The Common Core State Standards and College Readiness

At the recent Forum on mathematics in the first two years (college), we had several very good presentations — some of these very short. Among that group was one by Bill McCallum, a primary author of the mathematics portion of the Common Core State Standards. Bill focused his comments on 9 expectations for the high school standards intended to represent college and career ready.

The expectations listed are:

Modeling with mathematics
Statistics and probability
Seeing algebra as based on a few coherent principles, not a
multitude of unrelated techniques
Building and interpreting functions to represent relationships between quantities
Fluency
Understanding
Making sense of problems and persevering in solving them
Attending to precision
Constructing and critiquing arguments

Of these, Dr. McCallum suggested that fluency is the only one commonly represented in mathematics courses in the first two years. The reaction of the audience suggested some agreement with this point of view.

So, here is our problem: We included all 9 expectations when the Common Core standards were developed. We generally support these expectations individually. Yet, students can … in practice … do quite well if they arrive with a much smaller set of these capabilities. Clearly, the Common Core math standards expect more than is needed.

What subset of the Common Core math expectations are ‘necessary and sufficient’ for college readiness?

For example, even though it is critical in the world around us, modeling does not qualify for my short list; neither does statistics and probability.

We are basically talking about the kinds of capabilities that placement tests should address Measuring 9 expectations (all fairly vague constructs for measurement) is not reasonable; measuring 4, perhaps 5, might be.

I think we should develop a professional consensus around this question. The answer will clearly help the K-12 schools focus on a critical core, and can guide the work of companies who develop our placement tests.

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Assessment in Math Classrooms, Math curriculum in general, placement | Jack Rotman | October 20, 2014 8:43 am

6 Comments

By Bruce Yoshiwara, October 20, 2014 @ 2:29 pm

The National Center on Education and the Economy’s 2013 “What Does It Really Mean to Be College and Work Ready?” is available for download at http://www.ncee.org/college-and-work-ready/

The 2010 position paper from California’s Intersegmental Committee of the Academic Senate (representing the academic senates of the University of California, the California State University, and California Community College systems) on the expected competencies of entering college studeents is available at http://icas-ca.org/competencies-in-mathematics
By Jack Rotman, October 20, 2014 @ 5:29 pm

Thanks for the information, Bruce!
By schremmer, October 20, 2014 @ 10:24 pm

I am amazed at the fact that all we can think of is always what we expect from the students and, other than improved teaching methods and all, what we can do to let the students achieve that.

So, it is only poetical justice that Khan Academy and the publishers are beating us at our own game—and that we are going the way of the dinosaurs. At least, the dinosaurs were not whining all the way.

Yes, I know, one of the principles is “Seeing algebra as based on a few coherent principles, not a multitude of unrelated techniques”, but what I don’t see is neither any discussion of what such a “coherent view” would be, nor any tangible implementation of any such view.

And I have seen nothing to convince me that all the brouhaha is not just that: mere lip-service.

Sad.
Regards
–schremmer
By Jack Rotman, October 22, 2014 @ 11:49 am

Surprisingly (perhaps), progress is being made towards a goal of students experience valuable mathematics in a mathematics classroom (even if we are not as advanced as we might like). Those seeking evidence of this progress will need to connect with multiple efforts at various stages; the evidence is not cryptic nor available from a single source. All of us need to be engaged with this work in order to achieve a ‘coherent view’.
By schremmer, October 22, 2014 @ 5:00 pm

(1) I just realized that I left our a rather crucial “not”in my previous post. The last line of the first paragraph should read “but not what we can do to let the students achieve that.”

(2) How each one of us lets “students experience valuable mathematics in a mathematics classroom” is difficult to assess and to transmit to others.

So, I am not speaking of whatever “progress is being made towards a goal of students experience valuable mathematics in a mathematics classroom”. I am speaking of a discussion of the mathematical contents that are the object of this experience. To my knowledge, these are never discussed—as if they went without saying.

Mathematics is in the relations between topics rather than in the topics themselves. So, more than in just a table of contents listing a number of topics, I am interested the architecture of these contents, how this leads to that.

A good content architecture is a necessary condition for the students to develop some of the items in the above “listed expectations”: Fluency, Understanding, Making sense of problems and persevering in solving them, Attending to precision, Constructing and critiquing arguments. (Which, while unarguably good, rather feels like a disorganized laundry list.)

Regards
–schremmer
By Jack Rotman, October 22, 2014 @ 7:17 pm

Ahh … now I understand the comment about contents. For developmental math courses, we actually spent quite a bit of time on this from 2008 to 2010 when a group of us in the New Life Project identified outcomes and then looked at a reasonable structure to create courses. The result of this work are the two new courses — Mathematical Literacy and Algebraic Literacy — which can be used to replace the existing artifacts known as basic math & pre-algebra & beginning algebra & intermediate algebra. Some colleges have done this replacement; more often, the process occurs in stages. That is still progress.

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