Last Updated on October 3, 2023 by Editorial Team
The history of fractions dates back to 1586. While they are taught in every school in every country, they can often be a challenging concept for many students to grasp. Unfortunately, this can lead to the development of misconceptions that can make it even harder for students to understand and work with fractions.
There can be various reasons why a learner might face challenges with fractions, including difficulty understanding the concept, complex operations, lack of visual representation, and more. These difficulties can hinder with the student’s potential and understanding of the concept. Hence, in this article, we will debunk some common misconceptions about fractions that students may develop and why they struggle with them
Fraction Folly: Clearing up common misconceptions
Fractions are an important concept in mathematics, however, students may have misconceptions that can lead to confusion and misunderstandings while solving problems. Some of the common misconceptions include
1. Leaving the denominator unchanged in fraction addition and multiplication problems.
A common misconception small children make when working with fractions is that the denominator does not need to change when adding or multiplying fractions. In reality, the denominator is an essential part of a fraction and needs to be considered when adding or multiplying fractions. When adding fractions, the denominators must be the same in order to add the fractions together. When multiplying fractions, the numerators are multiplied together and the denominators are multiplied together
2. Failing to find a common denominator when adding or subtracting fractions, unlike denominators.
it is not necessary to find a common denominator when adding or subtracting fractions with unlike denominators. In reality, finding a common denominator is a crucial step when adding or subtracting fractions with unlike denominators. The denominator of a fraction represents the total number of parts in the whole, and in order to add or subtract fractions together, they must have the same total number of parts.
3. Cross multiplying instead of row multiplying
One of the most common misconceptions is that students will cross multiply instead of row multiply when working with fractions. This is often because students do not understand the reasoning behind why we use row multiplication instead of cross multiplication. To avoid this misconception, it is important to not just teach students the algorithm for row multiplication but also to explain the reasoning behind it.
4. Multiplying fractions by whole numbers
Sometimes students also multiply both the numerator and denominator when working with fractions and whole numbers. This is because students may not understand why we only multiply the numerator by the whole number.
5. Whole numbers vs. non-whole number rational numbers
Students may believe that whole numbers are fundamentally different from non-whole number rational numbers. An example of this would be believing that 2 is different from three-fifths. It is important to help students understand the relationship between whole numbers and non-whole number rational numbers.
6. Failing to understand the invert-and-multiply procedure
Other misconceptions include treating numerators and denominators as separate whole numbers, failing to find a common denominator when adding or subtracting fractions with unlike denominators, believing that only whole numbers need to be manipulated in computations with fractions greater than 1, leaving the denominator unchanged in fraction addition and multiplication problems, and failing to understand the invert-and-multiply procedure for solving fraction division problems. For the same, teachers can indulge kids in some fraction-dividing games.
7. Fractions with larger denominators are always larger:
Fractions are often compared by finding a common denominator, but this is not the only method to compare them. Fractions can also be compared by cross-multiplying or converting them to decimals. For example, 3/4 is larger than 1/2 by cross multiplying and converting them to decimal but it is smaller than 9/8 by comparing with a common denominator. Students can also explore some multiplying fractions games for better understanding.
8. The numerator and denominator of a fraction must be real numbers:
This is not always the case as numerators and denominators can be any real numbers. For example, the fraction 3.5/2 is a valid fraction, even though the numerator and denominator are not whole numbers.
Why do students struggle with fractions?
Students struggle with fractions for many reasons. The first one is that fractions make students think hard about whole numbers[1] and the division of these numbers can be challenging to grasp. With the introduction of a concept like fractions, the students need to establish an understanding where they can establish a relationship between the numerator and the denominator, which can often turn out as a struggle for many students as they might have to perform addition, subtraction, multiplication, and division at various steps.
Since these steps come with their own rules and regulations, they can be complex. Lastly, fractions can be abstract, and connecting the visual representation[2] of a fraction to its conceptual understanding can also be a bit of a task hence it is common that students might face misunderstandings and challenges, especially when they are holy and solely dependent on rote memorization of procedures.
Furthermore, fractions can also become tough for students who have learning disabilities, like dyscalculia.
Conclusion
It is essential to teach students algorithms for working with fractions and help them develop a conceptual understanding of the underlying principles behind these algorithms. This will help them avoid common misconceptions and develop a deeper understanding of fractions.
As students struggle with fractions for various reasons, it is essential for educators to provide students with multiple teaching methods, including visual aids and hands-on activities, to help them better understand and apply the concepts of fractions. Additionally, providing students with ample practice opportunities and real-world examples can help them see the relevance and importance of fractions in their everyday lives.
Reference
- Gabriel, F., Coché, F., Szucs, D., Carette, V., Rey, B., & Content, A. (2013). A componential view of children’s difficulties in learning fractions. Frontiers in Psychology, 4. https://doi.org/10.3389/fpsyg.2013.00715
- Singh, Parmjit & Hoon, Teoh & Md Nasir, Nurul & Cheong, Tau Han & Rasid, Syazwani & Hoong, Joseph. (2021). Obstacles Faced by Students in Making Sense of Fractions. The European Journal of Social & Behavioural Sciences. 30. 3282-3299. 10.15405/ejsbs.287.
An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’,