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36 ^ (1/2) = + or - 6
27 ^ (1/3) = 3
64 ^ (1/6) = 2
I slipped her a little note saying, "Why not all three cube roots of 27 and all six sixth roots of 64? 36 ^ (1/2) = 6" I thought she might leave it a few minutes and then find a subtle way of getting them to correct their notes but no, she let it stand.
It turns out that she doesn't accept that she made a mistake.
What would you do?
http://socyberty.com/work/correcting-colleagues-grammatical-errors/
Null It turns out that she doesn't accept that she made a mistake. What would you do?
What level was the class?
NullIt turns out that she doesn't accept that she made a mistake.
The other thing we need to know is the context in which the lesson observation was taking place. Was this a formal lesson obs? Are you line manager to the colleague, etc.?
My note was facetious.
My point was not that the other roots should be included, rather that only the positive square root should have been given.
googolplexWas this a formal lesson obs?
It really isn't right DG.
36^(1/2) = 6 by definition.
It is not the same question as "Solve the equation x^2 = 36".
I wouldn't do something as discourteous, confusing or undermining as sending a sarcastic note to her. I feel it's always a priviledge to observe a colleague's teaching.
In this situation I would mention (later, after the lesson) that I "used to believe the sqrt of 36 was plus or minus 6, but now I know it's only +6 and that I was previously getting confused with solving equations" or somesuch comment.
brookesdiscourteous confusing undermining sarcastic
I wasn't my intention to be discourteous and I don't see how what I wrote could be interpreted as sarcastic but with hindsight I can see that it could have waited until after the lesson and I'm sure it would have been better received that way.
Oh well, live and learn.
Thanks for your reply. You've made me realise that my mistake was the more serious of the two.
yep. There's a time and a place - given the context of the observation as you describe, the time for this one is certainly not during the lesson.
I have observed some shockers in my time, and remember one ITT who was teaching a Year 7 about factors and multiples, had clearly not prepared a decent lesson, and who was interchanging the terms as if they were synonymous. I had to slip him a note and, had he not acted, I would have had no hesitation in stopping the lesson and taking over. A bit like a driving instructor with dual controls...
But, a colleague - in a sharing of ideas context - no. To a year 10 class, I would regard this as a minor infringement which would become a more significant issue at A-level. You have to respect their space. Raise it as an issue outside of the lesson, and if you can't think of a way, don't go there until a suitable opportunity arises.
NullSearching the internet for some wise words on this subject I found this. http://socyberty.com/work/correcting-colleagues-grammatical-errors/
To save others reading it, this is hilarious. The writer advises others on the pitfalls of correcting the grammar of others. There are at least ten spelling, punctuation and grammar mistakes in the article, so I suppose it's a warning to others that 'people in glasshouses...'! Too right. I just hope people realise it's a spoof. (It IS, isn't it? She says, nervously...)
brookes I In this situation I would mention (later, after the lesson) that I "used to believe the sqrt of 36 was plus or minus 6, but now I know it's only +6 and that I was previously getting confused with solving equations" or somesuch comment.
I In this situation I would mention (later, after the lesson) that I "used to believe the sqrt of 36 was plus or minus 6, but now I know it's only +6 and that I was previously getting confused with solving equations" or somesuch comment.
Oh blimey. I can't be the only one wondering about this, so I'll put up my hand....
You'll be relieved to hear I only teach KS2/KS3, but why isn't the square root of 36 'plus or minus 6'? I would have said it was!
I think I do vaguely remember learning that the square root symbol only refers to a positive square root, but the symbol isn't being used here.
Have just double-checked in a GCSE textbook (as the lesson was given to Year 10), and it says 'Because -4 x -4 = 16, there are always two square roots of every positive number.
And anything to the power of 1/2 equals its square root, doesn't it?
Could one of you explain to me (and other lurkers, I'm sure!) why the teacher was incorrect, so that I can put right my misconception?
With many thanks.
It doesn't matter that an index is used here rather than a square root symbol.
If a square root could be both positive and negative we wouldn't need the plus or minus sign in the quadratic formula would we?
So is the statement in the textbook incorrect? Doesn't 'two roots' mean a positive and a negative? Sorry if being dense, but can't be the only one. Need to be sure, as if ever covering-for-GCSE-class-despite-not-being-qualified, don't want to impart incorrect information and don't want to look a twit!
Also, the quadratic formula uses the square root symbol, which would equate to what I think I was told once - that the symbol refers to a positive square root only.
But I still don't understand why the square root of 36 isn't +/- 6. As the GCSE teacher observed didn't either, need one of you maths-degree people to spell it out in very simple terms for (some of) us. We'll be the richer for it!
Both +6 and -6 are square roots of 36. The expression sqrt(36) or, equivalently, 36^(1/2), represents the positive square root of 36.
OK - well, that makes sense to me, algebraist - thanks. So fractional powers refer to positive square roots only. It's just that Brookes implied with his/her post that the square root of 36 wasn't +/-6 and, as I would teach children that it is, had me worried!
algebraist Both +6 and -6 are square roots of 36. The expression sqrt(36) or, equivalently, 36^(1/2), represents the positive square root of 36.
Does it?
http://www.ucl.ac.uk/Mathematics/geomath/powsnb/pow5.html
"
"So x1/n means the nth root of x, i.e. the number that, when multiplied by itself n times, gives x."
"This shows that if we square our expression "x to the power a half" then we get simply x. Therefore "x to the power a half" must be the square root of x. The square root of a quantity is the number which when you square it gives the original quantity.Similarly the cube root of a quantity is the number which you have to cube to get the original quantity.For example the square roots of 16 are 4 and -4, since 4 squared is 16 and (-4) squared is 16.We have found out above that we can write the square root function as the power of a half, so we can rewrite the last sentence as:
161/2 = 4 or -4.
Similarly,
251/2=5 or -5,
since 5 squared is 25."
That's what I thought but correct me if I'm wrong.
As someone said on page 1 (I think), the square root (whether in index form or "ticky" symbol) is, by definition the positive root. When it comes to equations, x^2=16 there are two solutions. Again, as someone said, why else would we have the "plus or minus" symbol.
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