fractions aren't hard, the human race is simply too stupid to do anything that can be construed as "difficult", like actually thinking.
And that's why the obsession with AI, cuz humans are stupid.
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On his website andertoons.com, illustrator Mark Anderson has a cartoon in which a boy is handing his teacher an assignment. “To show how well I understand fractions,” he says, “I only did half of my homework.”
Certainly this is a sentiment that many of us share, as we all struggled with fractions in grade school. A recent study found that U.S. eighth-graders in an advanced math class performed at chance on a multiple-choice test of fractions. Adult students at a community fared no better. And while grade school math teachers did understand how to add or divide fractions properly, most couldn’t explain why you need to find the lowest common denominator in addition or invert the second fraction in division. Small wonder they had difficulty explaining these concepts to their students.
But why do so many people struggle with fractions? In a recent article, psychologists Robert Siegler and Hugues Lortie-Forgues outline the reasons why rational number arithmetic is so difficult. By this term, the researchers include not only fractions expressed in the form a/b but also in decimal and percent formats. Although fractions of the a/b form present the most difficulties for children and adults, decimal notation and percentages pose significant problems of their own. In fact, expressions such as “She gave 110% on her performance” belie the fact that many people don’t completely understand that percentages are fractions.
The researchers looked at performance on rational number arithmetic among students and teachers in North America and East Asia. They identified a number of reasons why rational number arithmetic is so difficult, but these reasons can be divided into two classes—inherent and cultural sources of difficulty.
Rational numbers are more complex than whole numbers, and so they’re more difficult to understand and use. Inherent sources of difficulty are universal, and even students in East Asia, who famously outperform their peers throughout the world in math, still have difficulty with fractions. The authors point out two inherent sources of difficulty:
Although these inherent complexities plague all of us, other sources of difficulty with rational number arithmetic are cultural in original. It’s these “culturally contingent sources of difficulty” that account for the better performance among East Asian students compared with their North American counterparts. Specifically, these include:
One reason why so many people experience math phobia is because they don’t see the relevance of mathematics in their daily lives. Traditionally, algebra has been the standard math course in high school—and it’s often repeated at the college level. But many people protest—and I think rightly so—that they never use algebra in their daily lives.
In higher education, there’s an ongoing debate about whether algebra or elementary statistics is a more appropriate math course for non-STEM majors. After all, students in the liberal arts will never need to solve a quadratic equation, but they will need to deal with statistical information, such as polls, surveys, census data, and economic reports. And these kinds of data are frequently presented as rational numbers—fractions, decimals, and percentages.
A recent survey found that 82% of white-collar workers, 70% of blue-collar workers, and 40% of service workers used fractions in their work. (And you just used fractions as you interpreted these statistics.) Clearly, rational number arithmetic does have relevance in people’s lives, and so we need to do a better job teaching it.
However, improvements are going to have to start at the very top, with better education for our teachers. We can also benefit by looking at how rational number arithmetic is taught in East Asia. After all, such an exercise can provide valuable lessons in how to improve our own math instruction here in North America.
References
Siegler, R. S., & Lortie-Forgues, H. (2017). Hard lessons: Why rational number arithmetic is so difficult for so many people. Current Directions in Psychological Science, 26, 346-351.
fractions aren't hard, the human race is simply too stupid to do anything that can be construed as "difficult", like actually thinking.
And that's why the obsession with AI, cuz humans are stupid.
You really hate yourself, fellow human. Every comment you post is in this vein. Getting worse too.
Sucks to be you apparently!
practical applications help. I managed to learn these things in school, but only felt comfortable with a clear understanding and ability to use in figuring things, when I started working in retail after graduating. Figuring out what the %off price, would be for things like 1/2 off or save 30% sales and employee discounts worked like a charm.
I'm from Singapore, and Maths is taught in English but many of us also learn Chinese. In Chinese a third is "三分之一" i.e. literally three parts, of which one". The order of the numerator and the denominator is reversed! We have to deal with this as we switch between two languages.
While teacher education needs to be strengthened, the curriculum also needs to be reviewed.
Math is a discipline loaded with concepts and skills, both of which need a lot of time under the supervision of the teacher. Hence the curriculum load needs to be reduced so that more time can be spent on visual and kinaesthetic methods to help children understand concepts and practice skills.
I was a consultant math teacher at the elementary level and found too often that teachers had a poor understanding of these concepts. Most did not like teaching math and failed to use visual and hands-on materials to help students understand the connection between the various ways to represent rational numbers. They all were receptive to guidance in how to teach these concepts and I suspect learned some things themselves. We need to do more at the local level to assist teachers and be sure they are conveying the same accurate message to students.
As a teacher (not of math but of science) I happen to think the issue with fractions is similar to issues with multiplication and division. I never realized it until I observed my young son learning to multiply and divide large numbers. To truly understand these operations his teacher started with place value. For example, he learned to multiply 75*15 as a matrix with 70x10 + 5*10 + 70*5 + 5*5 and he can now connect that to the traditional methods. The problem is that sometimes place value is taught without making the connection to things like multiplication. Similarly, with fractions, the minute you see a strip with 5 segments and an identical strip with only three segments, the issue calculating 3/5 + 1/3 becomes clear (as does the need for a common denominator). There needs to be a strategy for articulating the underlying principles before routines become set in and the meaning becomes lost in the routine. These connections take time to make and it is important to make them at a young age. He still says "1 out of 3" instead of "one third" because that is the meaning that was taught to him.
Enjoyed your post. We've been delivering math instruction online for over 15 years, and have enormous documentation that understanding fractions is clearly the single biggest deficiency for students, and one that persists for years. Over that time, I've been struck by the fact that even the best mathematicians don't agree on what a fraction "means". It seems to me the biggest problem is that we persist in defining fractions as "parts of objects." Fractions are not parts of physical objects. We use fractional units to measure the objects and their parts. The applications of fractions are related to measurement, yet we persist in focusing on objects to teach the concept. Until we recognize and deal with this fundamental misconception, I don't think there's much hope in overcoming the problems so common among students.
"Practical applications help" comments hit the mark. The biggest question little kids express constantly and all of us have is "why?" How often do teachers explain why one needs to know this stuff? As a former administrator I evaluated a few math teachers over the years and rarely did I listen to a lesson in which the teacher said something like, "the reason learning the pythagorean theorem is important is because it has application in building and designing houses" or other such real life application for other concepts. Curriculum typically focuses on process not practical application. Until one truly understands math concepts they are not likely to learn them well. Understanding requires more focus on answering "why."
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