Here is the draft progression for Statistics and Probability, Grades 6–8:

ccss_progression_sp_68_2011_12_26_bis

As usual, comments and suggestions are welcome. [New file with corrections uploaded 12/26/11, 11:38 am MST.]

[5 August 2012] This thread is now closed for comment. Please ask questions about Grades 6–8 Statistics and Probability here.

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## About Bill McCallum

I was born in Australia and came to the United States to pursue a Ph. D. in mathematics at Harvard University, met my wife, and never went back. I am a professor at the University of Arizona, working in number theory and mathematics education.

This is a wonderful summary of the expectations for middle school statistics and probability. It will be a huge leap for many middle school math teachers! However, it is the direction that is needed in order to bring math education into the 21st century. I myself have a lot to learn in order to be able to provide adequate professional development in this area…but am excited to begin the journey!

One minor typo error…On page 10, in your example of males and females doing homework…in the “Two random samples of size 10” both of the box plots are labeled as female. I believe that one of them should be labeled male.

“Progressions” tag is missing.

Bill,

Two quick comments regarding grade 6… then three questions:

Comment 1) On page 4, the dots on the first and third dot plots are not aligned, which makes the graph confusing to read and interpret. The same thing occurred on the dot plot appearing on page 13 of the Data Progression.

Comment 2) Also on page 4, there is a typo in the caption under those dot plots. It currently reads, “Students distinguish between dot plots showing distributions which are skewed left (skewed toward larger values), approximately symmetric, and skewed right (skewed toward

smaller values).” The skews are reversed.

Question 1) In the progression, a dot plot is defined as synonymous with a line plot. This is consistent with the examples shown. Does this mean the sixth grade does not have to address scatter plots at all? I had interpreted dot plots to include scatter plots, but the examples given lead me to think scatter plots are “owned” by 8th grade, correct?

Question 2) Some of the box plots (bottom of p. 5 and middle of p. 6) include outliers dealt with by disconnecting those points from the whisker. Do sixth grade students need to learn the very arbitrary “1.5 times the IQR above the upper median” rule for determining whether a data point is far enough to be considered an outlier? Teaching this convention seems far too detailed and isolated from the larger focus of the data standards and the focus of 6th grade to justify the time and confusion!

Question 3) The “Middle School Texting” graph (bottom of p. 5) has no lower whisker. I have never seen that before. I thought, by definition, the bottom quarter of the data points were represented on a whisker? The only time I have seen a box and whisker that is missing one whisker is when that entire quartile is comprised entirely of “outliers” that are represented by dots instead of a whisker. Please explain why there is no lower whisker for this graph.

Providing that explanation, along with the actual data, would really help to clarify this content for 6th grade teachers! I think, because sixth grade teachers are still generalists (certified in elementary ed., not math… at least in New York), 6.SP.5 will be the single most professional development demanding standard. To that end, anything you can include in this document would be greatly appreciated!

As always, thanks for taking the time to support us.

Brian

I think I figured out the answer to Question 3… no lower whisker would appear if more than 1/4 of the students sent no text messages. If this is the correct interpretation, including a table of the raw data (like what was provided for the Animal Speeds) would help people to quickly figure this out!

Thanks,

Brian

Firstly, gratitude to you and your team as well as Brian for highlighting the skewed dot plots on page 4. I think the skews are accurately labeled, I think it is counter-intuitive topic and I might have missed something, but the dot plots seem correctly labeled.

Kudos to the writing team for producing such an articulate description of the progression for Statistics and Probability into Grades 6-8 that includes the four-step statistical problem solving process. I was intrigued by the use of “shape”, “center”, and “spread” in the case of bivariate measurement data in place of the more common “direction”, “shape/form”, and “strength” that we use in statistics to describe a scatterplot.

Page 4: It would be great to get rid of the jitter in the Fathom dotplots. This seems an unnecessary complication to have to deal with in Grade 6.

Page 4: Why is 4.G.3 listed in the right column here?

Page 5: I think you’re missing out on the opportunity to ask about the difference in variability for the two age groups under 6.SP.4.

Page 5: Why the outliers in the boxplot? Earlier you said that we weren’t doing that at this point. Also, the texting boxplot is overlabeled (two titles) and the horizontal axis label should have “text messages”. The message on outliers seems unclear in the document so far.

There were a lot of boxplots used in the Grade 6 discussion. Boxplots do not display the data themselves, and so often hide important features of the data distribution. Just a cautionary note.

First, thank you SO MUCH for these progressions documents!!! I and my colleagues are finding them tremendously helpful in thinking about how to plan our Common Core units.

I am wondering why the link to this particular progressions document has not been posted on the progressons webpage? I have downloaded this file and shared it with colleagues – but – I have it only because I was fortuante enough to have wandered onto this page.

Thank you!

Patricia

Thanks for pointing out the missing link … it’s there now.

Bill,

Another re-post of a lingering question:

Some of the box plots (bottom of p. 5 and middle of p. 6) include outliers dealt with by disconnecting those points from the whisker. Do sixth grade students need to learn the very arbitrary “1.5 times the IQR above the upper median” rule for determining whether a data point is far enough to be considered an outlier?

Teaching this convention to sixth graders who are just being introduced to this sort of graph seems far too detailed and isolated from the larger focus of the data standards (and the focus of 6th grade, in general) to justify the time and confusion!

The standard itself does not seem to require nor forbid this, but including it in this Progression seems to say that this convention would be fair-game on grade 6 assessments. Please let me know if that was the intent or not! If it wasn’t, can a note be included in the Progression stating “the standards at grade 6 do not require nor forbid instruction focused on the ‘1.5 times the IQR above the upper median’ rule for determining outliers. This should not be a target on assessments.” Without a note like that, teachers will have to spend time, which should be focused on the RP and EE standards instead, teaching this convention to mastery just in case it is ever tested.

Thanks,

Brian

Good point, Brian, as usual. In some ways this is similar to the discussion we had about the geometry progression a couple of days ago. The progressions can be more expansive than the standards, but this should not be construed as a signal to add mindless rules to the assessments! I’ve been saying “that which is not mentioned in the standards is not thereby forbidden”, but maybe I should start saying “that which is mentioned in the progressions is not thereby required” as well.

The standards describe the achievements we want for students. These are not limiting, but describe where time should be focused if it is short.

Hi, 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.

Hi, I’m going to repost this over in the 6–8 Prob and Stats forum and answer it there.