As a good mathematics educator, we should solve the best quality math problems using as many ways as we could, because each solution has its own learning value. Who knows, students might gain something from the long and tedious method of problem solving method and one day, they will surprise us with the improved version of the solution!
One thing every mathematics educator has to remember is that our imaginations are vibrant, our hearts are open, everything about math amazes us, and we think anything is possible.
Showing posts with label plan of attack. Show all posts
Showing posts with label plan of attack. Show all posts
Challenging Math Contest Problem: Prove that $\tan^2 x+\tan^2 (x+60^{\circ})+\tan^2 (60^{\circ}-x)=9\tan^2 3x+6$
Given $\tan x+\tan (x+60^{\circ})-\tan (60^{\circ}-x)=3\tan 3x$,
prove that $\tan^2 x+\tan^2 (x+60^{\circ})+\tan^2 (60^{\circ}-x)=9\tan^2 3x+6$.
Wow! This is another exquisite problem that one cannot afford to pass it up but to take it as one tough learning example problem so to train students to be the best. Remember that good teachers will forever encourage learning for understanding and are concerned with developing their students’ critical-thinking skills, problem-solving skills, and problem-approach behaviors. This problem fulfills the these goals of training students to think creatively and that is the reason I bring it to our table.
I won't beat about the bush, so here goes my plan of attack:
prove that $\tan^2 x+\tan^2 (x+60^{\circ})+\tan^2 (60^{\circ}-x)=9\tan^2 3x+6$.
Wow! This is another exquisite problem that one cannot afford to pass it up but to take it as one tough learning example problem so to train students to be the best. Remember that good teachers will forever encourage learning for understanding and are concerned with developing their students’ critical-thinking skills, problem-solving skills, and problem-approach behaviors. This problem fulfills the these goals of training students to think creatively and that is the reason I bring it to our table.
I won't beat about the bush, so here goes my plan of attack:
Subscribe to:
Posts (Atom)