Not Your Mother’s Mathematics

 

Why has school mathematics changed?

 

During the first half of the 20th century, instruction in mathematics was justified on two grounds:

·         It disciplined the mind and promoted logical reasoning, especially among college bound students.

·         It provided a workforce with a common set of basic arithmetic and geometric skills.

 

During the second half of the 20th century, workforce and college admissions standards changed rapidly as a technological revolution swept through the U.S. economy.  Since the mid-1980s, the mathematics education community’s response to these changes has been a standards-based approach that expands the scope of school mathematics and shifts the emphasis from rote memorization and recitation to concept development, problem-solving, and applications.  

 

Today, the evolving mathematical needs of the workforce and rising admissions standards of colleges and universities are rapidly converging.  That is, high school graduates going into the workforce will soon need essentially the same set of mathematical concepts, skills and dispositions as graduates going on to higher education.  Individuals lacking these qualifications will face diminishing job opportunities, job security, and income.  The “old basics” are no longer an adequate foundation for success in higher education or the workplace. 

 

What are the new basics?

 

The National Council of Teachers of Mathematics’ (NCTM) Principles and Standards for School Mathematics has shaped the direction of state and local mathematics reform for over two decades.  Acquainting oneself with these principles and standards is the first step in understanding K-12 mathematics.   The principles are

·      Excellence in mathematics education requires equity—high expectations and strong support for all students.

·      A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades.

·      Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.

·      Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.

·      Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.

·      Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning.

 

The standards are listed in two categories, content and process. 

Content Standards

Process Standards

·     Number & Operations

·    Problem Solving

·   Algebra

·    Reasoning & Proof

·   Geometry

·    Communication

·   Measurement

·    Connections

·   Probability & Statistics

·    Representation

 

A recent NCTM publication, Curriculum Focal Points, provides perspective on key topics in Pre-Kindergarten through Grade 8 mathematics.  A free download of the document is available online.

 

For the most part, Mathematics Education Associates practices ”reform” mathematics education like that advocated in the Principles and Standards for School Mathematics.  Not everyone is persuaded, however, that reform mathematics is in the best interests of students or the nation.  The debate between these two positions has been called the “math wars”.  The following websites illustrate the passionate nature of this debate. 

 

Supporting Reform Mathematics

Supporting Traditional Mathematics

Mathematically Sane

Mathematically Correct

 

Readers need not embrace one or the other of the philosophies represented by these websites.  What is “best” for one child might not be “best” for all children.  We advise you to read thoughtfully and adopt those principles, standards, materials and practices that work best for your children as demonstrated by their engagement, achievement, and attitudes.  Emphasize concept development and understanding, but don’t forget to develop fluency with number facts, vocabulary, notations and formulas through regular practice.  Use calculators and computers to facilitate concept development and problem-solving, but don’t forget to develop and use mental math and estimation skills.    

 

Going beyond the basics.

 

Mathematics has served as a gatekeeper to higher education and well-paying jobs in the workplace for decades.  Many parents interpret this metaphor as follows:

  1. There is only one gate (i.e., college admissions);
  2. There is only one gate key (i.e.., satisfactory SAT/ACT mathematics scores); and
  3. The gate key is forged and finished during high school.  

 

In fact, mathematical readiness for higher education and workplace training/employment must be acquired gradually over a period of years.  Mathematical knowledge, confidence, and dispositions acquired in this manner are the “raw material” from which “gate keys” are forged:

·           Content and process knowledge like those listed in NCTM’s Principles and Standards for School Mathematics;

·           Confidence, persistence, flexibility, patience and collegiality; and

·           Knowledge, skill, confidence and flexibility in the use of information, communication and modeling technologies (e.g., web browsers, email, word processing, spreadsheets, algebraic & geometric modeling tools).

 

Acquired and developed over a period of years, these readiness factors do more than prepare students for examinations; they enable students to explore and discover their true talents and interests.  Education is neither a success nor complete until students develop a genuine understanding of and appreciation for their talents, accomplishments and opportunities.  Helping them to do so is the work of both teachers and parents.