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October 2006 Newsbulletin President's Message
A
few weeks ago NCTM released Curriculum Focal Points for
Prekindergarten through Grade 8 Mathematics: A Quest for
Coherence. This document of fewer than 50 pages presents three
major topics of emphasis at each grade level, pre-K8. The publica-
tion is intended to serve as a catalyst for important discussions and
decision making on curricular frameworks at the state and local
school district levels.
Why focal points? Walk into any classroom in this country
and ask a teacher what seems to govern the mathematics
taught in prekindergarten through grade 8 mathematics. They
are sure to point to their state or local school districts curricu-
lum frameworks. These frameworks come in all shapes and
sizes. Forty-nine of the fifty states have mathematics curriculum
frameworks that contain anywhere from 30 to 100 or so expec-
tations for any given grade level. Can you imagine the challenges
and frustrations that many teachers experience as they try to fig-
ure out what is really important at a particular grade level?
Of course, one might argue that this quandary is easy to
resolve. As most know, No Child Left Behind requires a formal
assessment of mathematics for grades 38. Thus, one way to
determine whats important is simply to teach whats tested. But
is it safe to assume that these assessed topics are actually essential
for a particular grade level? Does their assessment imply consen-
sus on the important mathematics that students should know
deeply and well before they encounter high school mathematics?
This is what NCTMs Curriculum Focal Points is all about.
It is our intent that mathematics leaders at the state and local
school district levels will use the Curriculum Focal Points docu-
ment to begin discussions to help determine the important
mathematics at each grade level. Such discussions, perhaps even
debates, are needednow. Over the years, I have regularly
asked teachers, What do you hope your students will really
understand when they leave you to enter the next grade? Their
responses are pretty much the same, regardless of locale,
because most experienced teachers and teacher leaders know
where to place their focus. Now we need others to join in the
discussion. By including mathematics leaders at the state and
local school district levels, textbook publishers, and assessment
developers, we can ensure that all students have the opportunity
to learn important mathematicsdeeply and well.
What is a curriculum focal point? In the Curriculum Focal
Points, NCTM identifies three major mathematical concepts, skills,
or understandings for each grade level. These are the areas of focus
or emphasis at that grade level. The curriculum focal points and
their connections can be used as the foundation for mathematics
learning in that grade and for extended understandings in subse-
quent grades.
A focal point is much more
than a topic of emphasis. Con-
sider this example from grade
4: Developing quick recall of
multiplication facts and related division facts and fluency with
whole number multiplication. Underlying this point of emphasis
is understanding place value, multiplication, models for multiplica-
tion, and the use of the properties of operations, particularly the
distributive property. Although the quick recall of facts and fluency
with the operation is important, particular attention must be paid
to how and why such procedures, including the standard algo-
rithms, work and how they can be used to solve problems.
Whats the point? Mathematics leaders at every level need to
be mindful of the important mathematics that should be taught
and learned at each grade level. Even the most experienced teach-
ers can use assistance with this issue, particularly if they change
grade level or school level assignments. Focal points comprise the
concepts, skills, and understandings that are the building blocks
for higher-level mathematics. In the end, this may mean shorter,
but more incisive lists of expectations for deeper learning.
Why publish this now? Questions about mathematics educa-
tion and what should be taught from grade to grade are cur-
rently receiving a lot of public attention. And the oft-repeated
criticism that U.S. mathematics curricula are a mile wide and
an inch deep has caught the attention of parents, school board
members, publishers, policy makers, and the U.S. Department
of Education. In addition to these influences, a report by
NCTM and the Association of State Supervisors of Mathematics
entitled Standards and Curriculuma View from the Nation
(2005), along with the ongoing work of the Center for the Study
of Mathematics Curriculum (CSMC), have prompted the Coun-
cil to develop the Curriculum Focal Points. NCTM should take
the first step in this initiative.
In developing the Curriculum Focal Points, the writers
reviewed the mathematics curriculum frameworks from many
states, Japan, Singapore, and other countries. Drafts were vetted
by 70 reviewers representing a cross section of state and local
school district mathematics leaders, mathematicians, policy
makers, classroom teachers, and mathematics educators. Cur-
riculum Focal Points is now ready for you.
Use Curriculum Focal Points for Prekindergarten through
Grade 8 Mathematics to guide your curriculum discussions.
Adapt the recommendations, if needed, to meet your needs, but
think seriously about the important mathematics that all chil-
dren should learn deeply and well in prekindergarten through
grade 8. Use the Curriculum Focal Points as the starting point
or launch pad for such endeavors. Presidents Message
Curriculum Focal Points:
Whats the Point?
Francis (Skip) Fennell
Originally published in the NCTM News Bulletin (October 2006).
Copyright 2006, The National Council of Teachers of Mathematics. All rights reserved.