6th grade statistics – what are they constructing?

[kkirnie]

I am looking for clarification on box plots and mean absolute deviation.

According to the blog on mode and range, Bill has written.

 

“A curriculum could meet the Grade 6 standards on Statistics and Probability by working with large data sets arising from real contexts, using technology to plot them and compute their summary statistics. Students should be able to answer statistical questions, display data graphically, choose appropriate summary statistics and interpret them in terms of the context. That’s what the Grade 6 standards say.”
This leads me to believe that students are reading and interpreting data using measures of center and variability in 6th grade. Which would mean not finding the Mean Absolute Deviation but looking at the value of the MAD and applying it to understanding the data. Leaving the figuring out the mean absolute deviation in 7th grade.
Does the same reasoning apply to box plots?

[Cathy Kessel]

The grades 6–8 Statistics and Probability Progression discusses box plots in grade 6. It can be downloaded here: http://ime.math.arizona.edu/progressions

[kkirnie]

Cathy,

I have read the progression many times.  Hence the confusion between Bill’s blog and the progression document.  Do students need to be skilled at creating box plots and Mean Absolute Deviation OR should they be skilled at interpreting them when they are given a mean absolute deviation?

[Bill McCallum]

First, sorry for the long delay in replying. I got hijacked by my day job for a while.

I guess when there seems to be confusion we should try to go back to the text of the standards and see what we can get from it. The second cluster under 6.SP is called “Summarize and describe distributions.” It doesn’t use the word “construct”, although one could argue that in order to summarize a distribution you need to construct a summary. But, as I said in the earlier post, you could do this using technology, and it seems to me that this would be a strategic use of tools in Grade 6, falling under the meaning of MP5. So my inclination would be to stick with my original interpretation (surprise!) and say that Grade 6 students could be using technology to produce summary statistics.

As the question of box plots, 6.SP.B.5c says:

Summarize numerical data sets in relation to their context, such as by

c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

Taking the first choice in each parenthetical, we get median and interquartile range. Box plots are a possible way of representing these, so it would be natural to use them in this context. Although I would certainly not expect Grade 6 students to be skilled in producing them by hand, for the same reasons outlined above.

I haven’t actually checked if this contradicts the progressions document or not, and feel I should move on to answer other overdue questions!

[TR]

I am a parent of a 6th grader that is now in a school that teaches common core. My child has an IEP for learning delay. How can I help my child deal with the statistics in her math class. She can do the math but the application in a real world setting does not present itself easily. I do not even see the practical application of some of the course work. Please help. My daughter does have one period of ‘Transmath’ but it does not back up or re-enforce what is taught in her regular math class.

[TR]

Also, my daughter is coming out of DODDEA which has not picked up common core. So far, I will be honest I am not pleased. When a parent must consult the internet to answer questions for 6th grade math then there are issues. Please sell me on the new curriculum standards.

Thanks

[Bill McCallum]

I need a more specific question to be able to answer this. The purpose of this blog is to help people understand the standards; what does a particular standard mean, what’s an example that illustrates it, and so on. It looks like you are having a problem with a particular curriculum. Not all curricula that claim to be Common Core aligned really are, and even with curricula that are aligned I don’t think I can take on answering every question about every curriculum. (This is an entirely volunteer effort.) Still, I’d be happy to try to help if you can give me something more specific. I would encourage you to read the Grade 6 statistics standards themselves and see if you think the work your child is doing is related to them. You can read them at corestandards.org or illustrativemathematics.org.

[lhwalker]

I must disagree that having to consult the internet means there is a problem. There is a huge problem with math education in this country, but it is because too often we math teachers have presented math as a series of compartmentalized, memorized steps. That’s what most adults remember, but I wonder if they are aware of how few consider themselves to be good at math. There are some instructional techniques that research shows develop solid number sense that goes with the math procedures, connecting them and making them meaningful, easier to remember. Those techniques need names. I have had to look up a few myself. Better yet, I have watched a few demonstrated on teachingchannel.org. It’s an exciting time to be involved with math instruction because, for the first time, I believe we are making a huge step toward making mathematics within easy reach of all students.

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