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

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Precalc Placement Exam Adjusted

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New Exam

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

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What is going on?

• Are Washington State students getting dumber in mathematics?

• Are external factors (video games, cell-phone 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..