Impacts of Dyscalculia in Learning Mathematics: Some Considerations for Content Delivery and Support

*Rajendra Kunwar*

## **Abstract**

Dyscalculia is one of the important but less prioritized areas in learning mathematics. A group of students about 3–7 percent of school-age are facing problems associated with dyscalculia. They are facing problems related to number comparison, symbols and reasoning. This paper discusses the general features of dyscalculia and ways to overcome it. This article mainly focuses on the problem related to mathematics learning due to dyscalculia. It further highlights the concept and meaning of dyscalculia, types, causes of dyscalculia, common difficulty areas in mathematics for dyscalculic children, the impact of dyscalculia in mathematics learning. Finally, it also brings out the effective ways of delivering the mathematical content in the classroom teaching and ways to support dyscalculic students.

**Keywords:** content delivery, dyscalculia, learning deficit, learning mathematics, student support

## **1. Introduction**

Mathematics is measured to be a difficult subject due to its abstract nature. The difficulty of learning mathematics is a worldwide issue. It is a very important and necessary subject in school education caused by its linkage to everyday human life. Therefore it is taught as a fundamental subject in schools all over the world and positioned as an important subject in the school curriculum. Mainly in mathematics and science, many students believe that it takes inherent ability or even brilliance to achieve well, rather than perseverance, good strategies, help from others, and learning over time [1]. As a result, it has always been given special attention in school education globally. Although the expected outcomes in mathematics could not be achieved to date and the students' negative attitude towards learning mathematics also could not be reduced [2]. For many years, it was believed that the numerical cognition of the children could be developed according to the child development and the learners can be taught effectively using Piaget's child developmental stages [3]. The focus of Piaget's philosophy was that the child understands space, time and causality of number and quantity and classes and relations of invariance and change [4].

In recent times, however, the researchers are focusing increasingly on the causes of mathematical learning difficulties as the procedural as well as neurobiological foundations of the learner [5]. Mathematics is conceived as a product of human activities in the process of adapting to the external environment [4]. The precise acquisition of mathematical abilities involves a broad range of different general cognitive skills including auditory and visual working memory, pattern recognition, speed of information processing, spatial perception, and attention [6]. These skills enable students to perform different mathematical activities and performance. Among them, working memory is a strong predictor of mathematical skills across time, achievement or achievement growth in mathematics [7]. It helps to perform fast and accurate arithmetical calculations in adolescence and adulthood [8]. Researchers have generally agreed that the deficit in working memory, brainrelated condition, genetic cause, environment, and brain difference is considered dyscalculia [9]. These deficits affect the learners' mathematical learning capability particularly computation and reasoning [10]. Such problems of the learner gradually tend to create frustration to learn mathematical problems regarding computation and application [11]. The objectives of this chapter are to state mathematics learning components, concepts and meaning of dyscalculia, types, causes, areas of common difficulties in mathematics for dyscalculic children, impact of dyscalculia in mathematics learning, effective ways of content delivery and student support.

## **2. Components of learning mathematics**

Mathematics is a very essential and important subject that encompasses numbers, measurement, probability, and algorithms [12]. It cannot be separated from the particular cognitive processes in operation whenever we apply our minds to a mathematical task [5]. It is sometimes expressed as a difficult subject that is inaccessible, boring, particularly for cool and engaged people and girls [13]. Mathematics is considered an integral part of our everyday life. It is used in daily activities such as cooking, shopping, playing, arranging something, etc. Ziegler and Loos [14] stated that mathematics was developed from counting, calculation, measurement and the systematic study of the shapes and motions of physical objects. Historically, it was regarded as the science of quantity, or numbers. Thus, mathematics learning is essential for each person to continue their daily life too. Mathematics learning requires three equally important hierarchical components that can help to transform the mathematical concepts, ideas and knowledge effectively. The brief accounts of these components are as follows:


*Impacts of Dyscalculia in Learning Mathematics: Some Considerations for Content Delivery… DOI: http://dx.doi.org/10.5772/intechopen.99038*

meaning and intends to increase literacy in mathematics rather than stepwise teaching to find the solutions. It focuses on explaining the processes (why) rather than performing the process (how). Conceptual learning begins in early childhood by using different effective methods, modern tools and techniques. Conceptual learning makes the students able to transfer their knowledge to new situations and contexts effectively. Thus it is essential for success not only in mathematics but in all disciplines and in the workplace.

iii.Procedural component: This component refers to the ability to apply procedures accurately, efficiently and flexibly; to transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is more appropriate to apply than another [16]. It is more than memorizing facts or procedures. The procedural component can be used effectively when the conceptual proficiency is high. Fluency of the procedural component builds on a foundation of conceptual understanding, strategic reasoning, and problem-solving [16].

## **3. Concept and meaning of dyscalculia**

Dyscalculia is a specific learning difficulty that affects the learner's ability to retain mathematics skills related to calculating numbers, not with every branch of mathematics [2]. Dyscalculia is an umbrella term used to represent diverse conditions that cause specific difficulties with mathematics such as developmental dyscalculia, mathematical disability, numerical learning disability, and number fact disorder among other terms [17]. Thus developmental dyscalculia is an inborn condition that affects the ability of the learner to acquire arithmetical skills. However, dyscalculia may be caused by accidental brain damage (acquired dyscalculia).

The word 'dyscalculia' has both Greek and Latin origins. The Greek prefix 'dys' means 'badly', while 'calculia', from the Latin 'calculare', means to count [10]. The term dyscalculia or developmental dyscalculia was first defined by the Czechoslovakian researcher Kosc in 1974 [18], as difficulty in mathematics as a result of impairment to particular parts of the brain involved in mathematical cognition, but without a general difficulty in cognitive function. In other words, dyscalculia is also known as 'difficulty with numbers', 'being bad at mathematics', or 'number blindness'. It is not the only difficulty with numbers but a more deeplyrooted problem than just being bad at mathematics [9]. As stated by Hornigold [9], the dyscalculic learner always struggles with the common difficulties in mathematics such as remembering number facts and time tables, counting backward in steps, learning to tell the time, calculations involving money and fractions, decimals and percentages. Dyscalculic learners may have difficulty in understanding numbers, number facts, numerical operations place value, the principle of exchange and their mathematical procedures. However, mostly, these difficulties can be overcome with extra support and intensive intervention.

The specific learning difficulty or disorder affects the learners' ability to memorize number-based facts understanding the logical steps needed for solving a mathematical problem and performing daily numerical tasks. Dyscalculia refers to the inability or disorder in basic numerical processes in mathematics [19]. Such learning disorder affects the learner in numerical processing and computation throughout their life. It is the result of specific disabilities in basic numerical processing, rather than the consequence of deficits in other cognitive abilities [20]. According to Grant [21], the specific learning deficits in mathematics have number sense, memorization of arithmetic facts, accurate or fluent calculation and accurate mathematical reasoning. Among them, number sense can be classified as dyscalculia and the core deficit of dyscalculia is the lack of numerosity or the inability to understand the concept of more than/less than [21]. The term specific learning difficulties or deficits describe a range of disorders in which dyscalculia is one. Therefore, dyscalculia is also considered as the lack of numerosity or an inability to understand the concept of more than/less than.

Dyscalculia is a neurological disorder about learning abilities in mathematics. It has a strong correlation between neurobiology and dyscalculia [22, 23]. Dyscalculia is a brain-based disorder as indicated by genetic, neurobiological, and epidemiologic evidence [24]. The common range of dyscalculia lies between 3 and 6% of school-age children [22]. Similarly, Hornigold [9] states around 6% of the children have dyscalculia and are being equally affected regarding both girls and boys. However, Sharma [5], claimed that the occurrence of dyscalculia is about 6 to 8 percent of the school-age population. As affirmed by Khing [10], children with dyscalculia consist of two types of problems-mathematical computation and reasoning. The problem related to mathematical computation affects an individual to solve mathematical calculations like addition, subtraction, multiplication, and division. Similarly, mathematical reasoning affects the learner in the case of analyzing and way of thinking [19]. Such mathematical problems usually begin at the elementary level and generally continue throughout their lifespan [9].

## **4. Types of dyscalculia**

In the field of mathematical learning disability, different researchers have explored their ideas to categorize the major types of dyscalculia concerning the different dimensions of acquiring mathematical ability. In this context, Kosc [25], the researcher, who proposes dyscalculia into six uniform categories particularly focusing on the characteristics of knowledge deficits are as follows:


*Impacts of Dyscalculia in Learning Mathematics: Some Considerations for Content Delivery… DOI: http://dx.doi.org/10.5772/intechopen.99038*


Geary [26] has divided dyscalculia into three types particularly focusing on the way of knowledge processing and procedures. The brief descriptions of the type are as follows:


Karagiannakis and Cooreman [28] have categorized dyscalculia into four ways based on different aspects of mathematical ability or areas of mathematics that affect the learner. The brief accounts of the types are as follows:


recalling mathematical terminology, word problems, performing accurate mental calculations, remembering and carrying out procedures, rules and formulae, performing problem-solving steps.

iv.Visual–spatial: This way includes the difficulties concerning recognizing and understanding mathematical symbols, interpreting visual representations of mathematical objects, representing numbers on a number line, visualizing geometrical figures, interpreting graphs and tables.

## **5. Causes of dyscalculia**

There are different views about the causes of dyscalculia. However, researchers are generally agreed about dyscalculia as a brain-based condition. Arguably, the specific mathematics learning difficulty (dyscalculia) can be categorized within the cognitive, behavioral and biological aspects and contextualize in teaching and learning mathematics. It can also be considered as the fundamental cause of dyscalculia or the factors affecting dyscalculic learners. The category of the fundamental causes of dyscalculia is presented in **Figure 1**.

The causes of the dyscalculia as presented in **Figure 1**, in the cognitive factor, the acquisition of number concepts and the ability to acquire arithmetical skills and understanding, some huddles during the development stages of Piaget's child development theory can the cause of dyscalculia. Similarly, the information processing theories can also be the cause to accommodate the number concept and difficulty with numbers [29]. In behavioral factors, learning environment, various aspects related to effective teaching and learning such as teaching methods, materials, motivation, classroom environment, socio-cultural factors, stress, anxiety, etc. can also be the causes to acquire the number concept and arithmetic skills [30]. Frequent learning activities or drills and practice can also help to attain the learning problem related to numbers. The biological factor comprises brain structure and genetics. In brain structure, the cause of dyscalculia depends on the differences in the surface area, thickness and volume of the different parts of the brain that are used in memory and keeping track of a task [31]. The development of brain structure may depend upon prematurity and low weight birth. It can be identified by MRI scans. In the same way, dyscalculia can be transformed from the heredity too [32]. Thus, all the aspects can cause dyscalculia in a learner.

**Figure 1.** *Fundamental causes of dyscalculia.*

*Impacts of Dyscalculia in Learning Mathematics: Some Considerations for Content Delivery… DOI: http://dx.doi.org/10.5772/intechopen.99038*

## **6. Areas of common difficulties in mathematics for dyscalculic children**

As already discussed above, dyscalculic children often struggle with number and number concepts that can lead to a diverse range of difficulties related to numbers in mathematics. Jacobson [33] stated that dyscalculic children have difficulties related to recognizing and remembering numbers, counting, associate number symbol with the number value, identifying patterns and placing things in the right order. Some common areas of difficulty in mathematics for dyscalculic children are stated below in brief:

	- ix.Mental mathematics: Difficulty remembering procedures in mathematics recognize quantities without counting, recalling basic math facts, linking numbers and symbols and problem-solving.
	- x.Fraction: Poor visual and spatial orientation in fraction diagram.

## **7. Impact of dyscalculia in learning mathematics**

Dyscalculia impacts children from the early age of schooling onwards. It affects learning mathematics as well as in daily life activities due to the inability of basic arithmetic concepts like poor number sense and reasoning. Dyscalculia can also impact children in the varied areas of mathematics. The major impacts of dyscalculia in mathematics learning in everyday activities of the children are as follows:

i.Develop a negative attitude and avoid the tasks like judging distances, direction, depth and distinguish between left and right; larger and smaller numbers.


## **8. Effective ways of content delivery**

Content delivery describes the process of conveying subject matter to the learner through either the physical or virtual medium. There are a large number of ways to deliver the content. Effective content delivery depends upon how clearly the learner has internalized or understood the subject matter. The effective way of content delivery for dyscalculic learners also depends upon the students' background, interest, level and capability. However, the multi-sensory techniques incorporating best suited modern tools and techniques with the need and interest of the learner can make the content delivery more effective. Some major ways for effective content delivery are accounted in brief:


### *Impacts of Dyscalculia in Learning Mathematics: Some Considerations for Content Delivery… DOI: http://dx.doi.org/10.5772/intechopen.99038*

and unpleasant consequences [34]. Therefore, playing games with Dice, Dominoes, Ten-frames, etc. make learning fun and can also familiarize with the face of Dice, dot patterns of Dominoes and counting and number relations in Ten-frames, etc. By using such concrete materials help the learner to be familiar with dot patterns, counting and number relations.


make them know/solve the given task. In this teaching approach, those poor students can be benefitted who could not ask questions to their teacher due to hesitation. It also inspires the weak students to learn mathematics and get more practiced and may feel relaxed learning with their friends.

x.Teach less but regular: In this teaching style, the subject matter is divided into small separable parts. Then the small part is taught regularly using different effective techniques. The learner feels more comfortable to learn the small part because the small part takes less time to teach and also easy to understand for students. When the students are taught a long lesson, it takes more time and the learners also feel bored and tired. Such a method can be used effectively in the lower classes and also used to teach the weak students. Similarly, most dyscalculic learners do not prefer to carry on the lengthy way of teaching or calculating strategies. In this context, shortcut ways can be used more effectively than others.

## **9. Student support**

The student's support can help to promote their ability to process and understand information regarding mathematics for struggling children with dyscalculia. It can also assist them in conceptualizing and performing mathematical difficulties. It is essential to work with dyscalculic children both at home and at school to develop a positive attitude towards learning mathematics and provide additional support for learning mathematics effectively. Thus, the parents, as well as the teacher, should support the dyscalculic children to motivate them and overcome the particular difficult area of mathematics. The students supported by parents and teachers are accounted briefly as.

## **10. Student support from parent**

The children spend comparatively more time at home than school and they feel closer to their parents than others at the age of primary stage. So every parent can help their children effectively in several ways who struggle with dyscalculia. Some of the supports that can be provided by the parents to their children are as follows:


## **11. Student support from teacher**

Children with dyscalculia need additional support and instruction at school and home due to poor working memory. The teacher can support the dyscalculic learner at school in the real classroom environment that is also the best place for children to deal with some of their difficulties. Such support can help the stressed children to make it easier and less stressful by creating a fun indoor and outdoor learning environment. The strategies and support in either way to help the children with dyscalculia will work well and also make them self-motivated and encourage. Some strategies to support the dyscalculic learner by the teacher are as follows:


## **12. Conclusions**

Dyscalculia is a specific learning disorder that influences the arithmetical abilities of children. Generally, dyscalculic children struggle to memorize number facts, understanding the logical steps needed to solve the mathematical problem. They also have difficulties in numerical calculations related to daily life. Thus the arithmetical deficits not only impact their achievement but also on other related fields beyond the class. Generally, mathematics is considered a difficult subject due to its abstract nature to all learners. Then the dyscalculic student should face more difficulty due to their weak number sense and poor reasoning towards mathematics. There are certain areas of difficulty in learning mathematics for the dyscalculic learner. In these areas, they cannot attempt in time due to the low basic mathematics fluency and reasoning. Teaching in such difficult areas of mathematics, the dyscalculic students should be provided with specialized instructions and dedicated time. Similarly, they should be cared for and well treated at school through providing classroom outside and inside learning environment. Likewise, the parents should also provide sufficient time at their home for doing homework, playing, or doing something. Thus, the efficiency of the dyscalculic students can be uplifted through utilizing effective pedagogical intervention strategies and creating a collaborative working environment.

## **Author details**

Rajendra Kunwar Tribhuvan University, Mahendra Ratna Multiple Campus, Ilam, Nepal

\*Address all correspondence to: rajendrailam@gmail.com

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Impacts of Dyscalculia in Learning Mathematics: Some Considerations for Content Delivery… DOI: http://dx.doi.org/10.5772/intechopen.99038*

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## **Chapter 14**
