What's best: Prioritizing standards or integrating all?

[Kevin Lade]

I’m beginning to see states and ISDs creating documents that “prioritize” the standards based on importance to next level, inclusion on tests, etc.  I am wondering if these attempts are in line with the CCSSM developers’ thinking.  I’m especially interested in the standards at the high school level because they seem particularly prone to being weeded out until what remains are the same old predictable ones that match right up with textbook sections.

In planning scope and sequence for high school courses, should there be an effort to prioritize, or is it more appropriate to integrate all domains, clusters and standards into a cohesive whole?  If time restrictions prevent some content from receiving as much emphasis as other content, then how much can be skipped without ruining the intent and efficacy of a math program based on the CCSS?

Sincerely,

Kevin Lade

 

 

[Bill McCallum]

It’s hard to answer this question at this level of generality, it would be better if we have a test case to discuss. There are two opposing tendencies in implementing standards, both undesirable if carried to an extreme. One is the tendency to want to cover everything with equal intensity, so that the curriculum becomes choked with undergrowth; the other is the tendency to ignore things that you find inconvenient or that are not in the textbook you are using, so that the curriculum becomes parched and arid. So what I want to say in answer to this is “use your own judgement!”; but I also want the person using the judgement to have a thorough knowledge and understanding of the standards.

Trying to be more helpful, I would say that some high school standards are clearly more important than others. This is not a matter of subjective judgement, but a matter of seeing how the standards fit together and detecting which ones are really consequential because they have lots of connection to other standards. So, for example,

N-RN.3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

is an important piece of knowledge, but the student’s world isn’t going to fall apart without it. Whereas

A-SSE.1. Interpret expressions that represent a quantity in terms of its context.

is foundational to all the standards on algebra and functions.

In other words, there are peaks and valleys in the standards, and it isn’t wrong to point them out. This might be a good point to revisit Jason Zimba’s essay on examples of structure in the standards.

[Kevin Lade]

Dr. McCallum, thank you for your prompt response.

You mentioned a test case.  The first example that comes up in a Google search is some work from the state of Oregon:  http://www.mesd.k12.or.us/si/pdf/Prioritized_Mathematic_CCSS-1.pdf.

In their document I think they’ve used yellow highlighting to indicate the standards they feel are most essential; and when I examine the ones at the high school level in particular, my feeling is that there are several instances of non-marked items that represent deviations from what’s typically been in math courses.   But, they are careful to point out that they aren’t suggesting eliminating any standards, rather just prioritizing them.  I think my question to you was prompted by a concern that as soon as a prioritization like this is produced that only the yellow-marked items will end up being the curriculum in many classrooms.

 

Kevin Lade

 

 

[Bill McCallum]

I’m not sure how final this document is or how consequential; maybe it was just a useful exercise for teacher leaders, so I’m hesitant to single it out. But I agree it’s a useful basis for discussion and I agree that there is a worry here. Work like this has to pay attention to the structure of the standards, the language of the cluster headings, and the way domains fit together. It cannot be done one standard at a time. To give just one example, consider the following cluster:

Understand and apply properties of operations and the relationship between addition and subtraction.

1.OA.3. Apply properties of operations as strategies to add and subtract.

1.OA.4. Understand subtraction as an unknown-addend problem.

The document highlights the first standard as a priority standard but not the second one. But understanding that subtraction is an auxiliary operation derived from addition is crucial to the progression here. You can’t pull on that thread without unraveling the whole thing. This is a bit like deciding which leg has priority, the right or the left.

Looking through the document I see many cases where clusters are subdivided into some standards that are priority standards and some that are not. This is probably not a good approach, and is subject to the problems in the example above. I would recommend as a general rule that it should be done at the cluster level if it happens at all.

Note also that the PARCC assessment consortium’s classification of clusters into major, supporting, and additional clusters does indeed operate at the cluster level.

Sometimes this sort of work is driven by a desire to reduce the standard count. But in the example above, removing one of the standards makes for more work, not less. To return to my analogy, it’s like trying to walk on one leg instead of two.

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