[John McGowan]

Thank you for replying. I expect it is strange to be asked to explain your thinking from years ago. This is an experience that the internet has given us, I guess.

I agree that algorithms should have some value other than learning them for learning sake. However, much of what we teach our math students is essentially vocabulary; they have to learn certain concepts and algorithms so that they can do the applied and complex problems later on. Memorizing times tables comes to mind. It’s a mindless task, but if students are not required to do it, then they do not develop numerical fluency, which prevents them from seeing patterns in higher math concepts.

Also, in this context, the laws of exponents could be considered the same type of unapplied algorithm. I don’t see much difference between that and simplifying square roots in terms of lack of application.

I am a classroom teacher, and thus my perspective is necessarily restricted to only the students I see. I assume that you have a wider perspective, since you have access to research that I do not. Based on the your initial response to this thread, back in 2014, I guess you saw a trend in “worksheet instruction”.

However, my problem, which has nothing to do with you, is that the textbook I am using, CPM, eliminated instruction in simplifying square roots based on the fact that it was no longer in the standards, but also didn’t replace it with any alternate method. When I asked them why, their head of curriculum pointed me at your blog. So here we are.

Thanks for taking the time to explain your thinking.

[John McGowan]

“I don’t know what is meant by “standard simplifying roots algorithm””

The standard method I am familiar with is this:

root(24)
= root(4 x 6)
= root (4) x root (6)
= 2 root (6)

I am unclear why this method is being devalued. Using rational exponents to simplify is no more intuitive.

[John McGowan]

When one has a public blog, it must suck when some stranger from the internet asks you to explain a comment you made years ago.

This is a comment from a stranger from the internet asking you to explain a comment you made years ago!

I do not understand why you make the claim that an understanding of rational exponents are all the students need. I suppose one could do this algorithm:

root 45
= (45)^0.5
= (9 x 5)^0.5
= (9)^0.5 x (5)^0.5
= root(9) x root(5)
= 3 root 5

Am I reading this correct? Is this they type of algorithm you think is sufficient? If so, I can’t see why that is any easier or more intuitive than the standard simplifying roots algorithm. In fact, it seems like more work.

If I am misunderstanding you, can you explain how you think students should simply roots?

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