Math Education: It's Not Easy

"Dr. Jo Boaler is a leading math education expert and one of the writers of the California Mathematics Framework, a set of guidelines focused on improving equity in California's math classrooms. We first talk about her upcoming book, Math-ish, and the beauty of pursuing more "ish" in our lives. Then, we discuss a recent anonymous complaint that was filed with Stanford University, accusing Dr. Boaler of misrepresenting research to serve her own agenda."

Click on the link below for an example of a new approach to mathematics education that is not well-received in some academic circles:

Dr. Jo Boaler Tried To Improve Math Education. Then An Anti-woke Mob Came For Her

A "Knotty" Subject (But Not Pornography)

"There is an entire branch of math simply devoted to knots – and it has changed the world. We’ll rope you in."

Click on the link below for a fascinating look at a subject that relates to not only math but also chemistry, biology, and physics:

How the Most Useless Branch of Math Could Save Your Life

Math Education: How Much Is Needed And What Type?

One of the controversies in education is the amount and type of mathematics education needed in middle and high school. Click on the links below for examples of current thinking on the matter:

“We hear on all sides that we’re not teaching enough mathematics — you know, that the Chinese are running rings around us,” Hacker says. “I’m suggesting we’re teaching too much mathematics to too many people. … I would say everybody doesn’t have to know calculus. If you’re going to become an aeronautical engineer, fine. But most of us aren’t. It’s a bit like saying everybody should learn Arabic because they may need it someday.” (https://www.sciencefriday.com/segments/how-much-math-should-everyone-know-show-your-work/)

"Casual observation tells us that most people don’t use math beyond simple arithmetic in everyday life. Few people make use of fractions, trigonometry, or multi-digit division algorithms they use in school. More advanced tools like algebra or calculus are even less likely to be brought out to solve everyday problems." (https://www.scotthyoung.com/blog/2022/01/24/why-dont-we-use-the-math-we-learn-in-school/)

"How many people use algebra or geometry in their adult lives? According to Andrew Hacker, who teaches political science and mathematics at Queens College and is the author of The Math Myth and Other STEM Delusions, not many -- about five percent at most. And though most of us have taken these courses as requirements for high school graduation, a national survey found that 82 percent of adults couldn’t compute the cost of a carpet when told its dimensions and square-yard price." (https://www.nea.org/advocating-for-change/new-from-nea/how-much-math-too-much)

Mathematics: Primary Or A Language Of Nature

There is much discussion in mathematics, philosophy, and science circles regarding the reality of mathematics. Click on the links below for a sample:

The language of nature

Why mathematics is a language

Is the Universe Made of Math?

Mathematical Universe Hypothesis

A Mathematical Speculation Of Infinity

"If there's a hotel with infinite rooms, could it ever be completely full? Could you run out of space to put everyone? The surprising answer is yes -- this is important to know if you're the manager of the Hilbert Hotel."

Click on the link below for a unique way of presenting the concept of infinity:

The Hilbert Hotel Has A Large Capacity

Another Example Of The Difficulty Of Explaining Consciousness

"In this video I talk about a few approaches to mathematically describe consciousness and its shortcomings. I also briefly talk about what such studies could one day be good for."

Sabine Hossenfelder is a physicist who addresses the controversial topics within physics not only with knowledge but with discernment regarding the line between evidence and hypothesis. This video is a good example of her qualifications:

The Mathematics of Consciousness

Math And Logic Are Formal Sciences

Let's put Mathematics and Logic in proper relationship to Science:

"Formal science is a branch of science studying formal language disciplines concerned with formal systems, such as logic, mathematics, statistics, theoretical computer science, artificial intelligence, information theory, game theory, systems theory, decision theory, and theoretical linguistics.^[1] Whereas the natural sciences and social sciences seek to characterize physical systems and social systems, respectively, using empirical methods, the formal sciences are language tools concerned with characterizing abstract structures described by symbolic systems. The formal sciences aid the natural and social sciences by providing information about the structures the latter use to describe the world, and what inferences may be made about them." (link)

"Formal sciences – branches of knowledge that are concerned with formal systems. Unlike other sciences, the formal sciences are not concerned with the validity of theories based on observations in the real world, but instead with the properties of formal systems based on definitions and rules." (link)

"All of science relies heavily on the existing abstract frameworks of mathematics and logic to interpret and describe the evidence it analyzes and ultimately to express its conclusions. Put simply, science uses mathematics and logic as scaffolding to construct predictive models, using empirical evidence as building materials. In this way, all branches of science are concerned with these fields, but no branch of science is directly concerned with advancing them.

"In a similar way, applied fields such as Medicine and Engineering rely heavily on the natural sciences as a framework on which to build, but are not themselves concerned with advancing those fields." (link)

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The principles underlying mathematics and logic are axiomatic.

The "Wisdom" Of Focusing On Mathematics?

A very interesting counter to the prevailing “wisdom” of the importance of mathematics. Frankly, how about focusing on science based thinking instead?

Have you used trigonometry since you were 18?

The Myths in "The Math Myth"

" I kept track of errors, unreferenced claims, and misleading arguments as I read The Math Myth, and I found so many that I’m halfway tempted to publish an annotated edition of the book. (I’m not the only one frustrated by Hacker’s many specious arguments. Mathematician Keith Devlin and math and statistics teacher Amy Hogan, among others, have written posts pointing out other flaws in his arguments and conclusions."

It Doesn’t Add Up

Improbability

"We can unconsciously increase the odds of a “rare” event occurring by post hoc analysis, open ended criteria (wiggle room), and mining large sets of data. In fact, we are inherently good at doing all of these things. We might call the overall process pattern recognition. Our brains evolved to make connections, to see patterns, and then to imbue them with meaning."

The Improbability Principle

Is Infinity Real?

The Infinity Puzzle

Mathematician's Brains ARE Different Than The Rest Of Us

How Does a Mathematician's Brain Differ from That of a Mere Mortal?

It's Amazing What Was Happening In The Middle East Before - - -

- - - a religion thought it knew everything.  Sound familiar?

This ancient Babylonian map of Jupiter just changed history as we know it

A Mathematical Look At Grand Conspiracy Theories

"Conspiratorial ideation is the tendency of individuals to believe that events and power relations are secretly manipulated by certain clandestine groups and organisations. Many of these ostensibly explanatory conjectures are non-falsifiable, lacking in evidence or demonstrably false, yet public acceptance remains high. Efforts to convince the general public of the validity of medical and scientific findings can be hampered by such narratives, which can create the impression of doubt or disagreement in areas where the science is well established."

Math vs Conspiracies

Mathematics Education On The Cusp

"The Common Core math standards have been contentious since they were launched several years ago, with many parents taking to social media to complain about their kids getting incomprehensible homework. Kids are now expected, for example, to explain how multiplication works using the “box” and “lattice” methods. These methods take longer, and are harder to master at first, but have been shown by some research to be more effective than the multiply-and-carry method, particularly for kids who have trouble memorizing things. And while they may be new for this generation of parents, they have been around since at least the 13th century."

http://www.theatlantic.com/education/archive/2016/01/the-man-who-tried-to-kill-math-in-america/429231/