In my last post, I went in great detail into the structure
of the Common Core Math Standards for K-8. Long story short, the picture at the right is a visual of the structure showing the funnel effect – where the standard itself is the end product of so much more: Introduction, Domain, Cluster. The gist of the last post was that it is important to look at all the components, not just the specific standards themselves, so that you understand how the standard fits into the learning progression.
When looking at the high school content, the structure of
the standards is the same, with an additional component, the conceptual categories. There are six conceptual categories at the
high school level: Number and Quantity, Algebra, Functions, Modeling, Geometry,
and Statistics & Probability. Within these conceptual categories, there are the Introduction, Domains, Clusters and specific standards.
The idea behind the conceptual categories is that students
acquire these understands through repeated exposure across many topics, so
Modeling standards are embedded in all high school math courses, not a specific
course unto themselves. Similarly,
Functions & Number and Quantity are also standards that will appear in many
High School courses, such as Algebra, Geometry and Calculus. The High School
standards are not traditional course topics, but rather concepts that students
are exposed to throughout their High School mathematics learning.
Here is an example, using the conceptual category of Functions,
of the High School Structure. I chose just one standard to highlight again, the
structure and overall cohesiveness.
Conceptual Category: Functions
Relevant Excerpt from the Introduction: Functions
presented as expressions can model many important phenomena. Two important
families of functions characterized by laws of growth are linear functions,
which grow at a constant rate, and exponential functions, which grow at a
constant percent rate. Linear functions with a constant term of zero describe
proportional relationships.
Relevant Domain: Linear,
Quadratic, and Exponential Models
Relevant Cluster: Construct and compare linear and exponential
models and solve problems
Specific Content Standard: CCSS.MATH.CONTENT.HSF.LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
As you can
see from this example, this particular standard could be appropriate in a
Pre-Algebra, Algebra, Geometry, or Algebra II course. So the High School
standards cross traditional course structures and understanding this and really
exploring the High School standards when planning course content and curriculum
is an important. These are not isolated standards for a single course, but
rather pervasive standards that span several course content areas so that
students are continually exposed and using their understanding of mathematics
throughout all high school mathematics courses. This helps them see the
inter-connectedness of mathematics.
I hope that
these last few posts that focused on how the structure of the standards has
clarified that just knowing a content standard or knowing the title of a math
practice does NOT mean you know enough. It is important to really read through
the entire structure of both the practices and the content standards to fully
ensure that mathematics instruction is supporting what students need to know
and be able to do. It is important to spend time exploring these PRIOR to
developing curriculum or lessons, to ensure what is being taught, and HOW it is
being taught are truly supporting student conceptual understanding.
In my next
post, I am going to spend a little time discussing the key shifts that are at
the heart of the Common Core Standards. I think there is a lot of
misconceptions about coherence, focus and rigor, which leads to much of the confusion
that teachers, parents, the media and the politicians have about the standards.
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