Dyscalculia is a learning difficulty affecting children and adults across the globe. People with dyscalculia have persistent trouble understanding numbers and mathematical concepts, due to which they may face challenges in school, work, and daily life.

A study^{[1]} corresponding to primary school students in Germany estimates that around 3 – 7% of children and adults are affected by dyscalculia. Therefore, it is quite possible that your class may have a student with a math learning disability.

You may find students with dyscalculia struggling with math at different levels. The level of difficulty may vary from one student to another. Basic mathematical concepts like differentiating a smaller number from a bigger number, the addition of two numbers, quantities, etc., can be as challenging as learning tough concepts like geometry and algebra. Fraction is a math concept that seems difficult to learn at times for students. Hence, it comes as no surprise that those with dyscalculia also find the topic a little challenging.

**Dyscalculia and fractions: What do studies say?**

To understand if there is any relation between dyscalculia and difficulty in learning fractions, a study^{[2]} was conducted to see how the knowledge of fractions varies between typical students, those with low mathematics achievement (LA), and students with a mathematics learning disability (MLD).

After assessing 122 students from grades 4 – 8 it was inferred that typical students in grade 4 were more successful in answering one-half fractions, while students with MLD were not accurate in understanding the one-half concept until grade 7. The LA group of students also had a tough time understanding fractions initially, but by the time they reached grade 5, they could match the performance levels of typical students.

The study also suggested that students could comprehend visual representation of fractions better than Arabic number representation. This particularly helped MLD students until grade 8.

The study concluded that many students face difficulties in understanding and solving fractions. However, the nature and extent of difficulties vary for students belonging to each group.

**Challenges faced by dyscalculics in learning fractions**

Although students with dyscalculia may face different kinds of challenges^{[3]} while attempting a fraction problem, here are a few common challenges –

**1. **Students can have difficulty representing a fraction in a pictorial form.

**2. **Students may not understand fraction comparisons. They may have trouble explaining which of the two fractions is larger 1/2 or 2/3.

**3. **Even though students know the common denominator method, they may be unable to correctly apply the method when the denominators of two fractions are different.

**For example, **

Students can handle a simple fraction addition like 1/5 + 1/5 = ……

But get confused when the denominators of the two fractions are changed, as in 1/3+ 1/2 = ……

**4. **Students apply the common denominator method used for fraction addition to solve fraction multiplication problems.

**For instance, **

A simple fraction multiplication can be solved as,

4/5 x 2/3 = 4×2/5×3 = 8/15

But students with math difficulty use the common denominator method even when solving multiplication problems, as shown below (which is incorrect) –

4/5 x 2/3 = 12/15 x 10/15 = 120/15

**5.** Another common error is that students know that when solving fraction division operations, they should multiply with the inverse. However, they inverse the first fraction instead of the second, resulting in inaccurate results.

**To help you understand with an example,**

Here is the right method,

3/5 ÷ 2/3 = 3/5 x 3/2 = 9/10

Rather than reversing the second fraction, students go ahead and reverse the first fraction which gives a wrong result –

3/5 ÷ 2/3 = 5/3 x 2/3 = 10/9

**Why are fractions difficult for students with dyscalculia?**

Now that you know that dyscalculia affects a person’s ability to understand and acquire arithmetic skills, it may not be difficult to understand why these students struggle with fractions. Some of the reasons why dyscalculics find fractions hard to learn are –

- The fraction notation has two numbers which are often confusing for students. Thinking about two numbers in relation to each other is not easy for them.

- Students tend to consider a fraction as one number, not a part of the “whole.”

- Copying fractions from the board can also be a challenge because students may make mistakes like copying incorrect fractions or reversing the numerator and denominator of a fraction.

- Students find it hard to understand that numbers written in place of numerator and denominator have different meanings. For example, a fraction with a larger numerator makes its quantity larger. Whereas, a larger denominator indicates the quantity of fraction is smaller.

- Different models used to demonstrate a fraction like pizza pies, folded squares, fraction strips, etc., often confuse the students. This happens because they fail to grasp the similarity between the different models.

**A few tips to help teach fractions to students with dyscalculia**

Learning fractions is a little tricky. But with the right approach, parents and educators can simplify learning fractions for students. Here are a few tips to help students succeed in mastering fraction operations –

- The first emphasis must be on the language you use to explain the concept. Clearly communicate that fractions are equal parts of “whole.” A “whole” could be anything; an apple, a pizza, or a circle.

- Try to use real items to explain the concept, as students with dyscalculia benefit from visual learning.

- Always have the “whole” present as a reference point when explaining the concept of halves and quarters. Having the whole in front of the eyes lets students relate to the information shared in a better way. You can keep a whole orange and cut another orange to make halves and quarters.

- Don’t use the same terms to talk about numerator and denominator. Using distinct words helps avoid confusion and supports students’ knowledge in solving the problem.

- Use manipulatives like fraction tiles, fraction circles, 3D fraction shapes, or fraction tower linking cubes to make learning fun and effective.

- Kids love doing things on their own. Help the kids bake brownies or a pizza and discuss how to divide the “whole” into equal parts of fractions. Explain how a pizza slice is 1/6 of the whole pizza or how each person will get 2/6 of the “whole”.

- Utilize fraction games like Pot Luck and Fractions on a Number Line to conduct an enjoyable and productive session. Students can have some fun and get extra practice on the topic.

- Review concepts from time to time to strengthen their understanding of fractions. Reviewing is even more important when you wish to teach something new so that the students retain their previous knowledge and don’t get confused.

- Break the entire lesson into smaller chunks to let students concentrate on one thing at a time and not feel overburdened during the learning process.

**Concluding thoughts**

Students with dyscalculia often have trouble with numbers and mathematical concepts. However, these students can enhance their understanding of fractions with appropriate support at home and at school.

Creating an inclusive environment in the class where all students with different capabilities work and study together is the way to go. Also, helping students self-teach can be beneficial to engage kids with various concepts they have learned.

By using the right strategies and providing timely feedback, teachers can help children with dyscalculia. They may need a little more time to get familiar with the concepts of fractions, but with time, patience, and effort, these students, too, can develop their understanding of the topic.

**References**

- Haberstroh S, Schulte-Körne G. The Diagnosis and Treatment of Dyscalculia. Dtsch Arztebl Int. 2019 Feb 15;116(7):107-114. doi: 10.3238/arztebl.2019.0107. PMID: 30905334; PMCID: PMC6440373.
- Mazzocco MM, Myers GF, Lewis KE, Hanich LB, Murphy MM. Limited knowledge of fraction representations differentiates middle school students with mathematics learning disabilities (dyscalculia) versus low mathematics achievement. J Exp Child Psychol. 2013 Jun;115(2):371-87. DOI: 10.1016/j.jecp.2013.01.005. Epub 2013 Apr 13. PMID: 23587941; PMCID: PMC4000738.
- Ikhwanudin, Trisno & Prabawanto, Sufyani & Wahyudin, Wahyudin. (2019). The Error Pattern of Students with Mathematics Learning Disabilities in the Inclusive School on Fractions Learning. International Journal of Learning, Teaching and Educational Research. 18. 75-95. 10.26803/ijlter.18.3.5.