Ability with fractions and division aged 10 predicts ability with algebra aged 16

By Peter Rowlett On June 20, 2012

Last week we reported that the UK Government have released a draft primary school Programme of Study for mathematics for consultation. A report from the Telegraph quoted in that article mentioned that “the use and multiplication of fractions” was “a vital precursor to studying algebra”. A piece of research published in the journal Psychological Science, ‘Early Predictors of High School Mathematics Achievement‘, investigates this area. The findings indicate the importance of learning about fractions and division by showing that these “uniquely predict” students’ knowledge of algebra and overall mathematics achievement 5 or 6 years later.

To identify “the types of mathematics content knowledge that are most predictive of students’ long-term learning”, this research “examined long-term predictors of high school students’ knowledge of algebra and overall mathematics achievement”. Analysis was completed on “large, nationally representative, longitudinal data sets from the United States and the United Kingdom”. According to the press release,

The U.S. set included 599 children who were tested in 1997 as 10-12 year-olds and again in 2002 as 15-17-year-olds. The set from the U.K. included 3,677 children who were tested in 1980 as 10-year-olds and in 1986 as 16-year-olds.

Both sets apparently showed that

elementary school students’ knowledge of fractions and of division uniquely predicts those students’ knowledge of algebra and overall mathematics achievement in high school, 5 or 6 years later, even after statistically controlling for other types of mathematical knowledge, general intellectual ability, working memory, and family income and education.

With this sort of story it is of course necessary to consider the ever-present question of causation but if you’re interested the link to the original research paper is below.

Press release: Carnegie Mellon-Led Research Team Finds Knowledge Of Fractions and Long Division Predicts Long-Term Math Success: Results Demonstrate Immediate Need To Improve How Math Is Taught.

Paper:Early Predictors of High School Mathematics Achievement (Siegler et al., Psychological Science; DOI: 10.1177/0956797612440101)

Basketball project has Atlantic City students taking an active interest in math

By DIANE D’AMICO Education Writer

ATLANTIC CITY — Fifth-grader Drashti Lapsiwala, 10, was on her game, making more than half of her free throws in the New York Avenue School gym.

Azim Coley, 10, sat on the floor, tallying her results and keeping track of how many throws she had left in order to complete 12.

“How do we count by fives?” math coach William Heckman asked, reminding students they can put a slash through their four vertical lines to make a group of five.

Upstairs in a classroom, teacher Jerome Taylor’s seventh-graders had already completed their free throws and were tallying what percentage of throws each student had made, how the girls compared to the boys, and how class fared as a whole.

“I calculated it in fractions, then with a decimal point,” seventh-grader Ayannah Barnes explained.

Fractions and percentages are weak areas among students, math supervisor Ray Allen said. The basketball project is an effort to help students better understand them by applying them to a real-life exercise rather than abstract problems in a book.

To see the full article, click here.

Getting in Rhythm Helps Children Grasp Fractions

A recent study has found that tapping out a beat may help children learn difficult fraction concepts.

San Francisco State University researchers designed “Academic Music”, a 12-lesson program that uses music notation, clapping, drumming, and chanting to introduce third-grade students to fractions. The program was implemented at San Francisco’s Hoover Elementary School with students showing significant improvements, especially those who struggle with academics.

"Students who started out with less fraction knowledge achieved final test scores similar to their higher-achieving peers," said Susan Courey, assistant professor of special education at San Francisco State University. "Lower-performing students might find it hard to grasp the idea of fractions from a diagram or textbook, but when you add music and multiple ways of learning, fractions become second nature to them."

Courey developed the program with music teacher Endre Balogh. Their findings will be published in the journal Educational Studies in Mathematics.

Original article from MAA Digital Library