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Corey Andreasen says:
August 4, 2012 at 1:47 pmHi, Bill. I’m really impressed with the Common Core overall, and the Prob and Stats component in particular. And I like very much what the progressions documents do.
I haven’t read the progressions in a great deal of depth, but I did read looking for a couple particular things in 7th grade as they came up in a workshop I was doing.
Standard 7.SP.3 “Informally assess the degree of visual overlap of two numerical
data distributions with similar variabilities, measuring the difference
between the centers by expressing it as a multiple of a measure of
variability.” will be difficult for teachers to understand. And once it’s explained I think they’ll have trouble understanding the point. I suggest that this should be expressed directly in the progression doc. Specifically an example showing the same different in means with different spreads. Maybe the larger spread example could be two samples from the same population, for example. Then keep the means the same but show a small spread, and clarify how using the measure of variability as your gauge is a way of assessing overlap. The idea is somewhat discussed, but I don’t think this important point is made clear.I am struggling with this standard as well. I see the question posted but I do not yet see a response. Am I not using the forum properly?
The standard says that the student is to “assess the degree of visual overlap of two numerical data distributions with similar variabilities.”
The question above asks for an example “showing the same different in means with different spreads. Maybe the larger spread example could be two samples from the same population, for example. Then keep the means the same but show a small spread”
Since the standard required similar variabilities this seems to be contradictory.
The example about life expectancy in the progressions is a nice example but the variability of the sets is very different thus allowing the student to have some understanding of what that tells them about the range of the data set. This also seems to be contradictory to the wording in the standard regarding the two data sets having similar variabilities.
Thanks for all of you help and kudos on the new format.
I hadn’t written a reply to the other post yet. Your point about similar variability is well taken. Basically the idea of this standard is to get across the idea that if two distributions have different means, you have to look at the variability of each before you try to infer something from the difference in means. If they have very large variability, and so a lot of overlap, the difference in means doesn’t mean much; if they have narrow variability then maybe it does. The simplest case of this would be if they both have similar variability, so you can get a sense of how big the difference in mean is compared to the variability.
I’d like to invite all of you to visit the Mathematics Teaching Community at https://mathematicsteachingcommunity.math.uga.edu where there is a discussion about this standard. The specific url for the discussion is: https://mathematicsteachingcommunity.math.uga.edu/index.php/358/7-sp-3-common-core-standard-clarification
Could someone help me understand the difference between 7.SP.B.3 and 7.SP.B.4? Thanks!
Could someone help me understand the differences between 7.SP.B.3 and 7.SP.B.4? Thanks!
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