K-12 Mathematics: Some
Warning Signs
Professor Clifford Mass
Department of Atmospheric Sciences
University of Washington
Warning Sign One:
Students Are Less
Mathematically Capable in
College Freshman Courses
• Atmospheric Sciences 101 students today are clearly
less math capable than 10-15 years ago.
• Most have poor algebra skills. Many are
uncomfortable with even simple equations.
• As a result, we have had to “dumb-down” the class.
• Other professors in a variety of disciplines have
noticed the same thing.
Objective Evidence
The UW Gave the Same Math
Placement Exam Between 1990 and
1999
After Scores Plummeted…They
Created a New EASIER Exam
UW Precalculus Placement Exam
70
Score
65
60
Old Exam
New (Easier)Exam
55
50
45
AUT AUT AUT AUT AUT AUT AUT AUT AUT AUT AUT AUT AUT AUT
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Year
Year
AUT 2003
AUT 2002
AUT 2001
55
AUT 2000
AUT 1999
AUT 1998
AUT 1997
AUT 1996
AUT 1995
AUT 1994
AUT 1993
AUT 1992
AUT 1991
AUT 1990
Precalc Placement Exam Adjusted
70
65
60
New Exam
50
45
While Math Placement Scores
Have Dropped, It Has Become
More Difficult to Get Into the
UW And Their High School
Grade Point Averages Have
Risen Considerably!
High GPA of Incoming Freshmen
3.7
3.65
3.6
3.55
3.5
3.45
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Year
What is going on?
• Are Washington State students getting
dumber in mathematics?
• Are external factors (video games, cellphone usage, two-wage-earner families)
taking a toll?
• Could changes in math curricula be part of
the story?
A Relevant Side Issue
• Foreign-born and foreign-educated
individuals are increasingly dominating the
more mathematical disciplines.
• Why aren’t their enough Americans to fill
math-related positions?
1989: The National Council of
Teachers of Mathematics
(NTCM) Standards
• Really more of a set of guidelines then true detailed
standards.
• Promote the discovery approach—students are led
through exercises, experiments, and hands-on projects
designed to motivate them to discover mathematical
principles on their own.
• Far less emphasis on proven algorithms (e.g., long
division) and more emphasis on using calculators.
• Less emphasis on acquiring mastery through practice.
• Less emphasis on algebra and geometry.
• Also known as reform math…or by some as fuzzy math!
A Range of New Curricula Sprung
From the NCTM Standards
• Examples include TERC Investigations,
CMP, and the McDougal–Littell Integrated
Math.
• McDougal–Littell Integrated Math has been
around for over a decade and was initiated
in the Seattle Public Schools in the mid
90s—and is still in use.
McDougal–Littell Integrated
Math.
• Aside: Several math education
professors at the UW agree that
Integrated Math is substandard,
but claimed it wasn’t “real”
reform math.
• Not too fast!!… the teacher’s
edition of Integrated Math
mentioned NCTM many times!
• And the approach is clearly
“reform” and fuzzy
My Sons’ Experience with
McDougal–Littell Integrated
Math
• These books skip around topics in a frenzied way
that makes mastery impossible.
• They lack coherence and logical progression of
ideas.
• For my oldest son, I was so concerned about his
lack of basic skills that I signed him up for Kumon
Math, extra tutoring, and worked with him at
night. And it worked!
The Teacher’s Manual Tells the Story
What about the teacher teaching?
And the Most Serious Problem!
The meteorology examples are completely wrong!
IMP Math: Even
Less Substance
• My younger son in now taking Interactive
Mathematics Program (IMP)
• He is COMPLAINING to me that it is not
challenging, that he wants to learn more.
• Missing key mathematical elements.
• Perhaps OK for someone who is not
college-bound.
IMP (Year 4) Figures Say a Lot
The Bottom Line
• Whether the new “reform” curricula are contributing
to the decline in Washington State student math
performance is a matter of speculation. My own
personal experience suggest that it is.
• But what is clear, is that these curricula are
inadequate to meet the needs of most of our children,
including those interested in going into technical
fields.
• Ironically, the dominance of language in these texts
will work against those with problems with
expression and understanding English prose– i.e.,
will hurt those that need the most help.
Books and Curricula Matter
• Learning occurs in many ways…and not all of it is in
the classroom.
• Some students are visual self-learners--who learn best
on their home reading their books.
• Parental interaction can be very important…but they
must be able to understand and make use of the book.
• Therefore, books must be self-contained as much as
possible and not DEMAND extensive training for their
application.
• In contrast, most reform math texts require extensive
teacher training and are not self-contained.
Whose Math Wars?
• When some of us have pointed out our
discomfort with some aspects of the current
math education situation, supporters of the
reform status quo, accuse us of igniting “math
wars” --as if we are doing something
aggressive and wrong.
• We are simply looking to facilitate a more
balanced approach to math education. Basic
skills and higher-level, creative math are
inherently interweaved.
How Some Reform Math Types View Us
Shalimar
How We View Ourselves
The End..