Mathematics Background
Math
Instruction || Standards || SAISD || NEISD
Background: Mathematics
Instruction
The current organization of our nation's
schools is based on the needs of the industrial age. The goal of
industrial age schools was to provide most youth the training needed
to become workers in fields, factories, and shops as well as to
become literate and informed voters. Generally, minimum competencies
in reading, writing and arithmetic were expected of all students, and
a select few were provided advanced academic training. Future
business and governmental leaders were expected to emerge from this
select group.
The educational system of the industrial age
no longer meets the technology and economic needs of today. Modern
jobs which contribute to a world economy require workers who are
mentally prepared to meet a variety of challenges. A talent for
calculation (which is now done more efficiently by machines) is no
longer the prerequisite for high level jobs. Rather, it is the
talent for grasping new ideas, adapting to change, coping with
ambiguity, and working collaboratively to solve problems that will
empower a worker in today's marketplace.
Our current inherited mathematics curriculum
conforms to the past and contains little vision for the future.
However, new computer technology allows the introduction of pertinent
new material into the curriculum and provides new ways to teach
traditional mathematics. New technology challenges the importance
of some aspects of traditional curriculum. This leads to and can
result in the rethinking of what should be taught to meet the needs
of the 21st century.
Background: Standards
In the United States, the concern among
educators and textbook writers has been to explore many topics rather
than to relate concepts to real world situations. The future
requires students to be better learners by researching and locating
information, evaluating data, and correlating acquired knowledge from
several sources to produce a product. To meet these goals, our
students must be able to analyze information, develop problem solving
strategies and synthesize new data with previous knowledge.
President Clinton, in his State of the Union
Address, called for changes in education to meet the needs of our
increasingly technological society. He has set the following goal
for education and technology:
In our schools, every classroom in America
must be connected to the information superhighway, with computers and
good software, and well-trained teachers. ("Getting America's
Students Ready for the 21st Century")
To help our students meet this challenge,
the President recommended four simple pillars around which these
changes will center:
- Modern computers and learning devices
will be accessible to every student.
- Classrooms will be connected to one
another and to the outside world.
- Educational software will be an integral
part of the curriculum and as engaging as the best video
game.
- Teachers will be ready to use and teach
with technology.
More than ever before, citizens need to
think mathematically. According to The Curriculum and Evaluation
Standards for School Mathematics published by the National Council of
Teachers of Mathematics in 1989, new social goals for education
emphasize a mathematically literate populace, lifelong learning,
opportunity for all, and an informed electorate. These goals imply
that a school system be organized to serve as an important resource
for all citizens throughout their lives. The Standards for K-12
further articulate five mathematics goals for all students: learning
to value mathematics, becoming confident in the ability to do
mathematics, becoming mathematical problem solvers, learning to
communicate mathematically, and learning to reason mathematically.
These goals imply that students should be exposed to many experiences
that provide opportunities to develop mathematical habits of mind and
to understand and appreciate the role of mathematics in human
affairs.
The Conference Board of the Mathematical
Sciences views changes in the teaching of mathematics as a natural
outgrowth of the advance of technology. The Board's recommendations,
published in Educating the Americans for the 21st Century, state that
the development of computer science as well as computer technology
suggests new approaches to the teaching of all mathematics in which
emphasis should be on the following ideas:
- Algorithmic thinking is an essential
part of problem-solving.
- Student data gathering and the
investigation of mathematical ideas are essential activities for
facilitating learning mathematics by discovery.
- Calculators and computers must be
introduced into the mathematics classroom at the earliest grade
practical and should be utilized to enhance the understanding of
arithmetic and geometry as well as the learning of
problem-solving.
- Substantially more emphasis must be
placed on the development of skills in mental arithmetic,
estimation and approximation, and substantially less on paper and
pencil execution of the arithmetic operation.
- Direct experience with the collection
and analysis of data must be provided for in the curriculum to
insure that every student becomes familiar with these important
processes.
- The traditional component of the
secondary school curriculum must be streamlined to make room for
important new topics; and the content emphases and approaches of
courses in algebra, geometry, precalculus, and calculus need to be
reexamined in light of new computer technologies.
- Discrete mathematics, statistics and
probability, and computer science should now be regarded as
"fundamental," and appropriate topics and techniques from these
subjects should be introduced into the curriculum.
The impact of the Standards for School Mathematics has
had far-reaching consequences, one of which has been to impact The
Texas Essential Knowledge and Skills for Mathematics. In consideration
of the changing needs of today's educated citizen, the focus of
Algebra I and Algebra II in The Texas Essential Knowledge and Skills
for Mathematics must shift to include more work with functional
relationships and problem solving in real situations. This approach
to algebra allows students to develop logical reasoning by making
and justifying generalizations based on their experiences with fundamental
algebraic concepts. Technology must be an integral part of these
courses. Students must have regular access to technology that allows
table building, coordinate graphing, algebraic analysis, and computation.
Both national and state standards are powerful and influential forces
on mathematics education in Texas and call for the increased use
of technology at all levels of mathematics instruction.
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