REVIEWED BY NUMBERDYSLEXIA’S EXPERT PANEL ON MARCH 21, 2022

Operations may be perceived to be the foundational building blocks of math. One among these, multiplication has a unique essence not only due to the area of its application but also due to the abilities it obligates for the student to grasp it. This operation can be implemented for simple daily tasks or complex professional applications.

While complexities in multiplication skills are occasional for some students, is it an area of concern for Dyscalculics? Why is multiplication more than just an operation? As we comprehend that definitive inference may be challenging to derive, the insights provided here can, however, assist you in learning better about how Dyscalculics can deal with multiplication.

**Multiplication- A cut above operation?**

While there are four basic operations in math, Multiplication is one such distinct pick where the student may need to learn some additional traits. These problems can be addressed in two ways. Firstly, the young learners use the counting method in which a number is added multiple times to outstretch the answer. Secondly, the students may employ a retrieval process in which they can retain some previously learned regulations and facts to solve swiftly.

The operations in later stages ultimately obligate retrieval of multiplication facts to ensure precise estimation. These facts may not be applicable in all cases; nonetheless, comprehending these can assist complex arithmetics later. For this reason, Multiplication is often more than just an operation. Here are a couple of pivotal facts:

- The product of two numbers always gives larger outputs, but when multiplied with zero, the answer is ‘0.’
- For every Multiplication fact, there are two division facts. For instance, 2*4=8, this also implies ‘8/2=4’ and ‘8/4=2.’

Complications in multiplication often arise owing to the missout of such certainties. John B Cooney^{[1]} made a study on third and fifth-grade students to analyze their multiplication skills. It was noticed that as the pupils transitioned towards the fourth grade, they opted for retrieval strategies to solve problems- showing how retrieval strategies are crucial in higher grades. Finally, it was outlined that there are correlations between counting and retrieval strategies. Accordingly, retrieving multiplication facts can be taxing for some special students as well.

**Multiplication of numbers- Areas where dyscalculics need to advance? **

Being a step above operations like addition and subtraction, multiplication may be complex for some young learners. Special learners may identify multiple reasons behind this ineptitude. Here we look deep into some distinctive areas where they may feel hindered in accumulation:

**1. Transposed/Rotated numbers**

One of the most common compromises with numbers is the transposition of numbers. Some students may study values appropriately but may face issues with presenting these values on paper later. For example, 9*5 is studied as 45, but they may mention it as 54 in the class test. In a research by Mariela Alexandra Calderón Delgado^{[2]}, few eminent attributes that may show up in individuals with learning incapacity and calculus were mentioned. In which, it was also outlined that the “rotate or transpose the numbers” was one of the eminent attributes. In operations like multiplication, transposed numbers may create errors in the final answer.

### 2. **Counting Numbers **

Reckoning numbers is the essence of math concepts, and multiplication obligates it. Nonetheless, some individuals may hold off counting. Even if they had to, they might rely on finger counting. For these individuals, multiplication can be evidently an area to be boasted about.

Addressing various attributes of Dyscalculia, Roi Cuhan Kadosh^{[3]} in his research paper, mentioned an instance to demonstrate better. It is normal for six-year-old children to count with their fingers in order to solve arithmetic problems, but adopting the same strategy at ten years of age is a sign of age-inadequate arithmetic skills, probably signifying dyscalculia.

**3. Memorisation of Multiplication tables **

Probably the fundamental essential for addressing multiplication problems is ensuring to master multiplication tables. Some pupils who may feel it strenuous to infer numbers may feel it demanding to memorize these too.

Tables need remarkable memory to retain values and also a great working memory to recall those back later. Mojtaba Soltanlou^{[4]}studied if there is a role of working memory in multiplication fact networks in children. The team did research on grade 3 and grade 4 students. They found that early learning may need visuospatial working memory, but ultimately, the individual needs verbal and non-verbal working memory contributions. These conclusions can clearly depict that working memory- whether verbal or on-verbal are pivotal for drawing skills in an individual.

Looking deep into why dyscalculics may need to try hard memorizing, it can be observed that these individuals often have a delicate working memory. Vinod Menon^{[5]} made a study on working memory in children’s math learning. Outlining such memories is crucial for math; he also remarked that Dyscalculics could have a specific susceptibility in visuospatial working memory, which may lead to inferences that these individuals may encounter a few constraints with working memory while learning.

**Can dyscalculics address multiplications?**

The previously mentioned postulates show that number compromises can affect multiplication skills, especially in areas of memorization and reckoning. Once these areas are clearly outlined, relevant strategies can be fabricated to ensure they can compete. Thereby, while some individuals may not solve multiplications with ease, they can manage by mastering these skills later.

Dyscalculic mathematicians like Emma King have made sure they inculcate various personalized plans of action to manage glitches. Aspirants can consider these as motivating sources. Further, the following strategies may hone their multiplication skills finer:

**Break the Problem into uncomplicated parts**

Special pupils who have managed facile problems often may get anxious to comprehend complex ones. For that reason, splitting the challenge into easier parts can be a befitting strategy. Llaria Berteletti^{[6]} made research on children with mathematical learning incapacities and the reason why they may resist solving multiplication problems. The study made on students from third grade to seventh grade showed that dyscalculics have reduced activations in both verbal and numerical regions for complex problems. Fascinatingly, they had engaging verbal mechanisms for easier ones. These inferences precisely point out the need to break the problem to facilitate comprehension.

**Employ Manipulatives to Ensure concrete Foundation:**Manipulatives are often assistive to grasp composite notions with the ease of tactile learning. Employing picks like Multiplication keys and abacus. Flashcards and spins can ameliorate the learning experience.

**Multiplication games and activities:**As a part of the enticing game, pupils may learn implicitly. In the case of multiplications, board games like Say Cheese, Monster Sock, and pet me can be eminent picks to learn and exercise. Not only for strategy, even for multiplication facts, but dice games can also be convenient. In the classroom, converting pedagogies into interactive activities motivates the little ones to master concepts.- Personalized associates like times table sheets and Waldorf multiplication flowers can be encouraged till the learner has mastered these values.

**Concluding thoughts **

Math skills are a crucial part of life skills; multiplication can lie among the few crucial notions to be learned. That being the case, even though it may be arduous at inception, special aspirants need to try stronger to manage this. Successful people with number compromises may often be the source of motivation. Further, check out the areas of concern and probable working strategies to fabricate the best possible plan of action for you to compete.

**References**

- Cooney, J. B., Swanson, H. L., & Ladd, S. F. (1988). Acquisition of mental multiplication skill: Evidence for the transition between counting and retrieval strategies.
*Cognition and instruction*,*5*(4), 323-345. - Delgado, M. A. C., Delgado, R. I. Z., Palma, R. P., & Moya, M. E. (2019). Dyscalculia and pedagogical intervention.
*International Research Journal of Management, IT and Social Sciences*,*6*(5), 95-100. - Kadosh, R. C., & Walsh, V. (2007). Dyscalculia.
*Current Biology*,*17*(22), R946-R947. - Soltanlou, M., Pixner, S., & Nuerk, H. C. (2015). Contribution of working memory in multiplication fact network in children may shift from verbal to visuo-spatial: a longitudinal investigation.
*Frontiers in psychology*,*6*, 1062. - Menon, V. (2016). Working memory in children’s math learning and its disruption in dyscalculia.
*Current Opinion in Behavioral Sciences*,*10*, 125-132. - Berteletti, I., Prado, J., & Booth, J. R. (2014). Children with mathematical learning disability fail in recruiting verbal and numerical brain regions when solving simple multiplication problems.
*Cortex*,*57*, 143-155.