Not Your Mother’s Mathematics |
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Why has school mathematics changed? During the first half of the 20^{th}
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 20^{th}
century, workforce and college admissions standards changed rapidly as a
technological revolution swept through the 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. |
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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.
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.
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. |
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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:
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. |