Early Knowledge of Fractions and Long Division Predicts Long-Term Math Success

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.

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[Lorrie Morales]

When you go to college to study how to become a teacher, profesors do not include all these necessary explanations either. You take courses on how to teach Math, but profesors do not teacher you why you need to invert fractions when dividing them. It's just taken for granted you already know why. So we pass on our knowledge to students believing they will get it as well as we did when we learned it school.

[Lorrie Morales]

I'm a Science teacher and have also been an intermediate Math teacher for 12 years. I have seen over the 16 years of experience that some students may memorize the steps to multiply or divide fractions, but when it comes the moment to use these skills in Science, most students cannot understand why we use Math in Science, or use it to calculate the volume of a box or to find the equivalent measurement units of the SI units. It becomes a strugglefor students and teachers.

[Rocky Sq]

(I hope you're not trolling)

Let's say someone had lots of pies (of the same size), and he had cut the pies into halves and thirds, and he giives you three haves and five thirds. How much pie do you have? You've heard the old saying, "you can't add apples and oranges". You can't just add up how many pieces you have because some are bigger than others.

So you cut each half pie into three pieces (3/6), and each third pie into two pieces (2/6). Now you can add up how many sixtths you have.

[lsaario]

One of the studies referenced was Liping Ma's thesis/book, a stunning exposition of how teachers lack conceptual mastery. John Mighton of non-profit JUMP Math has done rigorous, detailed curriculum development (and digestible teacher prep that doubles as training) based on years of extensive testing of what works and doesn't and constant tweaking. In 3rd party studies, he moves bell curves way right and closes performance gaps unlike anything else out there (he was featured in nytimes in 2011)

[abcwritestartread]

Important information for us all. Thank you!

[24Adrian24]

Ok. Does someone mind explaining to me why you do need to have common denominators to add/subtract fractions and why multiplying the reciprocal works as a division.