Paper : 1

Dyscalculia: Prevalence and identification of students.

Research evidence from a study conducted in Panjim in the state of Goa, India

Abstract

This paper presents the results of a survey conducted in the only three schools with a resource room at the time, in Panjim in the state of Goa, India.The purpose of this survey was to find out the prevalence of Dyscalculia among students. Having done that, the author used a non-standardised dyscalculia test to identify students with dyscalculia in a resource room. This test also threw light on the academic needs of the students with dyscalculia. The prevalence of dyscalculia in the three schools surveyed was found to range from 6% to 19%. The average of all the schools was 11.13%. The prevalence of children with dyscalculia among boys was found to be 6.23%, among girls 8.54% andamong boys and girls 18.61%. A few of the results obtained from the Dyscalculia test were that very few students made mistakes in “Number recognition and regular perception of ‘6’ and ‘9’ correctly.” Majority of the students (more than 75%) had problems in “Knowledge of Number sequencing and recognizing ‘skip-counting’ sequence”. The author found that the 26 students tested had varying degrees of dyscalculia from mild to moderate to acute, based on the percentage of items they got right on the test.

Keywords:Dyscalculia, prevalence, identification, test, checklist, resource room.

1.      Introduction

Dyscalculia is a mathematical learning disorder where the mathematical ability is far below expected for a person’s age, intelligence and education. Researchers have found evidence that such a disability exists and because of their findings there is a need to address dyscalculia as an important learning problem in mathematics. Teachers, parents and students are often aware of the fact that there are a number of children with special difficulties in learning mathematics. Pupils with learning disorders may feel uncomfortable in learning situations, unless they are treated in a way that facilitates their learning. In order to give the proper education to a pupil with a learning disorder, it is essential to understand the most suitable ways in which students with learning disabilities can acquire mathematical understanding, which is closely associated with abstract thinking. Dyscalculia is a learning disability that affects the ability to acquire arithmetic skills. It is derived from the Greek generic name, “mathematics difficulty”. Until recently, very little was known about its prevalence, causes or treatment. Children with dyscalculia have difficulty understanding simple number facts and procedures. They tend to operate at average or above average levels in other subjects but demonstrate difficulties in Mathematics. They lack confidence, and practice avoidance strategies often manifesting in behaviour issues and helplessness. Individuals display a mathematics disability when their performance on standardized calculation tests or on numerical reasoning tasks is significantly depressed, given their age, education and intellectual reasoning ability (Mental Disorders IV (DSM IV)). When this loss of ability to calculate is due to cerebral trauma, the condition is called acalculia or acquired dyscalculia. Mathematical learning difficulties that share features with acquired dyscalculia but withoutevidence of cerebral trauma are referred to as developmental dyscalculia.(Hughes, Kolstad&Briggs, 1994). Students who show developmental dyscalculia (DD) have difficulty recalling number facts and completing numerical calculations. They also show chronic difficulties with numerical processing skills such as recognizing number symbols, writing numbers or naming written numerals and applying procedures correctly (Gordon, 1992). They may have low self-efficacy and selective attention difficulties (Gross Tsur, Auerbach, Manor &Shalev, 1996).  It is important to keep in mind that not all students who display low mathematics achievement have Developmental Dyscalculia.

1.1 Prevalence of dyscalculia

Research by Joffee, Fleischner and lately, Brian Butterworth, now acknowledge the recognition of dyscalculia in its own right and Butterworth further estimates that actually 3- 6% of the population are dyscalculic, based upon a proportion of pupils who have specific difficulty in Mathematics despite good performance in other subjects.Students whose only learning disability is developmental dyscalculia have been reported in several studies (Ozols& Rourke,1991).They comprise3% to 6.5% of the general school population,(Gross Tsur, Manor& Shalev1996,Von Aster, 1994), have average or above average intelligence and are found equally among both boys and girls. Dyscalculia is a learning problem which needs appropriate educational provisions. Its identification is complicated because it can be the only difficulty that a child has or it may occur as a part of a broader range of difficulties. It demands appropriate diagnostic procedures and educational interventions.The author believes that there is danger that incorrect diagnosis and classification can lead to helplessness on the part of the learner, in which the learner believes that the difficulties are too serious as to benefit from remediation.This study was conducted to achieve the following objectives:

Objective 1: To find out the prevalence of students with dyscalculia in schools with resource rooms

Objective 2: To identify students with dyscalculia and their academic needs

1.2 Significance of the study

 i.         There is a lot of research conducted on dyslexia, but less research has been carried out on dyscalculia in India.

ii.         Mathematics is a compulsory subject of school education. Its study has a profound and long lasting effect on the lives of its students. Every student must have an adequate knowledge of mathematics to get on in life. Parents and teachers find it difficult to deal with the problems of children with dyscalculia. They exhibit a certain level of helplessness.

iii.        Although children have been given an option to drop mathematics in favour of a vocational subject at the SSC Board Exam, if diagnosed with dyscalculia, parents are reluctant to allow them to do so, because of the importance of the subject.

1.3 Types of dyscalculia

Research by the Dyscalculia Centre, which has been published in SEN Magazine, has shown that there are five different types of dyscalculia – although inevitably many young people suffer from a combination of the types listed below.

Type 1 Dyscalculicsreport significant worries about math.  As a result they feel themselves living in an alien world in which everyone else can grasp math, but they can’t.  Self-doubt becomes so strong that it gets increasingly difficult to persuade the individual that with proper support they might well be able to undertake and understand mathematical calculations.

Type 2 Dyscalculicsalso experience this deep concern but have found strategies for understanding and coping with basic mathematics – yet they feel that they don’t have the automatic grasp that others have and often take twice as much time (or more) to do a mathematics problem as a non-dyscalculic person.

Type 3 Dyscalculicshave a profound difficulty in comprehending and dealing with the concept of time.  Sometimes this issue appears on its own, sometimes in combination with type 1 or 2 dyscalculics.  For such people time itself makes no sense and they are quite unable to estimate “five minutes” or any other time length while questions about timetables and the like are also quite meaningless.

Type 4 Dyscalculics may not always be dyscalculic in the genetic sense, although they display many of the symptoms of dyscalculic people because they have short-term and long-term memory problems.  These students generally have a problem with all sequences – and this, of course, affects their ability to handle mathematics perhaps more than any other subject.

Type 5 Dyscalculicstend not to see numbers as in any way related to the real world.  In one sense most of us have this problem; after all, what is “six”?   We know what six sheep are.  But “six”, alone is close to meaningless.   For such people, mathematics can be learned automatically, but when it gets to issues such as fractions, decimals, and percentages then life gets difficult. 

1.4 Signs and symptoms of dyscalculia

Afew of the signs and symptoms a student with developmentaldyscalculiahas are as follows:

Ø  difficulties in holding and processing information in the mind – a

weak working memory which results in: forgetting where you are in

the calculation; failure to carry a number accurately into the next part

of the procedure.

Ø  difficulties in understanding calendars, reading clocks and geometry.

Ø  difficulties in planning and a failure to check one’s answer.

Ø  difficultyunderstanding the information within the problem.

Ø  a weak working memory and difficulties with language and reading

comprehension, will find it difficult to understand information which is

presented in a symbolic or textual manner.

Ø  anxiety relating to mathematics and low self-esteem.

Because mathematics is very developmental, any insecurity or uncertainty in early topics will impact on later topics, hence the need to take intervention back to basics.

1.5 Causes of dyscalculia

Successful intervention is dependent on finding the cause or causes of a problem. Most problems can only be solved if one knows their causes. A viable point of departure would therefore be to ask the question, “What causes dyscalculia?”Mathematical performance deficits, Developmental Dyscalculia, may arisebecause of a wide range of factors, from poor teaching, to low socio-economicstatus, to behavioral attention problems. However, a subset of children with math difficulties, possibly with the most-severe impairments, appears to suffer from a developmental learning disorder that undermines the ability to process basic numerical magnitude information, and that impairment in turn undermines the acquisition of school-level arithmetic skills. This disorder, “primarydevelopmental dyscalculia,” should not be confused with “secondarydevelopmental dyscalculia,” which refers to mathematical deficits stemming from external factors such as those described above. Instead, primary Developmental Dyscalculia is associated with impaired development of brain mechanisms for processing numerical magnitude information and is thus driven by endogenous neurodevelopmental factors.      The causes of dyscalculia are still a gray area, and there is little concrete understanding about what causes it or how itcan be prevented.
Hereditary or congenital disorders may be a significant cause, but there is no concrete evidence to prove it as yet. Injury to the brain that affects working memory is seen as a major factor in mental addition disability.

1.6 Assessment and diagnosis of dyscalculia

Recent research has identified the heterogeneous nature of mathematical learning difficulties and dyscalculia, hence it is difficult to identify via a single diagnostic test. Diagnosis and assessment should use a range of measures, a test protocol, to identify which factors are creating problems for the learner. Although on-line tests can be of help, understanding the difficulties will be better achieved by an individual person-to-person diagnostic, clinical interview.

            Diagnosis could also involve several tests to determine the presence of a learning disability. Dyscalculia often requires a paper-pencil test. Check lists can also be used for initial testing. Further tests are required to reveal how a person practically applies mathematical concepts. Results are compared with the expected skill, based on educational level and age.

Areas that are assessed during dyscalculia tests include:

skills in adding, subtracting, dividing, multiplying and counting

skills in identifying when to use mathematical operations

skills in organizing objects

skills in measuring time, money, volume, and other quantities

skills in re-checking own work and using alternatives to come up with a correct solution.

2.      METHOD

The Lafayette Parish School Dyscalculia check list has 14 items which have to be rated using a four point rating scale and then interpreted. It was given to 15 Mathematics teachers along with a questionnaire to find out the prevalence of dyscalculia in their schools. The entire population of 1757 students was surveyed, belonging to three schools having resource rooms. Percentages were used to report the results. Identificationof students was done by the consistent observation of the students by the teachers. TheDyscalculia test (non-standardised) by Liz Weaverwas used to confirm the identification and to assess the needs of students with dyscalculia. A purposive sample of 26 students from a resource room was used to identify students with dyscalculia and their academic needs.Percentages were used to report the results.

3.    Results and discussion

The prevalence of dyscalculia in the three schools surveyed was found to be ranging from 6% to 19%. The average of all three schools was 11.13%.

 Table of prevalence of students with dyscalculia in three schools with resource rooms in Panjim

Standard	Total number of students	Number of students with dyscalculia	Percentage of students with dyscalculia
5	316	21	6.6%
6	247	28	11.3%
7	296	27	9.1%
8	315	26	8.2%
9	290	49	16.9%
10	293	34	11.6%

Graph of prevalence of dyscalculia class-wise in three schools

1. The prevalence of children with dyscalculia among boys was 6.23%
2. The prevalence of children with dyscalculia among Girls was 8.54%
3. The prevalence of children with dyscalculia among boys and girls was 18.61%

Research shows the prevalenceas 5-8% of school age children (Strauss, 2003),

3-6% of population (www.bda-dyslexia.org),6-7% of school age children (www.ldonline.org).Jovanovic G., Jovanovic Z.et.al (2013), conducted a study on, “The frequency of dyscalculia among primary school children”. The results indicated that: The frequency of dyscalculia in the sample was 9.9%. The difference between boys and girls according to the total score on the test was statistically significant (p<0 .005="" o:p="">

From the analysis of the results of the dyscalculia test all the students from the resource room of Our Lady of Rosary H. S. were found to have dyscalculia, but in varying degrees from mild to moderate to acute.

Range of mistakes made in the dyscalculia test by students from standards

 V-VIII

Standard	Range of mistakes made
V	70-90%
VI	10-75%
VII	30-60%
VIII	50-80%

The percentage of mistakes made by students of standards V and VIII in the dyscalculia test were more than those made by students of standards VI and VII. This shows that the former students were more dyscalculic than the latter.

ITEM WISE ANALYSIS OF THE DATA COLLECTED FROM THE ADMINISTRATION OF THE DYSCALCULIA TEST

ITEM1: Knowledge of Number sequencing and recognizing “skip-counting” sequence.

            All the students tested had knowledge of natural number sequencing, but recognizing skip-counting sequence and then being able to fill in the missing numbers, both forward and backward was a problem for 23 out of 26 (88.46%) students tested. From the selected sample only Saloni and Sanskruti got the item right.

ITEM2: Number recognition.

            15 out of 26 (57.69%) students had a problem with number recognition including three from the selected sample viz. Trishna, Tulsi and Reasham. Eight showed ‘6’ and ‘9’ reversals.

ITEM3: Memory of Number sequences.

            Eight (30.77%) students had a problem in counting backwards of which only two were from the experimental group viz. Ryanna and Trishna.

ITEM4: Memory of Number sequences.

            Four (15.38%) students had a problem with matching the sixes and nines. (reversals).  None of them were from the experimental group.

ITEM5: Pattern recognition and motor coordination.

            Seventeen (65.38%) students were unable to complete the pattern. Four students were able to draw only one row correctly. Trishna, Tulsi, Reasham, Ryanna, and Saloni from the selected sample were unable to do it correctly.

ITEM 6: Ability to copy the problems without number reversals and transpositions.

            Only one student showed one reversal in copying the problems and three students copied one number in one out of  four  problems incorrectly which is no cause for concern as it is considered to be normal for children who do not have dyscalculia. Three students worked out the problems but did not copy them again.  Twenty students had no problem with aligning the numbers one below the other to add them correctly. Only Saloni copied wrong.

ITEM 7: Skill in adding and subtracting, visual discrimination and mental flexibility in switching between addition and subtraction.

            Nine students were not able to visually discriminate and switch between addition and subtraction correctly. Tulsi and Reasham from the sample were not able to get this item right. Six students made a few mistakes which could be due to carelessness. Eleven showed no errors as they solved all the problems correctly. 57.69% students made mistakes in this item.

ITEM 8: Reading comprehension and/understanding of the Mathematics involved.

            Four students had no difficulty in understanding and solving the problem correctly. Seven students were able to solve only one part of the problem correctly. Fifteen students were unable to solve the problem showing that they had a difficulty with reading comprehension and understanding the Mathematics involved. All the students from the sample, except Ryanna and Trishna showed this difficulty. 84.61% students made mistakes.

ITEM 9: Understanding the difference between adding and subtracting.

            Only five students knew the meaning of subtracting. One of them was Saloni from the sample. All the others (80.77%) could not differentiate between adding and subtracting.

ITEM 10 and 11: Understanding of the concepts of hours and minutes.

            Eleven (42.30%) students did not understand the concept of hours and eighteen (69.23%) students failed to understand the concept of minutes. Sanskruti was unable to understand both units of time.

ITEM 12: Understanding of the appropriate use of units of time.

            Only ten students (38.46%) out of those tested were not able to understand the appropriate this difficulty.

ITEM 13: Understanding of a multi-step problem.

            Thirteen (50%) students including Tulsi and Reasham showed difficulty in understanding the multi-step problem and were unable to solve it correctly.

ITEM 14: Skip counting aloud by 4.

            Fifteen (57.69%) students had difficulty in skip counting aloud by 4. It is possible they difficulty.

ITEM 15: Understanding of the differences between units of measurement of length.

            Thirteen (50%) students had no understanding of the difference between units of measurement of length including Sanskruti from the selected sample.

ITEM 16: Ability to copy numbers without reversals.

            Only six (23.07%) students did not copy the numbers correctly but there were no reversals. Perhaps these students did not understand the question. None from the chosen sample had a difficulty with copying numbers.

ITEM 17: Understanding the nature of the task and adding correctly.

            Nine (34.61%) students made mistakes while adding. Only Sanskruti had this difficulty.

ITEM 18: Understanding the nature of the task and subtracting correctly.

            Twelve (46.15) students got the answers incorrect including Donea and Sanskruti. Perhaps they did not understand the relation between items 16, 17 and 18.

ITEM 19: Number recognition and regular perception of ‘6’ and ‘9’ correctly.

            Only one student (3.85%) had this problem. This shows that the students tested had mild to moderate dyscalculia.

ITEM 20: Capacity for remembering a short sequence of numbers and then reproducing it without reversals or transpositions.

            Twelve students could not remember the short sequence of numbers and showed reversals and transpositions. Nine students could remember a short sequence of numbers up to four digits, but could not remember and write the whole sequence correctly.80.77% students had a problem with this item. Tulsi and Reasham had a difficulty in this item.

ITEM 21: Ability to remember and orally repeatthe number sequences without reversals or transpositions.

            Twelve (46.15%) students were not able to repeat the number sequences correctly. Eleven students were able to repeat 2-3 of the 4number sequences correctly. Tulsi and Reasham had a difficulty in this ability.

ITEM 22: Ability to remember a picture and then reproduce it without reversals.

            None of the students were able to remember the picture and reproduce it correctly. However, they could copy it correctly with the exception of one student who showed a reversal.

ITEM 23: Capacity to identify the operations involved and perform the Math and fill in the blanks with the proper number or operation sign.

            Twelve (46.15%) students were unable to identify and perform the operations correctly. Neither were they able to fill in the blanks with the proper operation sign. Donea showed this difficulty.

ITEM 24: Understanding of replacing symbols with numbers and then performing the appropriate operations

            Seventeen (65.38%) students were unable to understand the replacement of symbols with numbers and perform the appropriate operations. Donea, Tulsi and Reasham showed this difficulty.

Very few students made mistakes in “Number recognition and regular perception of ‘6’ and ‘9’ correctly.” All the students made mistakes in the “Ability to remember a picture and then reproduce it without reversals.” They could not do so from memory, but were able to copy and reproduce the picture correctly. Only one showed a reversal. Majority of the students (more than 75%) had problems in “Knowledge of Number sequencing and recognizing ‘skip-counting’ sequence”, “Reading comprehension and/understanding of the Mathematics involved”, “Understanding the difference between adding and subtracting”, “Capacity for remembering a short sequence of numbers and then reproducing it without reversals or transpositions” and “Ability to remember and orally repeat the number sequences without reversals or transpositions”.

4.    Conclusion

Although the percentage of students with dyscalculia is similar to the results obtained by other researchers, a lot of work needs to be done in this area. The teachers’ consistent observation over a period of time of the common mistakes children with dyscalculia make can go a long way toward correctly ascertaining the prevalence of dyscalculia among children of a particular area. Also the teachers need to be familiarized with the signs and symptoms of children with dyscalculia and given training how to use the checklist mentioned. The non-standardised dyscalculia test used, helped in identification of students with dyscalculia in the resource room. It in a way confirmed that the students were indeed dyscalculic. It also helped in classifying students as mild, moderate or acute in relation to their being dyscalculic, on the basis of the percentage of items they answered correctly. This test could be standardized for future use.