San Antonio Technology Education Coalition


     

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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