51–60 of 80 posts
Earlier quoted context omitted.
I honestly don’t see how this version is any more intuitive than regular completing the square.
Pedagogically there's more to it than just the algebraic manipulations. The algebra here is basically as dull as all other algebra. It's the teacher's job to make it come alive.
> Now here comes the clever bit. Loh points out that the numbers, R and S, add up to -B when their average is -B/2. Is knowing to take advantage of that really any more intuitive than completing the square is?
Earlier quoted context omitted.
I'm a "pedagogically minded" reader, and I find these words unnecessary at best, and off putting at worst. Math needs better marketing based on actual science, not egotism
Teachers & the educational system in general should give examples of why stuff needs to be learnt instead of being dictated to, because they have one of the largest influences on the future direction of a country's success. Teaching was a cop out, a cushy number for those who couldn't hack it in the real world and liked to take their failure out on pupils. Many teachers couldn't run a business the way they treated ki…
"Imagine if, instead of wasting time on phonics, we inspired white upper middle class students like myself by giving them real literature!"
"Imagine if they inspired students with the kind of problems I think I would have found interesting!"
"Imagine if they taught to my learning style" (learning styles are mostly bunk, but everyone thinks they would have done better if only the teacher catered to them better).
"Imagine if a class of 20+ kids who are forced to be there was managed the way a team of 5 adult professionals was managed!"
The author should really remove the words 'simple', 'easy', and 'intuitive' from this article. They clearly know nothing of why most people detest math. If you're already familiar with the quadratic equation and you care about math and even enjoy it you might find this new equation interesting, useful, or intuitive, but I guarantee it is still a garbled mass of un-intuitive numbers and symbols to "[m]any former algeb…
Students get frustrated with trying out different numbers to get the right sum and product. It's easy for them to make a mistake or think they made a mistake.
This method is more mechanical and also looks easier than just chugging on the quadratic formula.
Is it dramatically better than well-taught and well-practiced traditional methods? Probably not, but I like it. It does seem slightly better, but then I'll never have to crank through a worksheet of these.
The result is called "the PQ-formula" in Swedish and is taught in schools.
The result is called "the PQ-formula" in Swedish and is taught in schools.
I assume you didn't actually read the article. It is not the QP formula.
I cannot find any link in English referring to it, but it is part of the standard curriculum.
One example of a website explaining it here below (in Swedish), but still, you can clearly see that it's the same formula OP has given:
I briefly looked at the author's paper. I find the account of the traditional method there questionable. He suggests it starts by going from: x^2 + bx + c to x^2 + bx + c + b^2/4 - b^2/4 This step is freaking weird, I've never seen it before, and I don't think this way. The process I follow is more like I observe that for general k: (x + k)^2 = x^2 + 2kx + k^2 so I observe that for k = b/2 I get (x + b/2)^2 = x^2 + b…
I briefly looked at the author's paper. I find the account of the traditional method there questionable. He suggests it starts by going from: x^2 + bx + c to x^2 + bx + c + b^2/4 - b^2/4 This step is freaking weird, I've never seen it before, and I don't think this way. The process I follow is more like I observe that for general k: (x + k)^2 = x^2 + 2kx + k^2 so I observe that for k = b/2 I get (x + b/2)^2 = x^2 + b…
BTW, if the notion of adding and subtracting the same amount bothers you: Yes, this is done all the time.