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)

Cryptoclub... coming to a school near you?

Beyond Secret Decoder Rings

Mathematicians at the University of Illinois at Chicago have developed materials to help fifth- through eighth-graders learn about cryptography.

CryptoClub is an after school program where students engage in fun coding exercises that enhance their mathematics, reading, and vocabulary skills.

The program was developed through a collaboration of UIC faculty from the Department of Mathematics, Statistics, and Computer Science, the Learning Sciences Research Institute, and the School of Art and Design.

For more information, click here.

If you find yourself in Paris this November (2012)...

The 12th forum of young women mathematicians is to be held at IHP (Institut Henri Poincaré), Paris, France, November 12th to 14th.

Its theme will be “Algebra and geometries”.

The forum is organized by the French association `Femmes et Mathématiques’ in association with the CNRS  (National Center of Scientific Research), its `Mission pour la place des femmes’ (Mission for women’s integration), its National Institute for Mathematical Sciences (INSMI), its Institute for Information Sciences and Technologies (INS2I), and with the French Ministry for Higher Education and Research. It is also supported by the French Mathematical Society (SMF), and the French Society of Applied Mathematics (SMAI).

There will be plenary lectures given by prominent mathematicians as well as parallel sessions with short lectures given by young mathematicians. Besides the scientific program, mentoring sessions will be provided to young mathematicians, as well as awareness activities on parity issues between women and men in higher education and research.

Original Announcement

Pi vs. Tau: Do we have it all wrong?

From Math Goodies Blog:

One of the major contributions Archimedes (287-212 B.C) made to mathematics was his method for approximating the value of pi. For centuries, the number Pi, Greek letter (), has been the symbol for the ratio of the circumference of a circle to its diameter. In 1761 Lambert proved that Pi was an irrational number, which means that the digits never end or repeat in any known way. Throughout history, mathematicians have been fascinated with calculating the digits of Pi. In 1999, millions of digits were calculated at the University of Tokyo using a computer. In 2011 the record was improved to 10 trillion digits.

Each year, Pi Day is celebrated on March 14 by math enthusiasts around the world (3, 1 and 4 are the three most significant digits of p in the decimal form). The earliest known official or large-scale celebration of Pi Day was in 1988. In 2009, the United States House of Representatives supported the designation of Pi Day. Pi Day has become very popular in the mathematics community.

There is now an online movement to celebrate Tau, the number you get when you use a circle's radius instead. Tau is approximately 6.28, instead of the familiar constant Pi, which is 3.14. There is much opinion and controversy surrounding this new movement.

The idea of celebrating Tau is now at least 10 years old, having cropped up in a 2001 essay by Bob Palais called "Pi is wrong!" But it exploded on the Internet on June 28, 2010, when Michael Hartl launched the Tau Manifesto, which explains why pi is confusing and should be replaced with tau.

Click here to read the original Tau Manifesto.

Museum of Mathematics Announces Grand Opening

The Museum of Mathematics (MoM) recently announced that it will open officially on December 15, 2012, in New York City.

According to the MOM website:

Mathematics illuminates the patterns and structures all around us. Our dynamic exhibits and programs will stimulate inquiry, spark curiosity, and reveal the wonders of mathematics. The Museum will have its grand opening on Saturday, December 15, 2012 at 11 East 26th Street in Manhattan.