Here is a statement that absolutely scares me. It is from Lesson 19: Interpreting Correlation from the NYS Common Core Mathematics Curriculum.
It is not necessary for students to compute the correlation coefficient by hand, but if they want to know how this is done, you can share the formula for the correlation coefficient given below.
It demonstrates, in a nutshell, a massive hypocrisy in the implementation of Common Core math here in NY. What starts out, in the lower grades, as a powerful attempt to make students consciously aware of what they are doing, has morphed into the old and disastrous "give them a formula or a calculator and they will be happy." When doing basic arithmetic the emphasis on understanding by expecting multiple methods sometimes seems like overdoing it. Here, understanding is just tossed aside.
Take a look at this Wikipedia page (https://en.wikipedia.org/wiki/Pearson_correlation_coefficient), read it carefully, and then tell me if anything related to this concept actually belongs in Algebra I. If that does not convince you, check out the Wolfram page. For a bit more, check out this one.
What really bugs me is that using a calculator to compute the Pearson correlation coefficient bypasses any attempt to teach understanding. No student will come out of this with any knowledge other than "this is what they told me in school". That is exactly the situation that "teaching for understanding" was supposed to avoid.
Why not let students actually get the opportunity to explore topics such as least-squares regression using software such as GeoGebra? Here is a small visual example of what GeoGebra can do. The labeled points can be dragged and the sliders control slope and y-intercept of the line. The best fit is the line that gets the sum of the squares as small as possible.
We should keep in mind that there is no need to have a line of best fit if we can see all the data plotted in front of us. A best fit line can help us if it can be understood as a model of prediction. If that is the goal, then it would make sense to have some strong connection between the modelling line and the correlation coefficient. Check out what New York State students experience and see if that connection is solidly made.
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