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General algebra

Solving Algebra

By means of formulas that students have become familiar with in arithmetic, algebra can be presented as a generalized arithmetic. It is more powerful than arithmetic, as it furnishes easier and more reliable ways of solving problems. It can be shown that algebraic equations have definite solutions and beginners can be shown that they can check their work very readily and have a positive assurance that their work is correct. It can be shown that the language of algebra makes reasoning easier, ?that algebraic notation is a method of expressing numbers by letters and figures and that the number relations expressing opposite directions, kind or quality, can be indicated by positive and negative numbers, while in arithmetic size is the only relation that can be expressed. The important objective that must be made apparent is the use of algebra as a powerful tool for problem solving. The fact that algebra is a source of mental training and logical reasoning should be kept in the background. The early work in algebra should not be done hurriedly. The power to interpret the meaning of algebraic expressions and the power to express relations in algebraic language should be most carefully developed. Concrete presentations by means of effective devices make the work real. Many examples may be given to illustrate the nature of positive and negative numbers. The thermometer may be used successfully here. Indicate the reading above zero, positive and below, negative and then calculate the temperate according to changes or calculate changes from successive readings. Concrete situations may also be gotten from pupils’ activities and interests. A boy who was having some difficulty with his algebra after having several days work on positive and negative numbers was made to see the significance of negative numbers by the use of the familiar expression “so many in the hole” and, thereafter, was able to compute readily in terms of signed numbers, for now they had some real meaning to him. Errors in algebra are often due to wrong experiences or to lack of experiences from the first. The old adage that an ounce of prevention is worth a pound of cure is applicable to all learning. Much remedial work in algebra would be un-necessary if the proper precautions were taken to lay the foundation of the subject on actual experience, so that students may be able to see the reason in certain procedures rather than rely on mere memorization of certain rules and formulas. After students grasp underlying principles, they are able to formulate rules for themselves. A background of reasoning serves as a bulwark at all times against future errors. The “general lack of understanding of mathematical method” referred to by Dr. Webber in his article “Some Common Errors in Algebra” is partly to lack of understanding of fundamental principles in the first learning and, also, to lack of proper drill provisions to fix those principles during the learning period. The drills are frequently weak to the extent that they give over-practice on simple phases of the work and little practice on those phases that give greater difficulty.