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It's long but well worth watching if you have any interest in science education. https://m.youtube.com/watch?v=WwslBPj8GgI https://m.youtube.com/watch?v=WwslBP

It's long but well worth watching if you have any interest in science education. https://m.youtube.com/watch?v=WwslBPj8GgI https://m.youtube.com/watch?v=WwslBPj8GgI

dredmorbius 9y ago
I'd very much appreciate if you could give some sense of what specific highlights or benefits I might expect to gain from an 80 minute time investment? 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 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_method 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.
- yequalsx 9y ago
  I teach mathematics at a community college. The lecture resonated with me and I found it captivating. Here is a synopsis based off of memory: 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.
  - qznc 9y ago
    The question is if "1=2" is really 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.
    - yorwba 9y ago
      My personal definition of equation is just "an equation is a statement of equality", no variables required. But if you want to talk about solutions, you usually need variables. (The example "1 = 2" could be saved by saying it has no solutions, while "1 = 1" is solved by the empty assignment of variables.) 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.
    - yequalsx 9y ago
      If you prefer, 1 + 0 x = 2. We agree that is an equation. It has no solution. Typically in math we don't write 0x in expressions. 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.

It's long but well worth watching if you have any interest in science education. https://m.youtube.com/watch?v=WwslBPj8GgI https://m.youtube.com/watch?v=WwslBPj8GgI

dredmorbius 9y ago

I'd very much appreciate if you could give some sense of what specific highlights or benefits I might expect to gain from an 80 minute time investment? 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 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_method 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.

yequalsx 9y ago
I teach mathematics at a community college. The lecture resonated with me and I found it captivating. Here is a synopsis based off of memory: 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.
- qznc 9y ago
  The question is if "1=2" is really 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.
  - yorwba 9y ago
    My personal definition of equation is just "an equation is a statement of equality", no variables required. But if you want to talk about solutions, you usually need variables. (The example "1 = 2" could be saved by saying it has no solutions, while "1 = 1" is solved by the empty assignment of variables.) 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.
  - yequalsx 9y ago
    If you prefer, 1 + 0 x = 2. We agree that is an equation. It has no solution. Typically in math we don't write 0x in expressions. 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.