Dyscalculia in Belgium: definition, prevalence, subtypes, comorbidity, and assessment.
Prof. Dr. Annemie Desoete, Research in Learning Disabilities, Department of Experimental Clinical and Health Psychology, Ghent
University, Belgium. 2006
ABSTRACT
After an introduction on the prevalence, definition and subtypes of dyscalculia, we will focus on the assessment of students with
dyscalculia in Belgium. We present the TEDI-MATH a Belgian dyscalculia battery (translated into French, Dutch, German and
Spanish) that can be used for preschool students until they reach grade 3. We then illustrate how currently dyscalculia is assessed
and dealt with in higher education in Belgium. The assessment currently is based on intelligence testing, checklists, a test on
number knowledge, a test on procedural skills, a test on number fact retrieval and a test on visual spatial skills and on word
problems). An assessment always aims to develop STICORDI-advice. This advice is designed to help students with dyscalculia.
STICORDI refers to STI(mulation), CO(mpensation), R(emediation) and DI(spensation).
DEFINITION
Although various authors agree that an operational definition of learning disabilities is meaningful (e.g., Kavale & Forness, 2000;
Swanson, 2000), most studies are rather vague when it comes to characterizing the children who fit in their category of ‘children
with learning disabilities’. Three main criteria in defining learning disabilities can be distinguished.
The first criterion that is currently used is the discrepancy criterion. This criterion stipulates that a diagnosis of a learning disability
only is justified when a great discrepancy between scholastic achievement and general performance or intellectual ability is seen.
Although the discrepancy criterion is used a lot in research and clinical practice, the criterion is very unclear. The problem is that a
lot of variation exists in the interpretation of the discrepancy.
Questions that can be raised are how big the discrepancy has to be and how general performance can be operationalised. In line
with the DSM-IV (APA, 2000), some researchers stipulate that the extent of the discrepancy has to be at least as big as two
standard deviations between the chronological grade of the child and the level of achievement that is reached (e.g. Klauer, 1992).
Other authors do not agree with that criterion and have replaced it by a grade equivalent of two years lag between general
achievement and the level of scholar skills (e.g. Gross-Tsur, Manor, & Shalev, 1996; Reynolds, 1984; Semrund-Clikeman et al.,
1992). In Belgium practitioners use a discrepancy of two years in children in grade four or older, mathematical disabilities in younger
children are diagnosed when a discrepancy of one year is met (Desoete et al., 2004). A second question that rises concerning the
discrepancy model is how the discrepancy can be operationalised. Most of the time an IQ-assessment serves as an indicator for the
general level of achievement (Gross-Tsur and colleagues, 1996). However, this base of an IQ- achievement discrepancy is strongly
debated. Siegel (1989) disputes the usefulness of IQ-measurement to detect learning disabilities and argues that many children
with low IQ-scores can read at an age-appropriate level. Siegel (1989) means that the discrepancy model has lead to a great
number of children with learning disabilities that are not detected. In line with these findings, Mazzocco and Myers (2003) more
recently state that the criterion is not sensitive enough to identify all children with mathematical disabilities. A child with a
discrepancy between his IQ-score and his math achievement may have a mathematical disability, but many children with MD may
not meet this discrepancy-criterion. Moreover, recent studies found a correlation of .50 between mathematical abilities and
intelligence as measured with the WISC-III (Kort and colleagues, 2002).
A second criterion we encounter is the severeness criterion. We see this criterion however as a variant on the discrepancy
criterion we just discussed. The severity criterion contends that the achievement on scholastic skills is not within the normal range.
An exclusion of children based on a normal distribution of achievement scores in se equalizes the use of a discrepancy as a
defining factor. We find the criterion in the studies of Geary (2004) and Lewis, Hitch & Walker (1994). Geary uses the cut-off
criterion of the 25th percentile but warrants that only children who have scores across successive academic years beneath this cut-
off may have a diagnosis of mathematical disabilities. An additional criterion for learning disabilities is the exclusion criterion.
Often mentioned exclusion conditions are handicapping conditions in the situation of the child (e.g. sensory impairments, mental
retardation or impairments in general intelligence, social or emotional disturbances, …) and external factors (e.g. insufficient or
inappropriate instruction, cultural differences, psychogenic factors, …).
A third and last criterion that can be found in definitions for learning disabilities is the resistance criterion. Authors who defend this
criterion argue that core learning disabilities only can be diagnosed after a period of remediation is offered. For example the ICD-10
(WHO, 1992) under scribes this criterion by stating that remediation does not lead to direct improvements.
PREVALENCE
The number of mathematical low achieving pupils has increased substantially over the last 20 years (Swanson, 2000). The current
theories and models of learning are still somewhat inadequate in dealing with the learning difficulties in these children, since the
majority of these problems persist well into the secondary school years and even adulthood (McGlaughlin, Knoop, & Holliday, 2005;
Sullivan, 2005). It is clear that the prevalence of mathematical disabilities will vary depending on the criteria used to define those
disabilities (Dowker, 2004; Mazzocco & Myers, 2003).
Most practitioners and researchers currently report that the incidence of children and adults with mathematical disabilities is not
exceptional. Geary (2004) finds that between 5% and 8% of school-age children have some form of mathematical disabilities.
These figures are confirmed in different countries by several researchers: Badian (1983) finds a prevalence of 6.4% in an American
study. Kosc (1974) finds 6.4% in Bratislava and English studies report prevalence rates of 3.6% (Lewis et al., 1994). German
researchers find prevalence between 4.4% (Klauer, 1992) and 6.6% (Haüber, 1995; Hein, 1999), Israeli researchers report 6.5% of
children with mathematical disabilities in their country (Gross-Tsur et al., 1996) and von Aster and colleagues find 4.7% in Swiss
(von Aster et al. 1997). In Belgium we found a prevalence rate between 3 and 8% (Desoete, Roeyers & De Clercq, 2004). Despite
those similar findings in current research, the DSM-IV (APA, 2000) still estimates the prevalence of mathematical disabilities as 1%
of school-age children.
Recent research findings demonstrate that the prevalence rate for mathematical disabilities is as high as the prevalence of other
well-known and well-studied disorders such as reading disorders and ADHD (Shalev, Auerbach, Manor, & Gross-Tsur, 2000; WHO,
1992). Although the prevalence of mathematical disabilities is high, the research focus on the domain of this disorder still remains
limited (Desoete, Roeyers & De Clercq, 2004; Gersten & Chard, 1999; Ginsburg, 1997; Mazzocco & Myers, 2003, WHO, 1992).
Nowadays a slight advance in research interest is noticed (Butterworth, 1999).
The gender ratio for boys and girls in mathematical disabilities is another point of discussion. In contrast with the disproportion in
gender ratio found for learning disabilities in general (male-female 3:1; APA, 2000), research of the last decade finds an almost
similar prevalence in boys and girls (Haüber, 1995; Hein, 1999, Lewis et al., 1994), with boys doing slightly better (Gross-Tsur et al.,
1996 (1:1.1), Klauer, 1992, von Aster, 2000).
SUBTYPES
Mathematical problem solving involves several cognitive skills (Desoete & Roeyers, 2005). The wide range of skills involved in
doing mathematics implies a spectrum of potential disabilities, based on failure in one or more of these cognitive skills. Many
researchers have attempted to describe subtypes in learning disabilities (Fuchs & Fuchs, 2002; Geary, 2004).
Table 1: Subtypes in mathematical disabilities: description of terminology and distinguishing features (Desoete, 2002; Stock,
Desoete & Roeyers, 2006).
Subtype
Procedural deficits
Used terminology
 Anaritmetria
(Hécaen, Angelergues & Huillier,
1961)
Characteristic Features
-
 Operational dyscalculia
(Kosc, 1974)
 Spatial dyscalculia
(Badian, 1983)

Verbal developmental
dyscalculia
(von Aster, 2000)
-
Difficulties with procedures in (written) calculation
Difficulties in sequencing multiple steps in
complex procedures
Difficulties in planning or execution of complex
arithmetic operations
Difficulties in mental calculations
Difficulties in routines
Use of immature strategies
Many mistakes in execution of complex
procedures
Time-lag in arithmetic procedures
Poor understanding of concepts in procedures
 Procedural subtype
(Cornoldi & Lucangeli, 2004)
 Procedural subtype
Geary (2004)
Semantic memory deficits
 R-S profile
(Rourke, 1995)
 Verbal developmental dyscaculia
(von Aster, 2000)
-
Difficulties in retrieval of numerical facts
Disabled acquisition of number-fact knowledge
Difficulties in the semantic-acoustic aspect of the
linguistic domain
Lower accuracy in mental calculation
Slower speed of mental and written calculation

Disabilities in mental and
automatized calculation
(Cornoldi et al., 2002)
 Verbal dyscalculia
(Njiokiktjien, 2004)
-
 Visuospatial deficits
(Hécaen et al., 1961)
-
 Practognostic dyscalculia
(Kosc, 1974)
-
 Semantic memory deficits
(Geary, 2004)
Visuospatial deficits
-
 Spatial dyscalculia
(Badian, 1983)
 part of Numerical dyssymbolics
(Njiokiktjien, 2004)
 Nonverbal learning disorder
(Rourke, 1995)
 Visuospatial learning disability
(Lucangeli & Bellina, 2002)
 Arabic dyscalculia
(von Aster, 2000)
-
Irregular reaction times
Lower enumeration speed for figures, symbols,
numbers and quantities
High error rate
Wrong associations in retrieval
Difficulties in conceptual knowledge assignments
Difficulties in language comprehension
Difficulties with passive vocabulary
Difficulties with orally presented assignments
Difficulties in placing numbers on a number line
Disturbance in setting out objects in order
according to magnitude
Inversions and reversals in numbers
Misalignment and misplacements of digits
Problems in symbol recognition
Disturbance in visuospatial memory
Difficulties in understanding geometry
Misinterpretation of spatially represented
information
Nonverbal deficits
Problems with insight in and notions of space
Difficulties with abstraction
Disturbance in visual imaginative faculty
Disturbance in enumerating groups of objects
Disturbance in estimating and comparing
quantities
Difficulties in the temporal order or planning
Difficulties with novel and complex tasks
Visual neglect
Eventually dyspraxia
 Visuospatial subtype
(Geary, 2004)
Number knowledge deficits
 Aphasic acalculia
(Hécaen et al. 1961)

Verbal dyscalculia, Lexical
dyscalculia and Graphical
dyscalculia, Ideognostic
dyscalculia
(Kosc, 1974)
 Ideognostic dyscalculia
(Njiokiktjien, 2004)
 Difficulties in number knowledge
(Cornoldi et al., 2004)

Arabic dyscalculia, Pervasive
dyscalculia
(von Aster, 2000)
-
Difficulties in comprehension of Arabic notational
system, mathematical ideas and relations
Difficulties with abstract number comprehension
Disturbance in number knowledge
Disturbances in basic sense of numerosity
Disturbance of encoding the semantics of
numbers
Difficulties in transcoding between the different
modalities
Disturbance in number reading
Disturbance in number writing
Disturbance in number production
Difficulties in size comparison
Difficulties in number ordening
Difficulties in enumeration
Difficulties in number dictation
In Table 1 we give an overview of the different subtypes, the terminology used by different researchers and the distinguishing
features as described here. Profiles of the children we meet in practice are not that clear and constitute several features of different
subtypes described above.
In addition, Ginsburg (1997) points out that perhaps some children can outgrow some mathematics learning disabilities and grow
into others.
CO MORBIDITY IN MATHEMATICAL DISABILITIES
All students with dyscalculia fall substantially below on mathematics than that expected for their chronological age, measured
intelligence, and age-appropriate education. Although Shalev (2004) reports that mathematical disabilities in general appear as
isolated and specific learning disabilities, mathematical disabilities are also common in many other neurological or psychological
disabilities (Shalev et al., 2000). The prevalence of a general mathematics and reading disability varies from 17% (Gross-Tsur et al.,
1996) to 43% (Badian, 1983). The prevalence of combined mathematics and writing disabilities is about 50% (Ostad, 1998). In
addition, the gravity of the mathematical disability is found to be associated with the severity of disability, lower IQ, inattention and
writing problems (Shalev, Manor & Gross-Tsur, 2005). In 26% of the children with mathematical disabilities comorbid symptoms of
ADHD are found (Gross-Tsur et al., 1996) and over 20% of boys with ADHD have mathematical disabilities (Faraone, Biederman,
Lehman, Spencer et al., 1993; Manor et al., 2001; McGlaughlin, Knoop & Holliday, 2005).
Children with learning disabilities exhibit more social problems than children without those disabilities (Greenham, 1999; Shalev et
al, 2005). Meta-analysis of studies on peer information confirms rejection of 80 percent of children with learning disabilities by
peers. 70 percent of them are not seen as a friend (Kavale & Forness, 1996). Different researchers found children with learning
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disabilities to have a lower social status than children without learning disability (Kavale & Forness, 1996; Nabuzoka & Smith,
1993). In contrast to children without learning disabilities, those children with learning disabilities tend to be more shy (33,3% versus
7%), they need to seek help more often (36,1% versus 11,9%) and they are more likely to become a victim of bullying (33,3%
versus 7,7%). This in turn is associated with rejection by peers (Nabuzoka & Smith, 1993). Tsanasis, Fuerst and Rourke (1997)
found children with learning disabilities to be less socially competent than their peers. Kavale and Forness (1996) argued that in
general, almost 75 percent of children with learning disabilities can be differentiated from children without learning disabilities by
their social skills. However, many children with mathematical disabilities do not foster psychosocial problems (Rourke & Fuerst,
1991). Greenham (1999) found 40 to 70 percent to be accepted by their peers as children without learning disabilities. It is clear that
many research findings in this area contradict each other. This often is due to the use of different definitions and methodological
issues (Gadeyne, Ghesquière & Ongena, 2004).
Comorbidity between mathematical disabilities and behaviour problems also seems to be high. Schachter, Pless and Bruck (1991)
estimate that 43 percent of the children with mathematical disabilities have behaviour problems too. Shalev, Manor, Auerbach and
Gross-Tsur (1998) found that the prevalence of these behavioural and emotional problems was higher for children with persistent
mathematical disabilities. Psychosocial problems do not increase with age, but older children tend to have more behavioural
disorders and physical disorder complaints (Tsanasis et al., 1997). Children with mathematical disabilities tend to have more
internalised problems (Osman, 2000; Prior, Smart, Sanson & Oberklaid, 1999; Rourke & Fuerst, 1992; Shalev, Auerbach & GrossTsur, 1995; Tsatsanis et al., 1997). Between 24% and 52% of children with learning disabilities have clinical scores for social,
emotional or behavioural disabilities. Children with learning disabilities tend to have lower academic self esteem than their peers
who do not have learning disabilities, but these differences can not be found in other domains (Donceel & Ghesquière, 1998;
Greenham, 1999). Greenham (1999) also reports a higher risk for substance abuse in adolescents with learning disabilities in
comparison to their non disabled peers.
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ASSESSMENT OF MATHEMATICAL DISABILITIES
It is clear that the manifestation of mathematical disabilities is different in every child. In Table 1 we give an overview of the main
characteristics of the different subtypes in mathematical disabilities. In clinical practice however, these categories are not that
mutually exclusive at all. The phenotypes we mostly encounter are combinations of features from different subtypes. Taking this into
account makes the diagnostic process of course difficult.
Nowadays, a lot of diagnostic tools are designed to diagnose mathematical disabilities (see also Denburg & Tranel, 2003;
Mazzocco & Myers, 2003; Njiokikitjien, 2004; Shalev, 2004; Shalev & Gros-Tsur, 2001; von Aster, 2000). The majority of these tests
seek to assess the performance of specific arithmetical abilities. The variability reflected in Table 1 however provides support for not
relying on a fixed test battery. Practitioners have to consider the appropriateness of individual measures and their combination to
identify the problems of children with mathematical disabilities (Kamphaus, Petosky & Rowe, 2000; Mazzocco & Myers, 2003). We
need tests based on a validated model of the specific learning process we are assessing.
Not many such tests are recently available. For young children, an instrument that is validated by a combination of theoretical
models and therefore can be used for an in-depth diagnostic assessment seems to be the TEDI-MATH (Van Nieuwenhoven,
Grégoire & Noël, 2001). This multicomponent instrument is based on a combination of neuropsychological (developmental) models
of number processing and calculation. It has an age range form 4 to 8 years of age (kindergarten to 3rd grade) and has already
been translated into a German, Dutch and French version. It was standardized on a sample of 550 Dutch speaking Belgian children
from the beginning of the 2nd grade of the nursery school to the end of the 3rd grade of primary school. The test highlights five facets
of arithmetical and numerical knowledge: logical knowledge, counting, representation of numerosity, knowledge of the numerical
system and computation. Table 2 shows the subtests of the TEDI-MATH and some examples of test items.
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11
Table 2: Subtests and examples of test-items of the TEDI-MATH
Subtest
1.Knowledge of the number-word
sequence
Content and example of item
- Counting as far as possible
- Counting forward to an upper bound (e.g. “up to 9”)
- Counting forward from a lower bound (e.g. “from 7”)
- Counting forward from a lower bound to an upper bound (e.g. “from 4 up to 8”)
- Count backward
- Count by step (by 2 and by 10)
2.Counting sets of items
- Counting linear pattern of items
- Counting random pattern of items
- Counting a heterogeneous set of items
- Understanding of the cardinal
3. Knowledge of the numerical
system
3.1. Arab numerical system
- Judge if a written symbol is a number
- Which of two written numbers is the larger
3.2.Oral numerical system
- Judge if a word is a number
- Judge if a number word is syntactically correct
- Which of two numbers is the larger
3.3. Base-ten system
- Representation of numbers with sticks
- Representation of numbers with coins
- Recognition of hundreds, tens and units in written numbers
3.4. Transcoding
- Write in Arab code a dictated number
- Read a number written in Arab code
4. Logical operations on numbers
4.1. Seriation of numbers
Sort the cards form the one with fewer trees to the one with the most trees
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4.2. Classification of numbers
Make groups with the cards that go together
4.3.Conservation of numbers
e.g.: Do you have more counters than me? Do I have more counters than you? Or
do we have the same number of counters? Why?
4.4. Inclusion of numbers
e.g.: You put 6 counters in the envelope. Are there enough counters inside the
envelope if you want to take out 8 of them? Why?
4.5. Additive decomposition of numbers
e.g.: A shepherd had 6 sheep. He put 4 sheep in the first prairie, and 2 in the other
one. In what other way could he put his sheep in the two prairies?
5. Arithmetical operations
5.1. Presented on pictures
e.g.: There are 2 red balloons and 3 blue balloons. How many balloons are there in
all?
5.2. Presented in arithmetical format
- Addition (e.g.: “6+3”; “5+..=9”, “..+3=6”)
- Subtraction (e.g.: “9-5”, “9-…=1”, “…-2=3”)
- Multiplication (e.g.: “2x4” “10x2”)
5.3. Presented in verbal format
e.g. “Denis had 2 marbles. He won two others. How many marbles had Denis in
all?”
5.4. Understanding arithmetical operation properties (conditional knowledge)
e.g.: addition commutativity: “You know that 29+66=95. Would this information
help you to compute 66+29? Why?”
6. Estimation of the size
6.1. Comparison of dot sets (subitising)
6.2. Estimation of size
Comparison of distance between numbers. E.g.: target number is 5. What number
is closed to this (3 or 9)?
13
14
A validation study showed that the TEDI-MATH could discriminate among pupils with different levels of mathematical knowledge
according to the teachers. The raw scores of the TEDI-MATH are converted into percentiles. It is suggested that attention be paid to
scores under pc 25 and to consider possible disabilities under pc 10.
For older students no such instruments are currently available. The CDR was created from this purpose, based on a nine-skills
model . According to this nine-skills model, mathematical problem solving depends on adequate non-semantic number-naming or
reading (NR) skills where numbers are translated from one kind of presentation (e.g., the Arabic presentation ‘9’) to another kind of
representation (e.g., the verbal oral representation of the number word ‘nine’) (Collet, 2003; Fuson, Wearne, Hiebert, Murray,
Human, Olivier, Carpenter, & Fennema, 1997; McCloskey & Macaruso, 1995; Seron & Noel, 1995). Children need to know that
‘nine’ is not written as ‘6’ and that '47' is not read as 'seventy four'. The second problem solving skill has to do with the non-semantic
translation within the mathematics lexicon (e.g., Verschaffel, 1999). To solve mathematical problems, children have to deal with
operation symbols (S) (e.g., x, +, <, >) without making mistakes of a perceptual (e.g., x or +, - or =, < or >) or phonetic type (e.g.’
min’ or minus, ‘maal’ x or times).
Furthermore, mathematical problem solving depends on insight into the number structure or on the knowledge (K) of the position of
tens and units and the ability to establish base-ten structural relationships (Collet, 2003; Dehaene & Cohen, 1997; Fuson et al.,
1997;Veenman, 1998). K skills are semantic tasks, required to be able to know that 47 is composed by 4 tens and 7 units and that
15
47 is 1 more than 46 on the number line. In addition, mathematics depends on procedural (P) knowledge and skills to calculate and
to solve mathematical tasks in a number problem format (e.g., 47-9=_) (e.g., McCloskey & Macaruso, 1995; Noel, 2000; RittleJohnson, Siegler, & Alibali, 2001; Veenman, 1998). Children have to know how to subtract to solve 47-9 as 38 and not as 42. Those
P-skills seem to depend on a visual system used for multidigit operations, although to succeed in these calculations a child also has
to have access to stored subtractions and arithmetic facts (Dehaene, 1992).
Linguistic skills (L) are cognitive conceptual skills enabling children to understand and to solve one-sentence mathematical
problems in a word-problem format (e.g., 9 less than 47 is_) (McCloskey & Macaruso, 1995; Campbell, 1998; Rittle-Johnson,
Siegler, & Alibali, 2001; Rourke & Conway, 1997). L-skills can be situated within Dehaene’s auditory-verbal word frame, using
general language modules. Some children may have no problems with formula tasks (47-9=_), but seem to have problems
translating words (e.g., 'less') into calculation procedures (e.g., 'subtraction'). A mental representation (M) is required in most word
problems, since a simple 'translation' of keywords in a problem (e.g., ‘less’) into calculation procedures (e.g., ‘addition’), without
representation, leads to ‘blind calculation’ or ‘number crunching’(Geary, 1993; Montague, 1998). This superficial approach leads to
errors as answering '38 to tasks such as '47 is 9 less than _', ’29 is 9 more than _' and ‘76 is half of _’. Contextual skills (C) are
cognitive skills, also using general language modules, enabling the mathematical problem solving in a more than one-sentence
word-problem (see Table 1). Some children can have problems with this task due to problems with the limited capacity of the
working memory ( ‘cognitive overload’) and to an insufficient knowledge base (or ‘expertise’) in mathematics achievement
16
(Baddeley, 1999; Keeler & Swanson, 2001; Logie & Gilhooly, 1998; McCloskey & Macaruso, 1995; Schneider & Pressley, 1997;
Swanson, 1990; Sweller, 1994). In addition, some children fall behind in selecting relevant information (R) in order to create an
adequate mental representation of the problem (Feuerstein, Rand,& Hoffman, 1979, Greenberg, 1990). Those children can have
difficulties in ignoring the irrelevant number or information in an assignment. They believe all numbers have to be ‘used’ in order to
solve a mathematical problem. They answer ‘59’ (47+3+9) to the problem ‘Willy has 47 cards. Wanda has 3 books and 9 cards
more than Ann. How many books had Wanda?’Number sense skills (N) are the ninth cognitive skills enabling the solving of tasks
without giving the exact answer. Those skills depend rather on an semantic magnitude judgement (Cipolotti & Butterwoth, 1995).
Some children fail to estimate in advance in an approximate way the solution of a formula-task (e.g., 250-49=_ will be around 200)
(e.g., Dehaene, 1997; Edwards, 1984; Reys, 1984; Schoen, & Zweng, 1986; Sowder, 1992; Verschaffel, 1999). The Cognitive
Developmental skills in aRithmetics (CDR) for higher education is a 45-item test on the nine mathematics building blocks,
(NR,S,K,P,L,C,M,R,N) (see Table 3 and Appendix B).
Table 3
Cognitive building blocks for mathematical problem solving in higher education (Desoete & Roeyers, 2005).
Symbols
Numeral reading and production
e.g., Read (or write down) 1309,03
NR
17
Operation symbol reading and production
e.g, Put the correct sign ( <, > or = ) on …
4 x (12,7 – 0,9)
… 30 + 20
Number system knowledge
e.g. , Put in order, start with the smallest number:
8,52 95,02 85,2 9,25
Procedural calculation
e.g. , 30563,7 - 137,95 =
S
Language comprehension
e.g. , 283 more than -71 is _
L
Mental representation
e.g. , 1250,8 is 4 tens more than _
M
Context information
e.g., Lisse has a temperature of 36,4°C. After one hour the
temperature raised to 37,2°C.What is the raise?
Selecting relevant information
e.g., A bottle of camping gas has a weight of 6.750 kg. There can 2.7
kg gas in a bottle. Before you go on holiday the bottle weights 5 kg.
After the holiday the bottle weights 4.050 kg. How much gas was
there before the holiday in the bottle?
…
Number sense
e.g. , 18.15 is nearest to ?
Choose between :
6 am
15 hr
half past 3 in the morning 18.55
C
K
P
R
N
For grade 2 and 3 there is a computerversion (EPA 2000) (De Clercq, Desoete & Roeyers, 2000).
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However the majority of the tests for older students address the assessment the performance of specific arithmetical abilities. The
choice of the mathematics test(s) was found to be crucial. A cocktail assessment - or test on number facts and tests on number
system knowledge, procedural calculation and visuo spatial aspects of mathematics - are needed to prevent the chosen test for
determining the diagnosis. In Belgium for instance, practitioners often use the KRT-R and TTR. The Revised Kortrijk Arithmetic test
(Kortrijkse Rekentest Revision, KRT-R; Centrum voor Ambulante Revalidatie, 2005) is a 60-item Belgian mathematics test on
domain-specific knowledge and skills, resulting in a percentile on mental computation, number system knowledge and a total
percentile. The percentile and observations during mental computation is used to assess eventual procedural deficits. The
percentile and observations during number system knowledge is used to assess eventual number knowledge deficits. The
psychometric value of the KRT (with norms January and June) has been demonstrated on a sample of 3,246 children. Older
students are compared with the grade 6 (or 4) norms. A standardized total percentile based on national norms can be used.
Another diagnostic tool that is used a lot in Belgium is the Arithmetic Number Facts test (Tempo Test Rekenen, TTR; de Vos, 1992).
This is a test consisting of 200 arithmetic number fact problems (e.g., 5 x 9 =_). Children have to solve as many number-fact
problems as possible out of 200 in 5 minutes. The test has been standardized for Flanders on 10,059 children (Ghesquière &
Ruijssenaars, 1994). Older students are again compared with grade 6 norms. The percentile and observations are used to assess
eventual number fact or semantic memory deficits. At last a school test of grade 6 (Leerling Volgsysteem, meetkunde) on geometry,
19
interpretation of spatially represented information and insight in and notions of space is given to assess eventual visuo spatial
deficits.
However in clinical practice the tests can not be the only indicator of dyscalculia. Often checklists are used to get a picture of the
severity, the exclusion and the resistance criterion. In such checklists we check familial and medical conditions, and ask students
and parents when the problems started, what the difficulties where in mathematics, if there are family members with learning
disabilities, what was tried out when encountering the problems and if this has made some difference and so on (see checklist in
Appendix).
Currently, a study is ongoing with CDR, TTR and KRT-R and dyscalculium in higher education and in adults. This study is still
ongoing and will last at least for the next three years.
STICORDI-ADVICE
An assessment always aims to develop STICORDI-advice. This advice is designed to help students with dyscalculia. STICORDI
refers to STI(mulation), CO(mpensation), R(emediation) and DI(spensation). With such a device we can provide support for all
students, regardless of disability status. Students with dyscalculia work through this remediation device with specific mathematics
techniques (see also Levine, 1999) and they perform at a higher level than without this STICORDI device. We give a list of such
advice in Appendix C. It is obvious that not all of this advice is needed for children with dyscalculia. We have to adapt the device to
the strengths and weaknesses of each individual.
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27
Appendix A
Checklist for dyscalculia
Checklist dyscalculia – relevant items
Date:
Name:
Date of birth:
PART 1
REASON FOR THE ASSESSMENT
Name of the school:
What kind of education are you following?
When did you start?
What are your previous schools?
Kindergarten
Elementary school
Did you repeat a year in school?
What kind of secondary education did you follow?
What were your grades in secondary education?
28
Overall academic achievement; general grade
Grade obtained for mathematics
Grade obtained for language
General
Yes
1. Are there problems at school, according to you
Learning problems

Behavioral problems
Inattention

Other

2. What did you do about these problems?
Nothing
Extra lessons
Extra exercises
Assessment by …
Other: …
No





Remarks







Yes
3. do you go to school on a regular basis
If not, why not:
Yes
No

Remarks

No
Remarks
No
Remarks
4. How would you describe your working habit
Motivated

Attentive

Yes
5. How would you describe your working fluency
Slow

Irregular

Depending on what has to be studied 
29
Yes No
6.How would you describe your relationship with other students
Nothing special to mention

Afraid

Being teased often

Remarks
Yes No
7.How would you describe your relationship with your teachers
Nothing special to mention

Introvert

Squared to fail

Remarks
Yes
8 Are there problems at home
Please add some information, if you answer yes:
No

Remarks
Yes
No
9. How would you describe your mood
Nothing special to mention
Irregular
Depressed
Remarks



10. Do you have problems with hearing/vision Yes 
Yes
11 Are you on medication?
Add some information, if yes:
In which area do you have problems:

Yes
No 
No

Remarks

No
30
1. Are there problems with reading comprehension
2. Do you have problems with reading fluency 
3. Do you have problems with written language
4. Do you have problems with language
5. Do you have problems applying rules





How do you do in mathematics/economics/statistics
Good
Speed

Insight

Techniques

Automatisaton




Normal




Bad




Other remarks:
Other questions
Why do you think you are being tested by us? What is the problem according to you?
Do you agree with these problems?
What is the biggest problem according to you? What do you worry most about?
What do you currently do about these problems?
31
What do you think about this approach?
What do your parents/ friends/school do about the problems?
What do you think about this approach?
Can you do something yourself about the problems?
What are you satisfied about: what does go well for you, what are you good at, what do you like about your family/friends/school…
Yourself:
Your school/teachers:
Your parents:
What do you expect from this test?
Please give your opinion on the following skills
Good
Remembering arbitrary facts
(f.ex. < sign)

Time tables

Division facts

Writing and/of copying number of figures

Naming mathematical concepts, terms or operations
Decoding context into mathematical symbols 
Interpretation and use of symbols and signs

Remembering formula in measurement

Estimate approximate answers to problems

Remembering arbitrary data in history

Following a working direction

Writing numbers without reversions

Diagrams,maps,tables,charts,abbreviations, arrows 
Normal













32
Bad













Understanding terminology(product, acute, vulgar..)
Placing numbers on a number line

Reading the clock

Measurement

Use of a calendar

Knowing what exercises will be correct

Knowing if an exercise is correct

Working in an efficient way

Being able to predict ones result

Knowing when to start to be ready in time

Knowing how to handle a task

Adapting the working speed to the task

Remembering terminology and symbolisms

Knowing how to study

Knowing ones own strenghts and weaknesses 
Being sure of oneself

Enjoyment and pleasure in arithmetic

Feeling good in the group

Having friends

Not panicking if something goes wrong









































PART 2
ACTUAL SITUATION IN HIGHER EDUCATION
Why did you choose this course, college, university?
Do you like this kind of education?
What do you do after college hours? What are your hobbies or interests? What do you like most?
Do you have problems with studying at home?
What courses are you good?
33
Do you have problems concentrating on tasks?
Are you motivated for your tasks?
Are you unsure about your tasks? Do you often think ‘here I will fail’? Do you give up if work gets hard?
Here you find problems students can encouter. Look what fits you and give some examples.
PROBLEMS
Getting in fights, being angry,
oppositional behaviour
Introvert, quiet, sad, afraid, defeatist
attitude
Hyperactive, restless, impulsive
Problems with peers, family and friends
Problems with adults, teachers and
parents
Other problems
EXAMPLES
Do you have ideas about your problems with mathematics. What caused them, according to you?
-It is because I
-High school/university …
-My parents
What should change: what solutions are there for your problem, according to you?
-I can
-High school/university … can
-My parents can
Social contact
Yes
No
Remarks
34
1. Do you have good contact with your mother 

2. Do you have good contact with your father?


3. Do you have good contact with brothers/sisters? 

4. Do you have regular friends?


5. Do you have good contact with teachers?


If no, what are the problems?
On who can you rely: with who can you talk and who can help you? (think about: teachers, mentor, grand parents, uncle/ant, a
previous partner of your parents, family, friends, neighbours)
Do you have problems with eating/sleeping?
Do you drink alcohol?
Do you use drugs?
Yes


No



Remarks

Other information that you find relevant:
PART 3
INFORMATION ON THE PAST
What are the nice memories on the past?
What were some less nice events in you life?
Are there problems at school or at home?
When did they start, according to you?
Are there other things about the past, that we should know about?
35
Appendix B
CDR
Complete the following details
First name
Surname
Course/Subject
School/Department
Organization/Institution
Make these exercises without calculator. You get 40 minutes. Success!
Write the numbers on the ….
…………….
………eggs
……books.
NR1
NR2
NR3
LXVII
1 set of eggs
4 pare of books
NR4
NR5
Write in words on the ….
1309,03
.......................
date of birth 12.08.1958
.......................
Put the correct sign ( <, > or = ) on the….
S1
610 m
…
61000 mm
36
S2
S3
S4
S5
14.25 hour
900 ml
4 x (12,7 – 0,9)
906
1000
…
…
…
…
5 before half past 2 in the afternoon
9l
30 + 20
9,06
Put in order, start with the smallest number
K1
K2
K3
K4
K5
P1
P2
P3
P4
P5
L1
L2
L3
L4
L5
M1
M2
2
5
0,5
0,2
5
2
8,52 95,02 85,2 9,25
56700
1230,7
432,17
Put the correct number on the
56800
56900
…
1230,8
1230,9
…
432,18
432,19
…
1263 + 861 + 73 + 445 =
30563,7 - 137,95 =
7,25 x 11 =
27681 : 90 =
72 : 9 =
10
Solve the exercise
………..
………..
………..
……….
……….
283 more than -71 is
One-half of 3/5 is
…
is 3 hundreds less than 4125,15
The biggest mean divisor of 27, 6 and 12 is
One-half of 140 has as double
1250,8 is 4 tens more than
2458,26 is 3 hundreds more than
37
…
…
…
…
…
…
M3
M4
M5
…
270,6 is six times
Four times 180 is one-half of
370,5 is 0,9 less than
…
…
C1 Lisse has a temperature of 36,4°C. After one hour the temperature raised to 37,2°C.
What is the raise?
…
R1 A bottle of camping gas has a weight of 6.750 kg. There can 2.7 kg gas in a bottle. Before
You go on holiday the bottle weights 5 kg. After the holiday the bottle weights 4.050 kg.
How much gas was there before the holiday in the bottle?
…
C2 Wim has 4.8 kilograms of sugar. Jan has twice so may sugar. How much sugar has Jan and Wim together?
…
C3 A piece of paper is 10 centimeters long and 5 centimeters broad. What is the surface of this paper?
…
R2 Passport photo’s are ready in 300 seconds. Ordinary photo’s need 45 minutes to develop.
You come in on 17:45 to make some passport photo’s. When will they be ready? …
R3 For a concert there are 2542 tickets available. There are 20 groups on this concert.
The past week 769 tickets were sold. How many tickets are left?
…
C4 From town A to town B there are 9 routes. You can drive in 36 ways from town A to town C
In how many ways can you drive from town B to town C?
…
C5 A book costs 3.60 euro. Now you can buy this book for 2.52 euro.
How much reduction (in %) did you get?
38
….
R4 Farmer Teun has on Monday 426 chickens and 318 rabbits. On Tuesday he sells half of the chickens and
one third of the rabbits. How many chickens does farmer Teun has left?
…
R5 Every bike has two wheels and 6 lights. In the shop there are 20 bikes How many wheels do these bikes have?
…
What is nearly the same?
N1
Choose between:
2500+3500
N2
Choose between:
1000-500
2498 + 3495?
2400+3500
2500+3400
2400+3400
1003,14 - 598,23 ?
10031-6002
100014-59823
1000-600
One pare of shoes costs normally 60 euro. You can get the shoes on –25%.
You buy two pare of shoes. You have to pay with?
Choose between :
100 euro
50 euro
3 x 20 euro
6 x 20 euro
N3
N4
Choose between :
6 pm
15:00
18:15 is nearest to ?
half past 3 in the morning
18:55
N5 All elementary school children go on a trip to lego-land. One bus can take 50 children.
There are 22 children in one group. There are 12 groups. How many busses are needed to
drive to lego-land?
Choose between : 5
6
10
12
Give your self points on 45
……../45
39
Appendix C
STICORDI devices
In general
 The support is always tailored to the individual needs of a particular student and their strengths and weaknesses. The strengths
are used to compensate for the deficiencies.
 College and university always asks if students are in need of additional mathematical support.
 All new teachers are informed of the ‘reasonable adjustments’ to ensure that disabled students are not placed at a substantial
disadvantage compared to non-disabled students.
 The reasonable adjustments also depend on the initiative of the student, who writes a (on tasks, exams, …) the abbreviation CH
(from charter) on the left upper corner of each paper he or she uses. If this sign is not on the paper, no special support is provided.
Instructions for teaching
 Implement multiple, flexible methods of content presentation, content expression and individual engagement in material. Utilize
visual, auditory and kinesthetic methods of learning. Instructional techniques should incorporate a verbal approach of explaining
concepts in addition to a algebraic notation and graphical plots. Visual models accompany written explanations.
 Always start with repeating the essence of the previous course.
40
 Check that the students understand the concepts you want to use. Instruction should include concepts as well as when and how
to apply them. Instruction should also include ways to translate specific words into numerical symbols or processes, to support a
student’s mastery of word problems.
 Students need more intensive, explicit teaching and practice of the number system, the use of maps and atlases, the use of
measuring devices, using a wide range of names for measuring units, the relationship between decimals and fractions. Use colour
coded concept diagrams and formula to support the insight of students.
 Students need support and explicit instruction and more time on skills and content (f.ex. arithmetic facts and concepts) that are
automatised in peers without dyscalculia. Students with dyscalculia have prolonged difficulty with learning and retaining number
facts.
 Teach in gradual stages so that students do not feel overwhelmed
 Explicitly teach short cuts and a small number of derived facts. Underpin rote learning with understanding. Avoid mechanical
recitation of the short cuts and derived facts. Avoid too many derived facts in students with memory deficits.
 Explicitly teach the method of working.
 Students should be provided by timely and good structured handouts in a dyscalculia friendly format. Students should get
textbooks, structured charts and information sheets, so that they do not only have to rely on what they copied during the lectures.
 Students can use recording devices or lap tops within lectures
 Utilize flashcards to develop automaticity for basic arithmetic and more advanced algebraic concepts, calculations, and
manipulations
 Provide the technology needed for problem solving. Use calculator and computer spreadsheets to compensate for difficulties in
recalling number facts.
41
 Students should develop an individualized mathematics glossary of terms, concepts; information (number facts, working methods,
mnemonics etc.) and formulae so they can be reminded of these definitions as they complete homework assignments. In some
cases this booklet can be used in exams.
 Specify mastery criteria for each skills on students’ conceptual and cognitive level.
 Provide one-to-one or group support to students with dyscalculia and/or dyslexia
Instructions for assessment
 Students need more practice and an extended period of time to acquire the basics. Therefore assessments are planned a lot in
advance.
 Support the student in the planning of when he or she is going to study for exams. Make this planning together in a one-to-one
support session with student and tutor. Time can also be spent on examination techniques and the best use of the 20 to 30% extra
time that has been awarded.
 Students get extended time to complete examinations (20 to 30% additional time for timed assessments and examinations –
starting earlier than peers without dyscalculia)
 The formulae booklet and calculator are available in examinations.
 Students get assistance in highlighting key words in examination tasks and in deciding which questions they will answer.
 Use an adequate font, double-space and off-white paper for text in examination papers and printed handouts
 The provision of squared paper in examination papers can assist in the lining up of rows and columns of numbers.
 Examination can be sat in a special room, without disturbance of other students
 No big numbers, fractions or decimals are used in tests, if not really necessary.
 Students should never have to come unexpectedly to the blackboard, answer a question or make a test.
42
 Students do not need to rely on mental computation; they can always use a calculator.
 Students may perform one task or subtask at a time and develop definite and consistent stepwise approaches to problem solving
 Students may use self-monitoring techniques (talking their way through a problem) to aid in problem solution
 Students may use stepwise approaches to problem solving
 Students may use graph/squared paper to aid in the spatial placement of numbers
 Students may use multi-sensory equipment or concrete applications of the maths concept as an example of the problem to be
solved
 In informal assessment an analysis of error pattern and a diagnostic interview in which students verbalize their thought processes
while they solve problems is added
 Alternative assessment methods can be used to replace multiple choice examinations, class tests, coursework, group project
work or written examinations during the school years. For some students it is advised to let them explain their answers orally.
43