Education Week - November 12, 2014 - Special Report - S22

S22 |
EDUCATION WEEK n
November 12, 2014
Making Sense of the Math: The Common Core in Practice > www.edweek.org/go/math-report
Q&A: WILLIAM G. McCALLUM
Behind the Math Standards
A common-core writer discusses aims, effects
By Liana Heitin
W
William G. McCallum,
a lead writer of the
common core for math,
says the biggest change
the standards pose for
educators is the increased
focus on fewer topics.
illiam G. McCallum accepted an offer about five years ago to lead a team in
developing the Common Core State Standards for mathematics. The Sydney,
Australia-born mathematics professor, who has worked at the University
of Arizona in Tucson since 1987, chaired the 51-person work group, which included
researchers, mathematicians, state education department representatives, and teachers.
Along with Phil Daro, a senior fellow at America's Choice, a school-improvement program
owned by Pearson Inc., and Jason Zimba, a math and physics professor who later
co-founded the nonprofit Student Achievement Partners, Mr. McCallum then
served as a lead writer of the college- and career-ready standards, which the
majority of states are now implementing.
In an interview with Education Week, Mr. McCallum, who is currently
collecting activities and diagrams for each of the standards through a project
called Illustrative Mathematics, discussed the thinking behind various
components of the math standards, and addressed some criticisms of the
framework. (The interview has been edited for length and clarity.)
"
It wasn't an
entirely new
idea to try and
describe what
mathematical
practices look
like, but it was
new to make
that part of the
standards."
You started the process of developing standards by writing
"progressions documents," which describe the order in
which particular topics should be taught. From there, you
broke the progressions into grade-level standards. But you
and many others say the progressions documents are key to
understanding the standards. Why and how should teachers be
using them?
We wanted the standards to be coherent across grade
levels. We wanted them to tell a story that made sense
about mathematics and we thought that was a good design
to start out.
The progressions documents tell the story of how
the mathematics in a particular domain, let's say the
fractions domain, progress. You can detect that from reading
the standards-for fractions, for example, you can look at the
grade 3 standards, you can look at the grade 4 standards,
and you can see how they fit together. But the progressions
documents have examples, and they have more narrative
explanation. So those are useful documents if you want to
understand this idea that the mathematics does progress,
and that what you're teaching in grade 3 you're teaching for a
reason so that kids going into grade 4 will be able to do what
they're supposed to do there.
Unlike most state standards, the math common core includes, in
addition to content standards, eight Standards for Mathematical
Practice. What exactly are those and why did you all decide to
include them?
They're various mathematical habits of mind that we
wanted to codify. They're an evolution of the National
Council of Teachers of Mathematics' process standards
and a National Research Council document called "Adding
It Up" that talks about the strands of mathematical
proficiency.
There have always been attempts to describe not only the
knowledge and skills that kids have to have, but how they
approach doing the mathematics-do they have persistence
and perseverance solving problems? Do they use language
precisely? It wasn't an entirely new idea to try and describe
what mathematical practices look like, but it was new to
make that part of the standards.
So will students be assessed on these? How will that work?
I know both assessment consortia are trying to figure
out how to do that, but of course it's limited to what
you can do with a large-scale computer-administered
assessment.
But I also think assessment of the Standards for
Mathematical Practice will happen in the classroom.
Not all assessment is about the tests that kids take at
the end of the year. Teachers observe students, they can
give performance tasks, they can see how they do. It
might be more in the form of formative assessment than
summative assessment, but that's an important location
for assessment of the practice standards.
In your view, what's the biggest misconception people have
about the math standards?
I think probably the biggest one is they think standards
are the same thing as curriculum. When their kids bring
home a homework problem that's a quote "commoncore
problem"-it isn't. It's a homework problem from a
curriculum, and the curriculum may or may not be aligned
to the common core. But the common core never said the
kid had to do that problem. But I think people don't see
that.
Standards are just expectations for what we want students
to know and understand and be able to do by the end of the
year or a particular course. Curriculum is how you get them
there. There can be good or bad curriculum implementations
for the same standards.
What do you think is the biggest specific change in the
standards, as compared with most previous state standards, for
math teachers?
I'd say the level of focus is probably the biggest change.
Every teacher is used to teaching a certain amount of stuff
in their grade level, and the common standards basically
rearrange the material so that at any given grade level,
you're focused on a smaller set of things.
So for every teacher that used to teach topic X,
and it's no longer there, they have to make that
PAGE S24 >
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Education Week - November 12, 2014 - Special Report

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