Textbook Limitations
Do your students say they don't understand fractions year after year? Why is this? Math textbooks present fraction concepts and fraction computation in a confusing manner for students who are not mathematically oriented. Fractions are shown as parts of different plane figures. Too many different denominators are presented at one time. Learners don't get a good background before they are given something different.
Students see halves of circles and fourths of rectangles and wonder how it is possible to add, subtract, or in any way calculate with those inconsistent shapes. With Progressive Ruling all calculations are illustrated with lines so they make sense to a visual learner.
Fraction calculations are presented with fractions that are not in the same family causing learners to stop thinking about fraction calculation and think about multiplication tables or mental pictres of thirds and fifths or ninths. Whenever a learner stops thinking about one thing and starts to think about something else they lose the connectivity of the learning. In that way, the process of learning to work with fractions becomes a series of un-connected steps. This lack of connectivity is the reason why learners cannot remember "how to do fractions."
Teach your students what fractions are, how they relate, and how to calculate with them by using one "family" of fractions--those commonly found on a ruler. Progressive Ruling separates the fractions so students can SEE them. Let students look at those fractions side by side until they grasp the relationships between them. How big is this fraction? How small is another one? Are these fractions equal? Are the lines the same length? Why do we use common denominators?
Do your students ask over and over again: How do you change 2 1/2 or some other mixed number to an improper fraction? Let them SEE on Progressive Ruling rulers that 2 1/2 is just "five halves" and they will never ask again. Once they SEE fraction concepts, they will understand fractions.
