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Towards a standard diagnostic tool for dyscalculia in school children

Published onFeb 17, 2020
Towards a standard diagnostic tool for dyscalculia in school children
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Abstract

When a child's ability to perform mathematical tasks at school is noticeably low, a possible explanation is dyscalculia. Dyscalculia is a specific learning disorder that is prevalent in 3-7% of children and adults. Although the incidence rate is comparable to dyslexia, much less is known about dyscalculia. Recent years have seen a marked increase in research on this topic. Unfortunately, a standard diagnostic tool does not yet exist. Researchers use different criteria in classifying dyscalculics which makes comparisons between studies uninformative. In this report, we present a brief description of what dyscalculia is. We continue by discussing three current assessment tools that we have identified as representative of the wide spectrum of diagnostic practices for dyscalculia.  We end the report with a proposal for a screener tool and with recommendations for further research.

Keywords: Learning disabilities, Dyscalculia, Number processing, Numerosity

1. Introduction

1.1 What is dyscalculia?

Dyscalculia is characterized by impairments in understanding and performing operations related to numbers.  Symptoms of dyscalculia include deficits in spontaneous focusing on numbers (Hannula et al, 2010), comparing non-symbolic numerical quantities (Piazza et al., 2010, Halberda et al., 2012), symbolic processing of numbers (Stock et al., 2010), linking non-symbolic representations to symbols (Budgen and Ansari 2011), subitizing (Koontz 1996), number naming, number writing and magnitude comparison (Geary et al., 1999) and more. 

Dyscalculia symptoms may first be observed in an educational context, manifested as school-related mathematics deficiencies, but the effects extend beyond school activity. Dyscalculics report the inability to read analog clocks, to perform mental operations related to timing and durations, to comprehend budgeting, to understand the value of prices in daily life, to perform physical activities that involve timing, etc. 

The consequences of suffering from dyscalculia carry on beyond low numerosity performance. Dyscalculics also have higher school dropout rates than the general population (Parsons et al., 2005), lower employment rates and develop a range of mental symptoms and disorders such as low self-esteem, aggressive behavior, anxiety, depression (Schulte-Körne G., 2016). Some studies have even estimated the monetary cost incurred by governments as a result of low numerosity (Gross et al., 2009; OECD, 2010).

Some researchers estimate the prevalence of dyscalculia in children of school age to be 5 to 6% (Shalev, 2004), while a more recent estimate of 3 to 7% includes adolescents and adults in addition to children (Haberstroh S. and Schulte-Körne G., 2019). This is roughly the same prevalence as developmental dyslexia (J. D. E. Gabrieli, 2009). In what concerns gender differences, several studies found a similar prevalence in girls and boys (Moll et al, 2014). 

1.2 What causes dyscalculia?

Dyscalculia is a specific learning disorder whose underlying causes are not yet completely understood. Several studies support the idea that arithmetic ability is enabled by a specific cognitive system which is different from those supporting general abilities. Dehaene puts forward a “number-sense” theory (Dehaene S., 2001), in which he proposes that we all possess an innate sense of the number of items in a set. We automatically estimate the magnitude of a set (its numerosity) and we order sets by magnitude. This mechanism is called the Approximate Number System (ANS). Dyscalculia, in this framework, represents a deficit of the ANS (Butterworth B., 2005). 

Other researchers argue that assumptions of a single core deficit in dyscalculia are too simplistic and that it does not account for all the symptoms seen in dyscalculics (Kaufmann et al., 2013). Moeller et al. 2012 sums up the different ways in which dyscalculia is conceptualized in the existing literature as follows: (1) the numerical core deficit (2) dyscalculia as a disorder with subtypes due to domain-general processes (3) dyscalculia as a disorder with subtypes due to domain-specific deficits. The domain-general deficits considered in the second approach include working memory, semantic memory, visual-spatial skills, and logical reasoning. The domain-specific numerical deficits include verbal number representations, arithmetic fact knowledge, visual-spatial number forms, base-10-system, etc (for a review, see Kaufmann et al., 2013). 

We should note that dyscalculia can affect individuals with normal intelligence (Landerl et al., 2004) and there is no overlap with mental retardation. Also, it is not a consequence of poor schooling or of socio-economic status of the family (Haberstroh et al. 2019). Furthermore, a distinction should be made between developmental dyscalculia (which we address in this article) and acalculia, which is acquired dyscalculia due to brain damage. A proper diagnostic tool should, therefore, these for the above conditions.  

At an anatomical level, structural and functional neuroimaging studies have identified some neural markers of impaired numerosity in both adults and children. Processing the numerosity of arrays of objects involves the activation of the intra-parietal sulcus (IPS), located on the temporal lobe (Castelli F et al., 2006). In children with dyscalculia, studies have found reduced activation of the IPS during arithmetic tasks (C. Mussolin et al. 2010, Price et al., 2007, K. Kucian et al., 2006) and reduced grey matter in the IPS (E. B. Isaacs et al 2001, S. Rotzer et al. 2008, E. Rykhlevskaia et al. 2009). Moreover, when magnetic stimulation disturbs the functioning of the IPS, the numerosity ability is impaired (Cappelletti M. et al., 2007). It is interesting to note that the IPS seems to be implicated in both simple and complex operations (Butterworth et al. 2011). Butterworth and Laurillard 2011 suggest that the IPS is only one part of a larger cortical network that is necessary for mathematical cognition. They point out that impairments at different locations in this network may give rise to different dyscalculia subtypes. 

1.3 Diagnosing dyscalculics

In the last decade, we have seen a marked increase in the number of articles studying dyscalculia (Kaufmann et al., 2013). Unfortunately, there is wide variability in the diagnostic procedures employed for selecting subjects for these studies: researchers not only use different tests to assess mathematical abilities but also use different threshold points (Peter L. and Ansari D., 2019). As Kaufmann et al. 2013 points out, one subject may qualify as dyscalculic in one study, but not in another one. As a consequence, comparisons between findings of different studies become impossible. Furthermore, suboptimal diagnostic tools may lead to high variability within the test group in some studies, which may obscure the effects under investigation. For example, this might explain why some studies find impairment in a particular cognitive function, while others do not. 

As the underlying causes of dyscalculia are still not understood, the diagnosing tests vary greatly between studies. Many studies use standard tests for Mathematical abilities. As Landerl K. et al 2004 points out, these tools also test for cognitive abilities which may not fall under the dyscalculia symptoms (the ability to follow instructions, attention, working memory). Other researchers (Butterworth B. 2003) devised a screening tool which tests only for the basic numerosity skills. Our approach is to find a middle ground. We stand by the objections against using standard mathematical tests, but we also believe that the simple approach of Butterworth B. 2003 may benefit from a few additional dimensions to be tested. In section 3 we go into more detail regarding our proposal.  

Scientists have recognized the necessity to unify the diagnosing procedures for many years. We identified two main approaches: one is to simplify the tests as much as possible and try to measure the most basic mechanisms involved in number processing while another approach is to include as many and as accurate tests as possible. In the following sections, we discuss the Dyscalculia Screener (Butterworth B. 2003) which illustrates the simplification approach and the guideline on the diagnostic and treatment of dyscalculia (Haberstroh S. and Schulte-Körne G., 2019) as an example of the second approach. We also discuss a third assessment tool, which is currently available to the general public (Cognitive Assessment Battery CAB-DC). Our approach is to find a middle ground. We stand by the objections against using standard mathematical tests, but we also believe that the simple approach of Butterworth B. 2003 may benefit from a few additional dimensions to be tested. In section 3 we go into more detail regarding our proposal. 

2. Existing Tools

2.1 Haberstroh et al. 2019 

Haberstroh et al. 2019 presents a consensus reached by twenty societies and associations under the leadership of the German Society of Child and Adolescent Psychiatry, Psychosomatics and Psychotherapy. This assembly has created a guideline on the diagnosis and treatment of dyscalculia (guideline No. 028-046 of the Association of the Scientific Medical Societies in Germany, Arbeitsgemeinschaft der Wissenschaftlichen Medizinischen Fac hgesellschaften [AWMF]).

2.1.1 Link to the tool 

The complete details for the proposed solution can be found at https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6440373/figure/F1/. We also include the flowchart that the authors devised to illustrate the assessment process (figure 1).

2.1.2 Objective and science of the Tool 

In the context of a systematic review of the literature, Haberstroh and Schulte-Korne present a diagnostic assessment of dyscalculia (Haberstroh and Schulte-Korne, 2019). This diagnostic tool combines three approaches: 1) a clinical examination, 2) history and psychosocial assessment, 3) a psychometric test of mathematical ability.

The clinical examination accounts for neurogenetic disorders, low birth weight, and prematurity, low intelligence, brain damage or disease or impairments of hearing and sight that were not detected for multiple years. The assessment also requires thorough documentation of the developmental biography, in addition to familial and scholastic background. Care needs to be taken so as not to allow certain factors to affect the assessment. The authors list such factors as prolonged school absence or performance-hindering conditions such as anxiety disorders. 

Figure 1. A flowchart explaining the algorithm proposed by Haberstroh and Scholte-Korne to diagnose dyscalculia (re-produced from Haberstroh & Scholte-Korne, 2019).

Lastly, a psychometric test of mathematical performance is conducted. Haberstroh and Schulte-Korne propose multiple mathematical ability tests, to which they assign a rank order according to certain methodological quality indicators chosen by the authors. The highest ranking tests are: BADYS1-4 (Merdian et al., 2015) designed for children ranging from first to fifth grade and BADYS 5-8+ (Merdian et al., 2012) for children between 5th and 9th grade. Unfortunately both the above mentioned mathematical tests and all the other ones recommended by Haberstroh and Schulte-Korne 2019 are only available in German language. Furthermore, Merdian et al. 2012 and Merdian et al. 2015, the two research articles detailing the two  BADYS tests are not available for free. Hence, the information we present in the following paragraph was extracted and translated from the freely available description brochure “Handout BADYS 1 - 4+ und BADYS 5 - 8+” (available on the website we provide in the references section). 

The BADYS1-4 mathematical abilities test assesses five groups of functions: general cognitive functions (memory, mathematics concepts, attention), spatial perception visuo-spatial basic skills), basic numerical skills (quantity detection and dealing with place value), more advanced numerical skills (addition, subtraction, multiplication and division)  and how participants deal with various measures (for example unit conversions, estimation of size or distance, reading an analog clock).

2.1.3 Review of the limitations

The evaluation mechanism proposed by Haberstroh and Schulte-Korne 2019 is, according to the authors, the world’s first consensus guidelines, which multiple German associations, laboratories and scientists adhered to. It takes into account most of the subject’s personal history and peculiar suboptimal education experiences which have been shown to be relevant for low mathematical performance. However, this approach has several drawbacks: the diagnostic algorithm has a large subjective component, dependent on the specialist’s interpretation, and it employs standard tests for Mathematical abilities which, as mentioned in section 1.3, have several disadvantages when used in the context of dyscalculia.  Furthermore, such a complex assessment tool is difficult to access by a large percentage of those who need it. 

2.2 Dyscalculia Screener

Butterworth 2003 proposes a Dyscalculia Screener as a quick evaluation tool that can be massively deployed with minimal training for the specialist who performs the test. The screener is based on the premise that children with dyscalculia lack the innate abilities related to numerosity and it proposes a set of computer-related tests for screening for the disorder.

2.2.1 Link to the tool 

https://www.mathematicalbrain.com/pdf/SENAPPT.PDF

2.2.2 Objective and science of the Tool  

Central to this tool is the concept of “numerosity”, which refers to an innate feeling that sets have a magnitude and that these numbers can be manipulated mentally (Butterworth, 2005). In order to test for numerosity, the “Dyscalculia Screener” was devised, which consists of three computer controlled categories of exercises: simple reaction time (pressing a button as soon as something appears on screen), a test of capacity (dot enumeration and number comparison) and a test of achievement (arithmetic tests containing addition and multiplication operations). 

In the dot enumeration test one half of the screen contains a set of dots and the other half contains a numeral. The participants have to compare the magnitude of the cloud of dots and the numeral on screen. Most subjects provide the correct answers, but dyscalculics take considerably longer to find the solution.

The number comparison test (numerical Stroop) consists of two numerals which are displayed on the screen. The two numbers have different font sizes and in some of the trials the relationship between the two font sizes is incongruent with the relationship between the two numerals. The participants must compare the two numerals. As for the dot enumeration task, dyscalculics offer the solution with a considerable delay.

In the arithmetic tests, the participants see on the screen either an addition or a subtraction, as well as a result proposed by the software for that particular operation. The subject is requested to answer whether the result of the operation is correct or not. 


2.2.3 Comments and limitations

The screening tool is simple, easy to use by non professionals and might provide more consistent results (across countries, different children, same child at different moments in time and when administered and interpreted by different specialists). On the other hand, it does not take into account the child’s history, possible brain trauma, education (or lack of) etc. Furthermore, as it relies on reaction time as differentiators, it might fail to detect mild cases of dyscalculia.

2.3 Romanian screening instrument for dyscalculia

2.3.1 Link to the tool

https://www.researchgate.net/publication/257715181_Romanian_screening_instrument_for_dyscalculia

2.3.2 Objective and science of the Tool

The Romanian screening test (ST) for dyscalculia is proposed by Gliga et al. 2012. This study was performed on 45 students aged between 8 and 11 years. 

This tool is based on the Number Sense battery (Jordan et al. 2007), NUCALC (Koumoula et al. 2004) battery and on the Romanian mathematical curriculum. An important consideration for this proposal is that, according to Mozzocco 2005, when testing mathematical ability in children it is important to use paper and pencil tests and to manipulate real world objects (for example, embedding the number tests in stories). The NUCALC is a paper-pencil test which assesses number concepts, number facts and arithmetic procedures. The Number Sense battery tests for counting, number knowledge (e.g. magnitude comparison), nonverbal calculations (using objects), story problems and number combinations.  

The ST first uses the Romanian standardization of the Dearborn nonverbal test of intelligence (Bontila 1971) to test for mental delay. It also assesses the language skills of the subject by employing the verbal subtest of WISC-R (vocabulary, comprehension, similarities, information and digit-span) to make sure the participants have “normal verbal intelligence”. 

Starting from NUCALC and the Number Sense battery, Gliga et al. 2012 constructs an ST that takes into account the guiding principles of Butterworth 2005, namely that a dyscalculia test should highlight difficulties with approximating numbers, subitizing, numerosity encoding and mathematical language. The proposed ST consists of 13 items that require subjects to: (1) orally count forward / backwords with and without the support of coins (2) estimate numerosities (3) read / write numbers (4) compare numbers (5) place numbers on a undivided horizontal scale (6) solve subtractions orally (7) memorize series of one digit numbers (8) solve simple calculations. The result of the test is a number between 0 and 14. The numerical results are next assigned to one of three categories of risk for dyscalculia: severe (2 S.D. from the mean value), moderate (2 S.D. from the mean value) or no-risk.  

2.3.3 Comments and limitations

Gliga et al. 2012 propose a much needed screening tool for dyscalculia in Romaian language and adapted to the local Mathematical curriculum. The ST was tested in a test pilot on a small sample (45 pupils). Further studies on a larger population are needed in order to confirm the cutoff criteria used by the authors, especially because the difference the study found between the at-risk pupils (severe and mild) and the no-risk group was not statistically significant. 

Although the authors of the ST detail the tests they used as starting point in devising their tool and the 8 types of requirements comprised in their proposed ST, there leave out the detailed composition of their test (e.g. what were the exact questions, how many repetitions there were for a particular test item etc). For example, test item number 2, estimating numerosities without counting can take multiple forms therefore this information is not sufficient for replicating the experiment of Gigla et al. 2012. For test item number 6, solving subtractions orally, the authors do not specify how the information is provided (either in written form or verbal instructions). If the task is communicated orally, it would rely more on working memory than a written task. All these details are important in order to assess what strengths and limitations the ST has.  

3. Enhanced dyscalculia screener

3.1 Summary

Dyscalculia is a learning disorder which is still not very well understood. One of the problems with dealing with dyscalculia is that there is still no standard diagnostic tool. Researchers use not only different tests, but also different thresholds for categorizing subjects as dyscalculics or not (Landerl et al. 2004). One clear consequence is that one participant may qualify as dyscalculic in one study and not dyscalculic in another study. A less obvious consequence is that a study with a more relaxed criteria of diagnosis may face a higher group heterogeneity and fail to reach statistical significance of between-group differences.

In this article we have examined three approaches for diagnosing dyscalculia. The first is a complex screening procedure developed by a consortium of German research groups, institutions and individual practitioners (Haberstroh et al. 2019). This diagnostic tool involves a clinical examination, a history and psychosocial assessment and a psychometric test of mathematical performance. The second tool we examined is a simple screener that tests for basic “numerosity skills” (Dyscalculia Screener, by Brian Butterworth). Our third examined tool was the Cognitive Assessment Battery for Dyscalculia (CAB-DC), which proposes its own mathematical abilities test and compliments it with a set of tests aimed at identified domain general cognitive deficits. 

The approach of Haberstroh et al 2019 and of the Cognitive Assessment Battery for Dyscalculia (CAB-DC) is to use standard mathematical ability tests together with screenings that would rule out other possible causes for poor mathematical abilities which are not relevant for dyscalculia. This method makes the diagnostic a rather complicated procedure which allows for subjective interpretation and makes the tool not easily accessible to the large population. A further objection to employing standard mathematical abilities tests is that they may tap into cognitive processes which are affected differently in different possible subtypes of dyscalculia.. 

At the other end of the complexity spectrum, Butterworth 2003 offers a screening tool which only tests basic numerosity skills. Its simplicity brings the advantage of making it easily accessible to the general public. However, we consider that the tool does not test all deficits specific to this disorder. For example, we know that dyscalculia is multimodal deficiency: it affects visual, auditory as well as tactile input. 

We are not implying that we should extend the test with questions tapping into dyscalculia subtypes, but rather that the core mechanisms that are affected regardless of the subtype are not completely tested in Butterworth’s screening tool. In the next sections we propose a screening tool that builds upon Buttherworth’s screener and adds slightly more complexity in an attempt to improve its detection accuracy.

3.2 The multimodal dyscalculia screener

Our recommendation is to enhance the Butterworth screening tool with tests that tap into more cognitive functions than the very basic numerosity skills than this tools assesses. At the same time, we will make sure we avoid testing for more complex mathematical abilities which might be imparied for other reasons than dyscalculia. Furthermore, as dyscalculia deficiencies should manifest themselves both for visual and auditory stimuli, we include both in our test. Ideally, we would like to include tactile stimulation (e.g. the participant must say how many times (s)he was touched on the hand by the specialist delivering the test), but the implementation of such a test would be more challenging and our goal is to produce a screening tool that can be easily deployed and used.

The proposed tool evaluates basic number processing skills and simple mental arithmetic. For assessing number processing, the test items we employ are: enumeration, linking non symbolic representations to symbols, transcoding, counting, number comparison, dealing with measures. The next section discusses in detail the deployment requirements and the individual tasks.

3.3 Deployment of dyscalculia screener

3.3.1 Protocol

Our dyscalculia screener is a computer based test. Participants should be familiar with reading instructions presented on screen and inputting their answer through a keyboard. The screener requires accurate timing. A training session should be provided to make sure the participants understand how to perform the required tasks. 

The tool is implemented as a browser based web application. It uses both visual and auditory stimuli. We recommend the participants should use headphones to facilitate the perception of the auditory stimuli.

The answers will be provided as key presses or as vocal responses. Therefore, the availability of a microphone is mandatory. 

The pupils should be tested individually, in a quiet room. 

3.3.2 Participants

The present dyscalculia screener is addressed to pupils ranging from 7 to 14 years old. Given the visual and auditory nature of the test, impairments in visual or auditory perception will hinder task performance. 

3.3.3 Tasks

The screener can be run on any computer that has a functional screen, keyboard and sound card. 

A. Basic number processing skills

Enumeration

This task will be performed with both visual and auditory stimuli. 

A cloud of dots is presented on the screen, with a magnitude ranging between 1 and 9. The participant must indicate the magnitude of the cloud by pressing the corresponding key on the computer keyboard.

For auditory stimuli enumeration, the participant will hear a tone which is repeated between 2 and 9 times. The participant must indicate the magnitude of the cloud by pressing the corresponding key on the computer keyboard.

Linking non symbolic representations to symbols

This task tests the ability to link non-symbolic representations to arabic numerals and to number words. 

A cloud of dots (from 1 to 9) is displayed on the left half of the screen. An arabic numeral or a number word (the word “one”, “two” etc) is also shown on the right half of the screen. The subject must press ‘Y’ or ‘N’ to indicate if the magnitude shown on the right is correct. 

Transcoding

This task consists of number reading and verbal naming or of number hearing and written naming. For the first task, the participant sees an arabic numeral and must say the corresponding number word. For the second task, a number is hears a number and must press the corresponding key on the keyboard.  

Counting

The participant is instructed to count, as quickly and as accurately as (s)he can: from 1 to 20 in increments of 1, from 45 to 65 in increments of 1, from 2 to 20 in increments of 2 and to count backwards from 20 to 1. The responses are provided verbally. The screener measures both the latency of the response start and the total duration of the response. 

Number comparison

The screener tests both non-symbolic and symbolic number comparison. For both task types, both cardinality and ordinality are tested. 

Children are presented with two clouds of dots, one on the left and one on the right of the screen. They are asked to select the largest or the smallest number. For ordinality testing, three clouds of dots are presented simultaneously on the screen (one on the left, one in the middle and one on the right) and the participant must indicate if the magnitudes are in ascending order. 

For the symbolic number comparison, the two tasks variants presented above will be used, but digits will be presented instead of clouds of dots. 

A third task type will test comparison of symbolic and non-symbolic representations. A cloud of dots will be presented on one side of the screen and an arabic numeral on the other side. The participant must indicate the largest / smallest number.  

Dealing with measures 

For testing the ability to deal with measure, we use three types of tasks: the mental number line, the estimation of measures and the analog clock reading.

One horizontal line is displayed on the screen and the two ends are marked with 0 and 100. The participant must place a random number (from 3 to 98) on this line. 

Two lines of different lengths are displayed on the screen. The participant must indicate the shortest / longest of the two.

The image of a clock is displayed on the screen and the participant must input in written form the time indicated by the clock. The answer will be in the form of HH:MM.

B. Simple mental arithmetic

The participants are presented with 20 simple additions, 20 simple subtractions, 20 simple    multiplications and 20 simple divisions. All involve 1- and 2- digit numbers, from 2 to 20. The items are presented on the computer screen (e.g. 3 + 6). The children are requested to input the answer (by pressing the corresponding keys) as quickly and accurately as they can. The screener records reaction latencies and errors. 

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Handout BADYS 1 - 4+ und BADYS 5 - 8+ obtained from http://www.paepsy-verlag.de/epages/es511754.sf/de_DE/?ObjectPath=/Shops/es511754/Categories


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