The online diary of a Maths / IT teacher from Melbourne, Australia.
Another puzzle
Get link
Facebook
X
Pinterest
Email
Other Apps
Those who enjoyed solving 100 pirates will want to take a look at the 2 Numbers puzzle, on Naught Much. Other people's solutions are in the comments, so be sure not to cheat!
Elias.
Get link
Facebook
X
Pinterest
Email
Other Apps
Comments
Anonymous said…
yes yes yes
v good
what about this?
using algebra to prove that 1= 0 Let x = y. (x,y are nonzero) Then x2 = xy. Subtract the same thing from both sides: x2 - y2 = xy - y2. Dividing by (x-y), obtain x + y = y. Since x = y, we see that 2y = y. Thus 2 = 1, since we started with y nonzero. Subtracting 1 from both sides, 1 = 0.
In the last instalment , I reviewed Conrad Wolfram's diagnosis of what is wrong, or outdated, about Maths education today. In this second part, I will review his "Math(s) Fix".
The Math(s) Fix is Conrad Wolfram's case for teaching mathematics with the assumption that computers exist! To be clear from the beginning, Wolfram is not advocating that we solve the same problems but with a greater reliance on computers and calculators. He wants us to recognise that computers have revolutionised the discipline of mathematics and that we need to reflect this change in our curricula. In the following lines, I will present a summary of Wolfram's thesis, as I understand it. My aim is to give you enough of an idea so you can decide whether you want to read the book for yourself. This part will concentrate on the case that the book builds for a radical change of the maths curriculum. Part 2 will explain the alternative in more detail.
Teaching in Melbourne, I am about to start my second round of online classes. I am taking some time to remind myself of the lessons I learnt from my and other people's experience in lockdown 1.0. Some of the best student feedback that I received from the last period was due to a question that was suggested by my school's principal: How did I, as a teacher, help you learn during the lockdown? (c) Can Stock Photo / lightkeeper
Comments
v good
what about this?
using algebra to prove that
1= 0
Let x = y. (x,y are nonzero)
Then x2 = xy.
Subtract the same thing from both sides:
x2 - y2 = xy - y2.
Dividing by (x-y), obtain
x + y = y.
Since x = y, we see that
2y = y.
Thus 2 = 1, since we started with y nonzero.
Subtracting 1 from both sides,
1 = 0.
what is wrong with this theory?
If x = y, then x - y = 0
You cannot divide by (x - y) since you cannot divide by 0.