The Concept of Basic Skills in Mathematics Must Encompass More Than Computational Facility
There must be an acceptance of the full spectrum of basic skills and recognition that there is a wide variety of such skills beyond the mere computational if we are to design a basic skills component of the curriculum that enhances rather than undermines education.
We recognize as valid and genuine the concern expressed by many segments of society that basic skills be a part of the education of every child. However, the full scope of what is basic must include those things that are essential to meaningful and productive citizenship, both immediate and future.
The agreement among parents, educators, and mathematicians on the need for teaching basic skills with greater effectiveness unfortunately does not yet extend to a common understanding and acceptance of exactly what these basic skills should comprise.
Some groups narrowly limit them to routine computation at the expense of understanding, applications, and problem solving. This would leave little hope of developing the functionally competent student that all desire.
It must also be recognized that individual capacities, interests, and future directions might call for different emphases and different selections in matching basic skills to individual needs.
The time and energy that teachers and programs should be devoting to building beyond minimal foundations are sometimes skirted, being considered risky deviations from the minimal targets on which educators believe they will be judged. There is great pressure today to use all such time, energy, and resources on overkill in the minimal target areas even though little added productivity may be achieved.
Rather than fostering a return to some acceptable common threshold of performance, the back-to-basics movement tends to place a low ceiling on mathematical competence—and this at the onset of an era in which daily life will be more deeply permeated by multiple and diverse uses of mathematics than ever before. Under these circumstances, even if improvement in rote computation takes place, a citizen who cannot analyze real-life situations to the point of recognizing what computations must be made to solve real-life problems has not entered the mainstream of functional citizenship.
It is dangerous to assume that skills from one era will suffice for another. Skills are tools. Their importance rests in the needs of the times. Skills once considered essential become obsolete, and this is likely to increase in pace and scope as advances in technology revolutionize our individual, social, and economic lives. Necessary new skills arise from the dimensions of the mathematics pertinent to an age of population explosion, space exploration, economic and fiscal complexity, and microelectronic wonders. Time and space for including these new skills in the curriculum must be purchased by eliminating the obsolete.
Insisting that students become highly facile in paper-and-pencil computations such as 3841 x 937 or 72 509/29.3 is time-consuming and costly. For most students, much of a full year of instruction in mathematics is spent on the division of whole numbers—a massive investment with increasingly limited productive return. A small fraction of that time is spent on the skills of problem analysis and interpretation, which enable students to identify and set up the computations needed. For most complex problems, using the calculator for rapid and accurate computation makes a far greater contribution to functional competence in daily life.
Common sense should dictate a reasonable balance among mental facility with simple basic computations, paper-and-pencil algorithms for simple problems done easily and rapidly, and the use of a calculator for more complex problems or those where problem analysis is the goal and cumbersome calculating is a limiting distraction.
Reasonable standards of time-effectiveness and cost-effectiveness should be applied to the use of instructional time, where the criterion is the productive applicability of the learned technique to real-life problems.
Professional knowledge of future trends, industrial, financial, engineering, and scientific need, and the demands of daily life are all better arbiters of what is currently essential and what has become obsolete than our nostalgia as parents or teachers.
2.1 The full scope of what is basic should contain at least the ten basic skill areas identified by the National Council of Supervisors of Mathematics' "Position Paper on Basic Skills.” These areas are problem solving; applying mathematics in everyday situations; alertness to the reasonableness of results; estimation and approximation; appropriate computational skills; geometry; measurement; reading, interpreting, and constructing tables, charts, and graphs; using mathematics to predict; and computer literacy.
2.2 The identification of basic skills in mathematics is a dynamic process and should be continually updated to reflect new and changing needs.
2.3 Changes in the priorities and emphases in the instructional program should be made in order to reflect the expanded concept of basic skills.
- There should be increased emphasis on such activities as:
- locating and processing quantitative information;
- collecting data;
- organizing and presenting data;
- interpreting data;
- drawing inferences and predicting from data;
- estimating measures;
- measuring using appropriate tools;
- mentally estimating results of calculations;
- calculating with numbers rounded to one or two digits;
- using technological aids to calculate;
- using ratio and proportion to deal with rate problems in general and with percent problems in particular;
- using imagery, maps, sketches, and diagrams as aids to visualizing and conceptualizing a problem;
- using concrete representations and puzzles that aid in improving the perception of spatial relationships.
- There should be decreased emphasis on such activities as:
- isolated drill with numbers apart from problem contexts;
- performing paper-and-pencil calculations with numbers of more than two digits;
- mastering highly specialized vocabulary not useful later either in mathematics or in daily living;
- converting measures given in one system to corresponding measures in another system;
- working with tables whose usefulness as aids to calculation has been supplanted by calculators and other technological aids (e.g., numerical computations with logarithms and cologs).
2.4 Teachers should incorporate estimation activities into all areas of the program on a regular and sustaining basis, in particular encouraging the use of estimating skills to pose and select alternatives and to assess what a reasonable answer may be.
2.5 Teachers should provide ample opportunities for students to learn communication skills in mathematics. They should systematically guide students to read mathematics and to talk about it with clarity.
2.6 The higher-order mental processes of logical reasoning, information processing, and decision making should be considered basic to the application of mathematics. Mathematics curricula and teachers should set as objectives the development of logical processes, concepts, and language, including:
- the identification of likenesses and differences leading to classification;
- understanding, making, and applying definitions;
- the development of a feeling for informal proof including counterexamples and generalizations:
- precise use of such language as at least, at most, either-or, both-and, and if-then.
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