초분수(2부): 분수에 대한 숙달을 확장하세요

Fractions: Where It All Goes Wrong. 

Why do Americans have such trouble with fractions—and what can be done?
  Part of an  Article published in Scientific American magazine.
By Robert S. Siegler on November 28, 2017.

On standard fraction addition, subtraction, multiplication, and division problems with equal denominators (e.g., 3/5+4/5) and unequal denominators (e.g., 3/5+2/3), 6th and 8th graders tend to answer correctly only about 50% of items. Studies of community college students have revealed similarly poor fraction arithmetic performance. Children in the US do much worse on such problems than their peers in European countries, such as Belgium and Germany, and in Asian countries such as China and Korea.

This weak knowledge is especially unfortunate because fractions are foundational to many more advanced areas of mathematics and science. Fifth grader's fraction knowledge predicts high school student's algebra learning and overall math achievement, even after controlling for whole number knowledge, the student's IQ, and their families's education and income. On the reference sheets for recent high school AP tests in chemistry and physics, fractions were part of more than half of the formulas. In a recent survey of 2300 white collar, blue collar, and service workers, more than two-thirds indicated that they used fractions in their work. Moreover, in a nationally representative sample of 1,000 Algebra 1 teachers in the US, most rated as “poor” their students  knowledge of fractions and rated fractions as the second greatest impediment to their students mastering algebra (second only to “word problems”).

Class Experience

In this class I will show students how to do an exercise on the white board  . I will repeat with another exercise and will explain as many times as needed until the students are ready to do the exercises by themselves.They will learn by actually doing example exercises during class.  Once started, I will check their answers for accuracy and follow up with any necessary explanations. I encourage all participants to try as many exercises as possible. I follow up the class with an upload of homework with the solutions.


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