Teacher2Teacher |
Q&A #2642 |
From: Gail
(for Teacher2Teacher Service)
Date: Nov 27, 1999 at 00:39:26
Subject: Re: Real life math
I searched he NCTM (National Council of Teachers of Mathematics) website, and found some informaiton that might get you headed in the right direction... http://standards-e.nctm.org/1.0/normal/standards/standardsFS.html "The standards address both mathematical content and mathematical processes. Roughly speaking, the content standards represent what students should know; the process standards represent ways of acquiring and using that knowledge. This separation is artificial, however. In practice, what one can do depends in important ways on what one knows and on how one can exploit that knowledge. Five standards describe the mathematical content that students should learn: Number and Operation Patterns, Functions, and Algebra Geometry and Spatial Sense Measurement Data Analysis, Statistics, and Probability Five standards describe the mathematical processes through which students should acquire and use their mathematical knowledge: Problem Solving Reasoning and Proof Communication Connections Representation It should be recognized that this set of ten standards does not neatly separate the content of school mathematics into nonintersecting subsets. Because mathematics as a discipline is highly interconnected, the areas overlap and are integrated. Some topics in data analysis, for example, could be characterized as part of measurement. Patterns and functions appear throughout geometry. Number pervades all the areas of mathematics. The arrangement of the standards is designed solely as a way of organizing the content and processes. Any method of dividing the content of mathematics will, at the top level, highlight some areas and obscure others. Consider discrete mathematics as an example. In this draft of Principles and Standards, the main topics of discrete mathematics are included, but they are distributed across the standards, rather than separated into a separate standard. The process standards point to major aspects of student competency that are essential to students' mathematical growth. As students learn mathematics, they will develop an increasing repertoire of problem-solving skills, a wide range of mathematical "habits of mind," and increasing sophistication in mathematical argument. Also, students should become proficient at expressing themselves mathematically, both orally and in writing, gain fluency in the language of mathematics and able to make connections within mathematics and from mathematics to other disciplines." "Each of the standards presented in this draft document has formal beginnings in the pre-K-2 years. The ten standards, rather than being separate topics for study, are designed to support the development of important, connected mathematical ideas and should be closely interwoven. At the core of mathematics in grades pre-K-2 are the number and geometry standards. Each of the other mathematical standards, including patterns, measurement, and data and the process standards, contribute to and are learned through the number and geometry strands. Children's number development moves through a pattern of increasingly sophisticated levels of constructing ideas and skills. In particular, children learn to count, group, combine, and separate numbers, sets, and shapes as they build their concepts of place value and the four arithmetic operations. The big ideas in number include the many meanings of numbers; systems of counting numbers (i.e., one-to-one correspondence, increasing and decreasing by one more and less, skip counting); composing and decomposing numbers, place value relationships, and part-whole relationships. Children develop understanding of space and geometry through their own movement and based on visual and tactile explorations. Two- and three-dimensional shapes, properties of shapes (including symmetry) and transformations are encountered and explored in the early primary grades. The discussion of the ten standards in this chapter reflects the inter-relatedness of content and process in young children's learning of mathematics. Children recognize patterns of all sorts in the world around them and gradually begin to use patterns as a strategy for solving problems. Both number and geometry are used in measurement, for example, as children answer questions such as "How heavy?" "How big?" "How long?" and "How tall?" The ability to gather, organize, represent, and use data to answer questions is likely to involve all of the process standards. Skills are acquired in ways that make sense to children. Teachers must continually attend to maintaining a balance between emphasis on conceptual and procedural (skill) aspects of mathematics. Children whose skills and strategies are based on understanding of fundamental mathematical concepts are more likely to retain and be able to expand their knowledge and understanding in later years. The pre-K-2 mathematics program should take advantage of technology. Guided work with calculators can enable children to explore number and pattern, focus on problem-solving processes, and investigate realistic applications. Through their experiences, and with teacher support, children come to recognize when using a calculator is appropriate and when it is more efficient to compute mentally. Computer environments also can make a powerful and unique contribution to the mathematics program. They enable children to manipulate virtual representations of numbers and see, for example, that "4 tens and 7 ones" is the same as "3 tens and 17 ones." Simple programming environments such as Logo can be used to engage students in geometric and spatial investigations. Children frequently possess greater knowledge than they are able to express in standard symbolic notation, and teachers need to determine through assessment what children already know and what they still have to learn. Information from a wide variety of classroom experiences-classroom routines, conversations, written work (including pictures), and observations-provides the teacher with an assessment of what young children already know, are in the process of learning, and still need to know. Quality assessments inform instructional decisions and allow teachers to monitor individual children's progress while focusing on how children are thinking about mathematics. Mathematics learning for pre-K-2 children is active, rich in mathematical language, and filled with thought-provoking challenges. Educational research and classroom experience together challenge us to hold high expectations for all children and look at what they can do with understanding rather than to plan programs around preconceptions about children's limitations. This does not mean abandoning children's ways of knowing and representing; rather, it is a clear call for creating opportunities for children to learn new, important mathematics in ways that make sense to them." You might be better off going directly to the site to read it. :-) -Gail, for the Teacher2Teacher service
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