Real talk: pure maths was way more fun, interesting, and applicable to my life as a software engineer than all the applied math and modelling that I wrote/learned/etc. Pure mathematics expanded my mind unlike any other subject matter.
Physicists make a similar complaint. "Why would anyone want to study physics, when kids are not shown any interesting physics?"
Chemistry education research characterizes pre-college chemistry education content as incoherent, leaving both students and teachers confused and deeply steeped in misconceptions.
Biology education... starts by deemphasizing it's core organizational principle, and goes downhill from there.
> The real tragedy
Here's another. "It has been more than a decade since science education research surprised us with how badly science education was failing students. But even now, how often are students told? Instead, K-13, students have been left to think their confusion and cluelessness, are strictly their own fault, their own failing. Left to think science is boring. They are not told that these are known defects of the wretched content we're giving them. Fixing the content is hard. But telling them isn't. At what point does our failing to notify them become an ethical failure?"
> pure maths was way more fun, interesting, and applicable to my life [as a software engineer]
It can be fun to create ELI5-ish stories about math in everyday life. Math as recognizing patterns. So for instance, moving one way on a "circular" path, you come back around to the same position. As with boardgames, clocks, parking, etc. Missed doing something at lunch today... perhaps try lunch tomorrow. Missed a parking space and can't back up... perhaps drive around the block. Category theory for kids.
Or maybe a clearer description of what constitutes the good and bad approaches?
What are the core organising principles, in your view, of biology (and physics and chemistry, if you can state them)?
It's an area of general interest to me.
Variation. Metabolic efficiency (to expressed effect). Selection. Inheritance (via genetics).
Take away any one part, you lose the whole.
No variation -- nothing on which to select.
No metabolic efficiency (and behavioural effect) -- no criterion for selection or efficiency.
No selection -- no bound on behaviour or constraint on metabolic input or expressed behaviour.
No inheritence -- any variation or selection lacks survivability to the next generation.
There's an 18 minute cut from the original lecture, I'm thinking of starting with that.
https://m.youtube.com/watch?feature=youtu.be&v=rvw68sLlfF8
Possibly related: the Scholastic Method -- origin of the lecture method of education.
https://en.m.wikipedia.org/wiki/Scholasticism#Scholastic_met...
Dates from a time when books were expensive but time was relatively cheap.
I also find the concept of lectio, meditatio, quaestio (vetted!), and disputationes to be interesting, perhaps an ideal model for the article / discussion online format. The better for having everyone actually listen to, and think over TFA.
Masur discovered that there is something called the Force Concepts Quiz. He learned that students of physics across the nation did very poorly on the test.
The test asks basic questions. For instance, a large truck and a small car collide head on. Which vehicle has more force imparted on it? This type of question requires no computations. It's easy if you really understand the concepts and hard otherwise.
He teaches at Harvard and thought his students would do well. They didn't. They did terribly. What he found is that regardless of the quality of the teacher (note he is a very good lecturer), type of class, or size of class students universally did bad. It didn't matter the quality of the institution either.
Conclusion, we are teaching physics wrong. He found that students who could do well on the Force Concepts Quiz could do tedious calculations and mastered that part of the course. Students who could master the calculus computations may or may not be able to pass the Force Concepts Quiz. Hence he decided to concentrate more on concepts and less on calculations. He does not lecture in the classroom.
In my own experience I've found similar things hold in mathematics. For instance, I ask College Algebra II students to give me an example of an equation that has no solution. Most can't do it even though 1=2 is a simple example of such an equation.
Wikipedia says "an equation is a statement of an equality containing one or more variables", but your example lacks a variable.
How about "-1=x²"? If x can be a complex number a solution is "x=i", but what if we only use real numbers? Wikipedia says "There are two kinds of equations: identity equations and conditional equations. An identity equation is true for all values of the variable. A conditional equation is true for only particular values of the variables." Does that imply that without a solution "1=x²" is not actually an equation? The two parts are not equal after all.
The distinction between identity equations and conditional equations is basically one of quantification. (Quantification should really be introduced as soon as you have variables, but is unfortunately often left implicit.)
An identity equation is essentially a statement of the form "for all valid assignments of the variables, ... = ...", where a valid assignment is constrained by conditions like "x is a real number". (Those are also often implicit when they really shouldn't be.) This means that "1=x²" is not an identity equation when x is taken to be real, but it is one when x is constrained to be a root of unity. (This is just another way of saying 1=x², but all identities are like that.)
A conditional equation amounts to "there is a valid assignment of the variables such that ... = ...". Then "1=x²" is a conditional equation that can be made true on the real numbers. The solutions are variable assignments that make it true, in this case 1 and -1. If you constrain x to be an imaginary number, then it has no solution; the equation and the constraint on the variable contradict each other.
If you are taking college level algebra, you should be familiar enough with equations to set up a contradiction like that.
Suppose we start with 2x+5 = x - 4 + x. If we solve this by showing all work we'll end up at the end with
5 = -4
At this point students are told this means that there are no solutions. But what they miss is what an equation really means. Anyone who really understands the concept of an equation can easily give an example of an equation with no solution.
An equation is a statement that two expressions are equal. What one tries to find is the solution set. That is, the collection of tuples (if more than one variable is present) that makes the expressions equal when evaluated at the tuple. An equation is really a question. How can these two expressions be evaluated at the same input to produce the same output?
Lastly, We agree that f(x) = 1 and g(x) = 0 are valid functions. Here is the equation 1 = 0 stated in a more sophisticated way. f(x) = g(x) where f and g are defined above.
Those two answers live in different conceptual categories, and most math lessons and problems live exclusively in one category and not the other.
This is related to Force Concepts because physics-as-math is taught as a series of algebra problems with a rather distant relationship to lived experience rather than the other way around.
Teaching physics as experience is harder than it looks. When I learned physics the course really tried to emphasise experience, but it did it in a stylised and abstract way with canned "experiments" using special equipment. This actually made it feel more distant and uninvolving, not less.
I suspect to do a better job you have to get out the classroom. E.g. introduce force, momentum, and acceleration to kids on bikes and skateboards, not with wooden trolleys on ramps.
That said, there was a small feeling of "And now the time for fun and games is over" when I stopped studying pure math. I enjoy my job, but math provides a certain satisfaction that business problems do not.