

Across the board, protesting parents wanted to be able to help their children with their homework. Since many parents do not know enough math to teach math to, well, anyone, this is a fantastically unreasonable demand. Occupy Math understands that a parent would not want to appear ignorant to their children – and there is a large need to offer parents help. Many parents, however, don’t want help. They are taking the position that their own level of confusion and innumeracy is the standard to which their children should be taught.

Adoption of this standard would be a death spiral for our economy, scientific endeavors, and, well, civilization.

Occupy Math has spoken before about the class in Integrated Physical Sciences that he co-developed. To briefly recap, we raised our expectations, setting students the task of finishing three semesters of mathematical material and two semesters of physics in an integrated setting in two semesters. Grades in the new class were significantly higher than those in the more standard classes they replaced and downstream performance was also better. Adding 50% more math content and absolutely insisting the students learn it with graded homeworks and quizzes enormously increased achievement and, with it, morale and confidence. Despair is always lurking, ready to tear the heart out of exhausted victims. It can be resisted and, in most cases, will retreat when confronted by steely-eyed, self-driven instructors and enthusiastic, curious students. This suggests we should encourage instructors and students with this character.

Occupy Math wants all people to learn enough math to defend themselves from con artists, to be able to manage their own finances, and on a good day to see the pervasive beauty of the universe illuminated by pattern and subtle mathematical truths. As always I solicit feedback from all my readers. Tweet! Comment! Speak of signs of hope and achievement, if you happen across them.

I hope to see you here again,
Daniel Ashlock,
University of Guelph,
Department of Mathematics and Statistics

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