> White supremacy culture shows up in math classrooms when... There is a greater focus on getting the "right" answer than understanding concepts and reasoning.
When designing airplane parts, there are definitely right and wrong answers.
When designing airplane parts, there are definitely right and wrong answers.
(However, this does not seem to have to do with white supremacy; it is something else.)
I believe that's what you quoted refers to:
>> White supremacy culture shows up in math classrooms when... There is a greater focus on getting the "right" answer than understanding concepts and reasoning.
> When designing airplane parts, there are definitely right and wrong answers.
Focus on getting the right answer makes kids not value the process to get to the right answers, getting the right answer is a result of a process they need to learn but if they are only tested on if the answer is right or wrong they won't learn the concepts and reasoning, they will memorise a formula and apply it at wrong times/places because they don't know why the formula is what it is.
Yes, I know that singularities are special cases, as well as two roots for the square root, etc.
> they won't learn the concepts and reasoning
Memorizing comes first for children. Concepts and reasoning comes later. In college, concepts and reasoning come first, and memorization is unimportant.
I remember memorizing the times tables when I was 5 or 6. I'd draw out the 10*10 matrix and fill in all the boxes, using addition. Eventually I noticed that "times" meant add the number that many times, and that I didn't have to memorize it anymore. But the work memorizing it laid the groundwork for the epiphany.
People have not evolved for math. Their innate math ability is similar to falling after making few steps in regards of running analogy. They need a whole lot of boring and painful base training to be any good. What we get with "but they need to understand!" is people who can barely walk 1km without losing their breath insisting that when children get fun carbon shoes and tasty carb gels they will run much better than children who are made to run laps until they drop.
Steelmanning "There is a greater focus on getting the "right" answer than understanding concepts and reasoning."
Correct understanding and reasoning leads to correct answers. I want my airplane engineers to understand the concepts and reason through them and not have a shallow understanding of memorized solutions.
So do I, and I had some disrespect for the engineers who relied on memorization, but memorization is the first step towards understanding.
For example, if you want to play guitar like Van Halen, you gotta start by memorizing the finger positions.
I disagree that it is always the first step towards understanding. It is for some people but it is not the only route. At the end of the day some memorization is needed in most disciplines not just math.
> "There is a greater focus on getting the "right" answer than understanding concepts and reasoning."
Approximate rewording to what should/can be done rather what should't be done ~"focus first on understand concepts and reasoning, then getting the correct answer"
Teaching 5 different routes to a classroom means focus is lost and little progress is made.
Besides, monkey-see monkey-do is an innate skill of humans, and it works. Especially with children, who have a very undeveloped ability to reason. Reason comes later.
Learning starting from basic principles is introduced in high school, but is foundational at the university level. By then the students can understand it.
> Approximate rewording to what should/can be done rather what should't be done ~"focus first on understand concepts and reasoning, then getting the correct answer"
How about my rewording here does that address your main concerns from the quoted approach?
> 12. There is never a single right solution. There are always multiple wrong ones, though.
I'm not sure simple arithmetic is really the focus there, though I suppose "2²" is a good an answer to "what is 2 + 2" as "4".
The real right answer is of course "can't say without knowing what the field is that we're operating in".
What is critiqued here isn't that people manage to add numbers the right way. What is critiqued here is in a metaphorical sense that students learn the results for any given input by hard, and don't understand what addition does and what happens when you add things.
As someone who had mechanical engineering classes if I had to pick someone to build my plane I'd pick someone who understands that the bend on a 5m aluminum rod is not going to be in the order of 2km over a person that accepts that result because they think they applied the rules they learned.
You only get the former kind of thinking by making people understand what they are doing. And a good way to avoid developing that understanding is by constantly focus on things being right instead of only doing so in special situations (e.g. a test).
The other way to know is to test it. Things are tested anyway, just to ensure the math was done correctly.
I designed the stabilizer trim jackscrew so it could withstand 151% of the maximum load. (The extra 1% was for tolerances.) The test people grinned and told me they were going to bust my jackscrew. Off I went to Plant 2 where they had the medieval torture rig all set up. It was two I-beams, hinged together at one end. There was a hydraulic ram connected to form a triangle. My poor little jackscrew was fixed to both I-beams.
And, with a grin, the testers started cranking up the pressure in the ram. I watched with my safety googles on. They ran it up to 150%, and the I-beam bent like limp noodle, and my jackscrew stood strong and proud! No creaks, no cracks, no spalling, no buckling. The testers were chagrined, and I simply went back to the office.
There were two takeaways here:
1. It was too strong. Evidently Saginaw Gear forged a masterpiece. I've always liked Saginaw Gear since. They're some bad mofos.
2. The test people didn't do the math.
Looking back at that education the important lessons there were to acknowledge that even if multiple people try for hours under high stress to get things right, chances are more than 50% will still be wrong. And to only way around that is to really know your shit inside out.
I had many colleagues who I met uears later which wouldn't even be able to explain basic mechanical laws as all they did back then is learn for exams like other people learn poems. That is what I meant when I said understanding is more important than being right in school. If you construct a plane you better check it ten times and then test it a hundred times.
(Shooting their mouths off does nothing, except cost them ego points when they're wrong.)
With aircraft parts, you can make mistakes up to a point, but those mistakes will make the airplane cost more, such as being overweight. There is always an optimum answer, and I took it as a point of pride to get things exactly right.
I knew some engineers who couldn't do arithmetic very well. The results were parts that were overweight and often would not even fit together, causing expensive redesign and rework. Engineering management knew who they were, and assigned them tasks where their deficient work was not going to cause much trouble.
But in no case was 2+2 not equal to 4.
Did the Wright brothers use a lot of math in their wind tunnel experiments or was it more empirical .. given that "correct" math for flight dynamics took a while longer to come about.
> With aircraft parts,
there are a lot of "right* answers; three pairs of wings, two pairs, a single pair, a single wing, push from the back, pull from the front, control surfaces here or forward canards there.
> There is always an optimum answer
There are multiple optimums in the field of avionics.
Yes, they did. They did a lot of math in their design (their notebooks survive). That's why they were successful and their contemporaries all failed.
They developed the first mathematical theory of propellers, for example, and used it to create a propeller that was twice as efficient as that of other experimenters.
See "The Wright Brothers as Engineers, An Appraisal" by Quentin Wand
> there are a lot of "right* answers
None of them flew if they got thrust/lift/drag/weight/cg/strength/stability wrong answers. Lots of people died as the result of wrong answers.
This is school-level mathematics. The 'wrong' answer isn't a different optimization of cost, strength, weight and endurance, which Boeing might consider.
It's an arithmetic or procedural error giving an incorrect result.
There's great value in understanding the method, discussing ways to make errors and so on — but I think it's nonsense to suggest this has anything to do with race.
get those baker's percentages wrong and it's gonna be inedible