Читать книгу Mathematize It! [Grades 6-8] - Kimberly Morrow-Leong - Страница 13

Many of us may assume that we have a strong operation sense. After all, the four operations are the backbone of the mathematics we were taught from day one in elementary school. We know how to add, subtract, multiply, and divide, don’t we? Of course we do. But a closer look at current standards reveals nuances and relationships within these operations that many of us may not be aware of, may not fully understand, or may have internalized so well that we don’t recognize we are applying an understanding of them every day when we ourselves mathematize problems both in real life and in the context of solving word problems. For example, current standards ask that students develop conceptual understanding and build procedural fluency in four kinds of addition/subtraction problems, including Add-To, Take-From, Compare, and what some call Put Together/Take Apart (we will refer to this category throughout the book as Part-Part-Whole). Multiplication and division have their own unique set of problem types as well. On the surface, the differences between such categories may not seem critical. But we argue that they are. Only by exploring these differences and the relationships they represent can students develop the solid operation sense that will allow them to understand and mathematize word problems and any other problems they are solving, whatever their grade level or the complexity of the problem. It does not mean that students should simply memorize the problem types. Instead they should have experience exploring all the different problem types through word problems and other situations. Operation sense is not simply a means to an end. It has value in helping students naturally come to see the world through a mathematical lens.