Here is a great presentation from a Carnegie Mellon-led research team articulating the need for students to master understanding of fractions and long division for long-term success, including teachers respecting the best ways to teach to that end. The MUS Math department pointed us to this editorial.
We want to shore up and encourage our boys who expose their deficits in this area, therefore our #MathLabMandate increases a student's instruction time by as much as 100% in any given week as he substitutes Study Hall period for Math Lab as prescribed by his instructor. No outside tutor, no extra expense, Math Lab offers a great value to these boys when they meet us half-way, arriving in lab with a good frame of mind, ready to dig down toward a demonstrated improvement in their grasp of fractions and long division. We even substitute math problems and fractions for the Rules of Civility from time to time in support of greater fractions and long division understanding.
PITTSBURGH—From factory workers to Wall Street bankers, a reasonable proficiency in math is a crucial requirement for most well-paying jobs in a modern economy. Yet, over the past 30 years, mathematics achievement of U.S. high school students has remained stagnant — and significantly behind many other countries, including China, Japan, Finland, the Netherlands and Canada.
A research team led by Carnegie Mellon University's Robert Siegler has identified a major source of the gap - U. S. students' inadequate knowledge of fractions and division. Although fractions and division are taught in elementary school, even many college students have poor knowledge of them. The research team found that fifth graders' understanding of fractions and division predicted high school students' knowledge of algebra and overall math achievement, even after statistically controlling for parents' education and income and for the children's own age, gender, I.Q., reading comprehension, working memory, and knowledge of whole number addition, subtraction and multiplication. Published in Psychological Science, the findings demonstrate an immediate need to improve teaching and learning of fractions and division.
"We suspected that early knowledge in these areas was absolutely crucial to later learning of more advanced mathematics, but did not have any evidence until now," said Siegler, the Teresa Heinz Professor of Cognitive Psychology at Carnegie Mellon. "The clear message is that we need to improve instruction in long division and fractions, which will require helping teachers to gain a deeper understanding of the concepts that underlie these mathematical operations. At present, many teachers lack this understanding. Because mastery of fractions, ratios and proportions is necessary in a high percentage of contemporary occupations, we need to start making these improvements now."