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Frequently Asked Questions about Mathematics in Colorado
Frequently Asked Questions About Mathematics in Colorado
- How many high school math credits are required to graduate?
- Where is the list of math programs and interventions that are approved to use in schools?
- How are Colorado's math standards like and not like Common Core?
- What's going on with HS.S-ID.C.9? It's not where I expected to find it and the numbering seems out of order.
- What are OGL and SHK? We see them on our CMAS score reports for mathematics, but what do they mean?
There are no state-level requirements for courses or credits, so technically the number could be as low as zero. However, because math is a tested subject and required for most (if not all) higher education admissions, school districts usually require at least two, commonly three, and sometimes four years of mathematics credits in order to graduate. For your specific requirements, check with your school.
There is no such list. You may be asking this question because a list of approved programs exists for K-3 literacy, but that's a special provision of the READ Act that does not affect mathematics or other content areas. If you're looking to adopt curriculum materials for your own school or district, there are guides and advice on the Tools for Curriculum Evaluation and Adoption page.
Colorado's State Board of Education adopted the Common Core State Standards (CCSS) in 2010 and reaffirmed that decision in 2018. We consider ourselves to be a Common Core state, but that does not mean that the content of Colorado's standards for mathematics is identical to what you will find at corestandards.org. Other statuary requirements in Colorado require that our standards for all content areas include support for the Colorado Essential Skills, often called "21st Century Skills." Therefore, Colorado's mathematics standards document is a longer and more robust document than what the CCSS provides, with the CCSS forming the parts of our standards listed as grade level expectations and evidence outcomes, while the sections under the heading "Academic Contexts and Connections" are uniquely Colorado's.
First of all, you should be applauded for your keen attention to detail! This is the one evidence outcome that Colorado's standards revision committee decided to move out of the cluster it is found under in the Common Core. In the CCSS, “Distinguish between correlation and causation” is under cluster HS.S-ID.C., “Interpret linear models.” The committee thought this was a mistake because correlation and causation are concepts that shouldn’t be limited to linear models. (And, word has it, the CCSS authors wouldn’t put it there again if they had the chance to move it.) We thought it would make more sense under S-ID.B, “Summarize, represent, and interpret data on two categorical and quantitative variables.” Correlation and causation might look different with categorical variables, but the ideas are just as relevant for categorical variables as they are for quantitative variables.
The result of this decision forced the committee to deal some messiness in our numbering system. We couldn't change the CCSS coding, because it is what it is. We could have numbered 5-6-9 on S-ID.B and 7-8 on S-ID.C, or we could have numbered 5-6-7 on S-ID.B and 7-8 on S-ID.C. Of two imperfect choices—a 9 out of order or two statements numbered as 7—we chose the latter. Part of the reason was technical: numbering continues and restarts all throughout the document, so the idea that a GLE starts with a value other than 1 is common. It just creates a second 7 under a different GLE that you’d think would be an 8. Numbering 5-6-9 would have created an instance of non-sequential numbering within a GLE, which never happens anywhere else in the document.
Both of these things are shorthand for “it’s a bunch of different standards—too many for us to list.” OGL is “on grade level,” and it refers to a combination of standards within the grade being assessed. SHK is “securely held knowledge,” and it refers to a combination of standards prior to the grade being assessed.
Here’s an example of SHK. In third grade, there’s a test specification called an evidence statement (not to be confused with evidence outcomes from the standards, although they are similar because the evidence statements were built from the evidence outcomes) that says we should assess this:
3.D.2 Solve multi-step contextual problems with degree of difficulty appropriate to Grade 3, requiring application of knowledge and skills articulated in 2.OA.A, 2.OA.B, 2.NBT, and/or 2.MD.B. i) Tasks may have scaffolding if necessary in order to yield a degree of difficulty appropriate to Grade 3. ii) Multi-step problems must have at least 3 steps. (MP.4)
You’ll see that this is for a Grade 3 item and it’s designed to have Grade 3 difficulty, but it’s relying on knowledge and skills from Grade 2 standards. It’s the way those Grade 2 standards are combined in a modeling context that gives the problem its difficulty at the Grade 3 level. Instead of saying all that, and listing all the evidence outcomes under 2.OA.A, 2.OA.B, 2.NBT, and/or 2.MD.B, we just say “SHK” to say that this item is based on a combination of Grade 2 knowledge that should be securely held by 3rd graders. “OGL” items would combine standards in a similar way but do so from the same grade level that is being assessed.
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