Fractions and division are widely used within all areas of mathematics, which means that you are likely to face them at some point in the coming academic year. Whether it’s your first time trying to understand fractions, or you are in a college class and still have trouble with them, it is never too late (or too soon, as one study demonstrates) to learn and revisit the fundamental concepts of mathematics that are the foundation to most complex theories and operations.
Fractions Are a Long-Term Predictor of Achievement
Understanding fractions has been shown to be a good predictor of long-term success in algebra and mathematics. A 2012 study led by Robert S. Siegler from the Department of Psychology at Carnegie Mellon University examined long-term predictors of high school students’ knowledge of algebra and overall mathematics achievement. Using data from the United States and the United Kingdom, the study found that elementary school students’ knowledge of fractions and division predicted their knowledge of algebra and overall mathematics achievement in high school. The same results were achieved even when considering other possible factors that could influence mathematical competence, like other mathematical knowledge, general intellectual ability, working memory and family income and education.
The study reasoned that, among other possible explanations, being able to do whole-number division is a unique predictor of future success in mathematics because it is required to solve and understand many algebra problems. What’s more, the differences in mathematical competence between students appear early on and prove to be stable over time, with those who start behind generally staying behind and vice versa. This continuity of skill is more prominent in mathematics than it is in other areas, such as reading.
Far from using this a reason to dissuade those who do fall behind from continuing to study mathematics, the study points out that the information can contribute to improving mathematics education greatly, both in and outside of the classroom, as both parents and teachers understand the importance of fractions and division and identify them as points of special interest. As Sigler himself says: “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.”
Mathematics and Giftedness: What the Research Says
A long-standing, widely-spread conviction that success in mathematics is purely the result of inborn giftedness and talent, or that little can be done to improve one’s mathematical abilities, has caused many students to give up on the subject altogether, and all too soon.
An article in The Atlantic written by professors Miles Kimball and Noah Smith, both of whom have taught mathematics courses for years, reveals that the “inborn talent” hypothesis does not withstand evidence from scientific research. Studies have repeatedly demonstrated that mathematical ability, especially at the level required in high school, has more to do with hard work rather than giftedness. According to the article, American middle school students score well in mathematics compared to other countries, American high-schoolers underperform significantly. Based on this, the article argues that American students do not lack native ability in mathematics, but rather fail to hone this ability by neglecting to emphasize the importance of hard work and dedication.
With the increasing demand for quantitative reasoning technical skills, and the wide applicability of fractions across all of mathematics, and especially algebra, makes studying fractions an investment worth your time and energy. For example, Siegler’s study was in part prompted by statistics showing that achievement in mathematics predicts college matriculation as well as earnings, especially in recent decades. Meanwhile, most students in the US meanwhile lack the necessary numerical literacy to be successful in most jobs in contemporary society.
Good knowledge of mathematics can also have a spillover effect into other areas. For example, competence in logic and in writing proofs can affect one’s ability to construct arguments and subsequently improve one’s writing and argumentation skills. As such, proficiency in mathematics is a valuable skill not only in and of itself, but because it enhances performance across the board.
Resources and Strategies to Master Fractions
Unlike many other theoretical subjects, mathematics requires a lot of manual work in addition to conceptual thinking. This means that, while understanding the theoretical parts is crucial, what success in mathematics primarily boils down to is sustained practice and hard work. “Getting it” isn’t enough – practice is what makes the real difference. Not fully understanding the theory isn’t a reason not to dive into solving problems, either – sometimes mastering the mechanical steps of solving a problem precedes theoretical comprehension. Make a habit of both solving problems and revisiting concepts until you’ve accumulated enough knowledge to reach a real, robust understanding.
Include your teachers in the process. Let them know beforehand about your goals and that you may potentially struggle with some of the concepts, so they can actively look for points of concern and more easily spot trouble or to know to offer support at the right time to help you or your child get back on track.
There are great resources that teach mathematics in increasing complexity interactively, perhaps the most widely used being Khan Academy. There are also plenty of other online resources and forums where you can study, practice, seek help, or exchange tips and strategies with both peers struggling with the same concepts or people who have already mastered them. Whether you find your community on or offline, it is always useful to have one as a space where learning can be a collaborative process, and roadblocks can be easily overcome.