It has clearly been a long while since I've done any algebra. When my daughter came home with algebra questions such as '3 + x = 5,' I never thought to question that it was not algebra. This article has set me on the straight and narrow.
There seems to be some controversy in the world of mathematics: some believe algebra to be a dead subject; others feel it is an invaluable tool to move students from numerical reasoning, to reasoning that can be expressed in more general terms. The author of this article feels quite strongly that algebra is conduit to a better understanding of what a variable and an equal sign really mean. Algebraic equations are an expression of how a specific pattern of events/ phenomena can be generalized and used as a means of prediction. It isn't enough, however, to come up with an equation. One must also be explain why it represents the problem situation it depicts. Growing patterns and repeating patterns as described by algebraic equations are what true algebra is all about. The equations in my daughters' math textbooks have unknowns, not variables.
To be perfectly honest, the more I learn about using different forms of representation and attending to patterns, the more I cannot wait to implement what I've been learning. It will take conscious effort on my part not to teach as I was taught as a child. I will do so gladly. To prepare my elementary education students for algebra, I will be sure to encourage them to look for patterns in numbers they use. Whether they be generating multiplication tables or creating equivalent fractions, the ability to recognize patterns is an essential skill. Should I have gifted students, I am glad to know how to extend their learning to generalization.
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