The Double Multiplicative Nature of Fraction or Ratio Equ...

Most real-world numbers aren’t always so nice and neat, with wholenumber multiples. If, say, Plant A grew from 2 to 3 feet, and Plant B grew from 6 to 8 feet, then we would say that Plant A grew 1/2 of its original height, whereas Plant B only grew 1/3 of its original height. Such reasoning exemplifies multiplicative thinking and necessarily involves rational numbers. Consider a final example. If you ask a rising 6th grader to compare 13/15 and 14/ 16, chances are that the student will say t...

 Math Exercise: Multiple Approaches to Problem-Solving

For example, if the problem was to fi nd the answer to 8 × 6, students may suggest three options: memorizing the multiplication table for 6, knowing that 8 × 5 = 40 and adding another 8 to equal 48, or adding a column of six 8s. Allowing students to personally choose among approaches all confi rmed as correct and to support their choice will increase their comfort levels. Th is process also builds math logic, intuition, and reasoning skills that extend into other academic subjects and real-li...

 How Physicians Were Once Like Today's Economists

The moral game of blame attribution is only one subtype of misattribution arbitrage. For example, epidemiologists estimate that it was not until 1905 that you were better off going to a physician. (Ignaz Semelweiss noticed that doctors doubled the mortality rate of mothers at delivery.) The role of the physician predated its rational function for thousands of years, so why were there physicians? Economists, forecasters, and professional portfolio managers typically do no better than chance, y...