After talking to some teachers at PCMI on Tuesday and hearing from my fellow standards writer Jason Zimba I decided to do a quick fix on the modeling progression. The previous version ventured into territory that has been discussed on this blog: the different possible meanings of the word “model.” I decided this could be confusing, so edited it down so that it now sticks to the meaning of the word as used in the standards. The new version is here.
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Thanks for the quick revision, I think that this version is clearer and more user friendly.
– I notice that in both drafts you separate statistical and mathematical models. Is there a reason that statistics is not considered a subset of mathematics?
– It seems on the first page you have lost the quote by Wigner, but not the citation.
– What was the thinking behind getting rid of the section on word problems being the bane of school mathematics? I thought this was a powerful statement addressing the needs of those students that don’t understand why they would ever want 84 grapefruit.
– I love the statement “These diagrams of modeling processes are intended as guides for teachers and curriculum developers rather than as illustrators of steps to be memorized by students.” (I wonder if this in in reaction to how some utilized the modeling cycle originally listed in the CCSSM).
– As you created a revision for this and some of the other progression documents, will you release any sort of “track changes” or “summary of changes” for those that are familiar with the previous version?
Thanks!
Thanks for these questions! Answers in order of the questions:
– Most statisticians do not consider statistics as a subset of mathematics. It uses mathematical tools, but also methods from science.
– Thanks for pointing that out
– The progressions documents are meant to be a translation of the standards into narrative form. There was too much personal opinion here that is not reflected in the standards.
– Good!
– No, that isn’t possible with the resources we have.
Though I do appreciate the increase in clarity in the body of the document, I am still concerned about the gray box on page 3. This seems to indicate that to what many teachers might be a tool, is according to the progression a mathematical model. Additionally, I noticed that on page 5, the section formally titled “Three Aspects of Modeling”, was abbreviated, deleting references to the NRC’s Framework for K12. I think that the idea of mental models is at the core of student thinking and teachers understanding of the process.
Thank you.
Andrew’s comment about page 3 touches on several issues. In a given situation, tables (in general) might first act as a possible tool (How can I represent the features of this situation that seem to be relevant? Let me consider available representations (created via technology or by hand): expressions, tables, dot plots, box plots, other types of diagrams, functions, . . . Oh, it would be strategic to use a table for reason X–or use a linear function for reason Y). Once the specific table (or function) is created, it is considered a model, given that the user understands how the entries of the table or variables in the function correspond to features of the situation. Depending on purpose and situation and model, those correspondences might need to be made clear by appropriate labeling. Terminology doesn’t usually acknowledge the use of tables as models so explicitly (although note “twoway frequency table”) but linear functions are frequently called “linear models” when they are used for applied purposes. (There are examples in the high school statistics and probability progression.)