I must admit that the Finding Errors activity was one of my favorites. For one, it satisfied the diagnostician in me. You see, as a physical therapist, one must examine objective and subjective findings to come up with working diagnosis. Analyzing errors was mentally much like examining an injury. Where had the students' thinking gone awry? How might it be rehabilitated? I like knowing that I will soon be helping kids like I was, ones that think they are no good at math.
The activity focused mainly on numbers and operations, one of the five content areas. Students were asked to solve problems involving addition, subtraction, multiplication, and division. They worked with whole numbers, fractions, and decimal fractions. It was clear, from many of the mistakes, that students had memorized procedures but had not understood them to enough depth to execute them strategically or with precision. Had students been taught concepts in a connected fashion, building new concepts upon those already mastered, the incidence of such errors might be reduced. Students must be taught to look for patterns in mathematical reasoning, as well as times when reasoning is repeated. To do this, one must be willing, as a teacher, to depart from the traditional algorithm and use movement and/or manipulatives to make steps more evident and logical for their students.
To be successful in mathematics, individuals must be able to move in and out of context, using both algorithms and elements of the real world to make sense of the process and product of their efforts. We, as teachers, need to help our students by presenting math as something logical, progressive, and accessible. By taking the time to analyze their errors, we can ensure that math is not a series of dance steps to memorized, but rather a rational problem-solving tool at their disposal.
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