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### Putting One Over Two: The Relationship between Fractions and Success in Secondary Math Education

"Why do I need to know this?" Almost every teacher has heard this cringe-worthy statement from a student who isn’t interested in the subject matter. While there are countless benefits to leaning math, it turns out there another reason that students need to master basic skills.

According to a new study by Robert S. Siegler and other researchers, a student’s success in upper level mathematics can be predicted based on their aptitude with fractions and long division in elementary school. The study controlled for I.Q., family income, gender, and a range of other factors. Across all controls groups, a student’s mastery of fractions and long division early-on led to an increased ability to master upper level mathematics in their secondary education.  In other words, a student who does well with fractions and long division in elementary school is more likely to do will with calculus in high school, regardless of their background or overall intelligence.

So, next time a student asks you why it is important to learn about fractions or long division, you have a simple answer: today’s basic conceptual understanding will make it easier when the math gets a lot harder!

Why does mastery of fractions and long division equate to success in high school math?  Does the application of problem solving techniques, such as finding the least common denominator, help the brain develop a mathematical knack early on? Or maybe frustration at an early age in mathematics turns them off to future interest in the subject. Why does this happen? Share your thoughts and experiences about the relationship between fundamentals and advanced concepts in math education.

### Five Recommendations for Effective Fractions Instruction

Just this past month, the U.S. Department of Education published a practice guide called Developing Effective Fractions Instruction for Kindergarten Through 8th Grade. It is definitely worth the read if you or your teachers are experiencing some challenges in teaching fractions.

The panel arrived at five recommendations for educators to improve students' understanding of fractions:

Recommendation 1*. Build on students' informal understanding of sharing and proportionality to develop initial fraction concepts.

Recommendation 2*. Help students recognize that fractions are numbers and that they expand the number system beyond whole numbers. Use number lines as a central representational tool in teaching this and other fraction concepts from the early grades onward.

Recommendation 3*. Help students understand why procedures for computations with fractions make sense.

Recommendation 4. Develop students' conceptual understanding of strategies for solving ratio, rate, and proportion problems before exposing them to cross-multiplication as a procedure to use to solve problems.

Recommendation 5*. Professional development programs should place a high priority on improving teachers' understanding of fractions and of how to teach them.

(*) These recommendations are supported by our newest program, Fraction Nation.

Do you think there is anything missing from this list?

What recommendations do you have for effective fractions instruction?

photo credit: http://ies.ed.gov/ncee/wwc/

http://ies.ed.gov/pubsearch/pubsinfo.asp?pubid=WWC20104039

### Fraction fluency with Fraction Nation!

It’s official. Fraction Nation is now available and on its way to helping students and teachers tackle one of the biggest stumbling blocks on the way to algebra – fraction fluency. We’re so happy to share the latest math intervention program in the Scholastic family.  Read the press release for more information on this happy milestone. Or, hear Chief Math Officer and fellow Math Hub blogger, Dr. David Dockterman, explain how Fraction Nation addresses the challenges of teaching fractions.

Find out more about Fraction Nation on our website or, better yet,  email us to request a personal walk-through of the program. Discuss the ins and outs of this program with one of our math experts from the comfort and convenience of your own computer!

While we're happy to share this news, we sincerely regret that there's no cake left to share...

### Fractions

Dennis Deturck, a noted mathematician and the Dean of the College of Arts & Sciences at the University of Pennsylvania, has provoked a little firestorm within the math education community by suggesting that schools consider delaying fraction instruction until students are dealing with higher level math. In a 60 Second Lecture a few years ago, Deturck said: “I have a simple suggestion when it comes to teaching fractions in elementary school: Don’t.” Decimals are sufficient. With a new book offering these and other ideas coming out next year, the UPenn dean’s thoughts about reforming math instruction have been making the news.

Critics of Deturck’s suggestion argue that fractions are a fundamental part of our daily lives, unless, of course, you live with the metric system. Some argue that his suggestion of pushing fractions higher up in the curriculum is elitist. Then again, we delay a lot of content until students are better prepared to handle it. Frankly, I welcome the conversations sparked by this controversy. Math instruction in the U.S. is failing a lot of kids. We should be challenging it.

I met Dennis about a year ago when we were both playing advisory roles for the PBS show Cyberchase (a good program), and we talked about fractions then. Dennis does a lot of work in the Philadelphia area schools. He has a good deal of direct experience with struggling kids, and he feels we push them into finding common denominators and computing with fractions long before they have an understanding of what fractions are. I agree.

We’re doing some work ourselves now at Tom Snyder Productions with fractions. We’ve found kids in upper elementary grades who don’t know that 3/3 is 1. They don’t know how to compare 0.6 and 5/10. And they don’t believe that a fraction can ever be greater than 1; after all, we tell them that fractions are parts of a whole. How could it ever be more than that whole? These students, who don’t get fractions, are being asked to add and otherwise manipulate them. The arcane rules they’re learning for these procedures are meaningless, confusing, and readily forgotten.

We’re seeing what we can do to build a better foundation, to help kids make the tough transition from discrete to continuous quantities, from counting how many to measuring how much. A rich, intuitive sense of fraction quantity and equivalence can provide a much stronger base for learning and understanding rational numbers. We’re working on it.
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## What's the Math Hub?

The Math Hub is a place for  sharing  expertise on math education and the use of adaptive technology to increase student achievement. We invite you to enhance our conversation by submitting your own comments.

Bloggers are compensated by Scholastic. The opinions expressed by the authors on this blog should not be taken to reflect the opinions of Scholastic or Tom Snyder Productions.

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