REMEDIATION

When Are Fractions Taught?

According to the National Standards for Teaching Mathematics, fractions are introduced by fifth grade. Fraction calculations are taught in sixth grade and reinforced in seventh grade.

Can older learners use Progressive Ruling?

Some learners passed through sixth and seventh grades and are not comfortable doing fraction operations. These learners need Progressive Ruling to show them what they do not yet understand. The methods used in modern textbooks are too abstract for these learners. They need to see the fractions concretely.  They need to feel the fractions in their hands. Their lack of understanding tells instructors, whether they are teachers or parents, that your learners need a different way to do fraction operations. Something is not working in the way they have been shown.

How Does Progressive Ruling Help?

Progressive Ruling allows each learner to draw the lines that represent the fractions and mixed numbers as they are adding, subtracting, multiplying, and dividing them. They can compare and contrast the sizes of each. Because they see each fraction or mixed number, they begin to estimate or predict what the answer will be. They will develop assurance that their estimated or predicted answer is correct. This assurance of success is what gives a learner the confidence to approach more and different problems.

Examples in Progressive Ruling are to be worked slowly and methodically to allow the learners the time to internalize the concepts of what they are seeing.

• When is the answer larger than the numbers you are calculating with?
• When is the answer smaller than the numbers you are calculating with?
• What is range of the answer?
• What will the answer be?  

Learners will ask themselves these questions, if they have the opportunity to work slowly enough to allow their minds to function. In many classrooms, learners rush through assignments just to get finished whether they understand the concepts or not. Progressive Ruling gives them a fun way to focus their learning. They cannot rush. Drawing the problems sloppily gives them wrong answers. In other words, they have to THINK while they are working. This process alone increases their learning and their understanding.