Standard Deviation in S-ID.A

[missbaldwin]

We are working on curriculum maps for Integrated HS Math 1 which would include S-ID 1 – 3 and are wondering whether students must know how to calculate standard deviation by hand without the use of technology.

[Anonymous]

I don’t see anything in the standards that requires students to calculate standard deviation at all – by hand, by technology, or otherwise. Seems like the standards want students to be able to use and understand standard deviation, but not necessarily calculate it.

[missbaldwin]

Agreed. There does not seem to be emphasis on calculating standard deviation. We’re wrestling with how students will understand what standard deviation is, and how outliers affect its value, without some introduction to its calculation.

[csteadman]

New York has one lesson in Algebra I where students walk through the formula. Then students calculate and interpret standard deviation. I wouldn’t restrict calculator use completely.

I think there is a fine line in how deep you go in certain areas at a ninth grade level. How far do you go when a student asks where the correlation coefficient comes from? Show them the formula and smile.

[csteadman]

New York has a lesson in Algebra I where students walk through the formula. Then students calculate and interpret standard deviation. I wouldn’t restrict calculator use completely.

I think there is a fine line in how deep you go in certain standards at a ninth grade level. How far do you go when a student asks where the correlation coefficient comes from? Show them the formula and smile.

[Anonymous]

I guess when I read the standard, my thought was more along the lines of how we can get students to understand that standard deviation is basically just a value that we assign a set of data in order to rank its spread from the mean. So given 8 sets of data with the same mean and different spreads, students can intuitively rank those sets from least spread out to most spread out. The fact that we have a fancy way of calculating that rank and the fact that we call it standard deviation are nice facts, but we don’t need to know those things in order to talk about and explore the idea of spread. I would hope that after students have a handle on the idea of spread they would be able to see that any outliers present would make a set of data more spread out. I don’t see the need for any calculation to have that discussion.

I think if one approaches the standard with the mindset that knowing how to calculate standard deviation is important, then you will find ways to try to work it in. My approach is that the standard seems to be silent on the issue so I’ll look for instructional methods that don’t depend on the calculation itself.

[csteadman]

I think that is a great interpretation of the standards considering they are at the Algebra I grade level in PARCC states and represent an additional cluster. There will be more work with standard deviation in Algebra II in S-ID.4, although that is in the additional cluster as well.

I think it is interesting how curricula will be written as writers across the country interpret the standards. There is a lot you could do with S-ID.1-3, but you have to make decisions timewise, considering the rest of the S-ID’s, while making sure the central purpose of the standards, as you mentioned above, are covered.

[Bill McCallum]

This is a good discussion, and I don’t have much to add, except to confirm that students are not required to calculate standard deviation by hand. Students should be seeing real data sets where this would be absurd.

[Author]

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