![]() We learn to add and subtract such distances. ![]() We start by exploring the concept of measurement: our children measure a path along the floor, sidewalk, or anywhere we could imagine moving in a straight line. Either way, the emphasis is on uncovering and investigating the conceptual connections that lie under the surface and support the rules. In contrast, a relational approach to area must begin long before the lesson on rectangles.Īgain, this can happen in a traditional, teacher-focused classroom or in a progressive, student-oriented, hands-on environment. Relational Understanding: Math as a Connected System Also, our answer will not have the same units as our original lengths, but that unit with a little, floating “2” after it, which we call “squared.”Įach lesson may be followed by a section on word problems, so the students can apply their newly learned rules to real-life situations. And with his meaning of the word, he does understand.Īs the lesson moves along, students will learn additional rules.įor instance, if a rectangle’s length is given in meters and the width in centimeters, we must convert them both to the same units before we calculate the area. Nor would he be pleased at our devaluing of his achievement. If we were now to say to him (in effect) “You may think you understand, but you don’t really,” he would not agree. “Oh, I see,” says the child, and gets on with the exercise. “The formula tells you that to get the area of a rectangle, you multiply the length by the breadth.” A pupil who has been away says he does not understand, so the teacher gives him an explanation along these lines. Suppose that a teacher reminds a class that the area of a rectangle is given by A=L×B. Richard Skemp describes a typical lesson: Under a more progressive reform-style program, the students may try to invent their own methods before the teacher provides the standard rule, or they may measure and calculate real-world areas such as the surface of their desks or the floor of their room.Įither way, the ultimate goal is to define terms and master the formula as a tool to calculate answers. In a traditional lecture-and-workbook style curriculum, students apply the formula to drawings on paper. The instrumental approach to explaining such rules is for the adult to work through a few sample problems and then give the students several more for practice. Instrumental Understanding: Math as a Tool In this post, we consider the first of three math rules that most of us learned in middle school. Click to read the earlier posts in this series: Understanding Math, Part 1: A Cultural Problem Understanding Math, Part 2: What Is Your Worldview? and Understanding Math, Part 3: Is There Really a Difference?
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