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).

DEFINITIONAlthough 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.

PREVALENCEThe 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).

SUBTYPESMathematical 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 Used terminology Characteristic Features

Procedural deficits Anaritmetria (Hécaen, Angelergues & Huillier, 1961)

Operational dyscalculia (Kosc, 1974)

Spatial dyscalculia(Badian, 1983)

Verbal developmental dyscalculia

(von Aster, 2000)

Procedural subtype(Cornoldi & Lucangeli, 2004)

Procedural subtypeGeary (2004)

- 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

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)

Semantic memory deficits(Geary, 2004)

Verbal dyscalculia (Njiokiktjien, 2004)

- 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

Visuospatial deficits Visuospatial deficits (Hécaen et al., 1961)

Practognostic dyscalculia (Kosc, 1974)

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)

- 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 & Gross-

Tsur, 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 3 rd 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 3 rd 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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Table 2: Subtests and examples of test-items of the TEDI-MATH

Subtest Content and example of item1.Knowledge of the number-word sequence

- 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 numbersSort the cards form the one with fewer trees to the one with the most trees

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4.2. Classification of numbersMake groups with the cards that go together

4.3.Conservation of numberse.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 numberse.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 numberse.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 picturese.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 formate.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)?

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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

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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; Rittle-

Johnson, 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

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(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).

SymbolsNumeral reading and production e.g., Read (or write down) 1309,03

NR

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Operation symbol reading and production e.g, Put the correct sign ( <, > or = ) on …4 x (12,7 – 0,9) … 30 + 20

S

Number system knowledge e.g. , Put in order, start with the smallest number: 8,52 95,02 85,2 9,25

K

Procedural calculation e.g. , 30563,7 - 137,95 =

P

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?

C

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? …

R

Number sense e.g. , 18.15 is nearest to ? Choose between : 6 am 15 hr half past 3 in the morning 18.55

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,

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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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REFERENCES

American Psychiatric Association (2000). Diagnostic and statistical manual of mental disorders. Fourth edition, Text Revision. Washington, DC: Author.

Anderson, M. (1992). Intelligence and Development. A cognitive theory. Oxford: Blackwell.Baddeley, A. (1999). Working memory. Oxford: Clarendon Press.Badian, N. A. (1983). Aritmetic and nonverbal learning. In Myklebust, H. R. (Ed). Progress in learning disabilities, vol 5 (pp 235-

264). New York: Grune and Stratton. Butterworth, B. (1999). What counts: How every brain is hardwired for math. New york: The Free Press.Butterworth, B. (2003). Dyscalculia screener. London: NFER Nelson Publishing Company Ltd.Centrum voor Ambulante Revalidatie (2005). Kortrijkse Rekentest-R (KRT-R) [Revised Kortrijk Arithmetic test]. Kortrijk:

Revalidatiecentrum Overleie.Campbell, J.I.D (1998). Linguistic influences in cognitive arithmetic: comment on Noel, Fias and Brysbaert (1997). Cognition, 67,

353-364.Campbell, J.I.D. (1994). Architectures for numerical cognition. Cognition, 53, 1-44.Cipolotti, L. (1995). Multiple routes for reading words, why not numbers? Evidence from a case of Arabic numeral dyslexia.

Cognitive Neuropsychology, 12, 313-362.Cipolotti, L. & Butterworth, B. (1995). Toward a multiroute model of number processing: Impaired number transcoding with

preserved calculation skills. Journal of Experimental Psychology: General, 124, 375-390.Collet, M. (2003). Diagnostic Assessment of the understanding of the base-ten-system. Paper presented at the Symposium ‘Current

Issues in Assement of Learning Disabilities’ of the congress van de European Federation of Psychologists Associations (EFPA). Vienna: 10th of July 2003.

Connolly, A. J. (1988). Key Math-Revised: A diagnostic inventory of essentials mathematics. Circle Pines, MI: American Guidance Service.

Cornoldi, C. and Lucangeli, D. (2004). Aritmetic education and learning disabilities in Italy. Journal of learning disabilities, 37, 42-49. Cornoldi, C., Lucangeli, D. and Bellina, M. (2002). AC-MT Test: Test per la valutazione delle difficoltà di calculo [The AC-MT

arithmetic achievement test]. Trento, Italy: Erickson. Cornoldi, C., Venneri, A., Marconato, F., Molin, A., and Montinaro, C. (2003). A rapid screening measure for the identification of

visuospatial learning disability in schools. Journal of learning disabilities, 36, 299-306.De Clercq, A., Desoete, A., & Roeyers, H. (2000). EPA2000 : A multilingual, programmable

computer assessment of off-line metacognition in children with mathematical learning disabilities. Behavior Research Methods, Instruments, & Computers,32, 304-311.

Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1-42.

20

Dehaene, S. (1997). The Number Sense. Pinguin books Ltd.Dehaene, S., & Cohen, L. (1997). Cerebral pathways for calculation: double dissociation between rote verbal and quantitative

knowledge of arithmetic. Cortex, 33, 219-250.Deloche, G., & Seron, X. (1987). Numerical transcoding: a general production model. In G. Deloche & X. Seron (Eds.),

Mathematical Disabilities: A Cognitive Neuropsychological Perspective (pp. 137-170). Hillsdale, NJ: Erlbaum.Desoete, A. (2002). Dyscalculie : stand van zaken. Tijdschrift voor Logopedie & Audiologie,32 (2), 57-74Desoete, A., & Roeyers, H. (2006). Metacognitive macroevaluations in mathematical problemsolving.

Learning and Instruction, 16, 12-25Desoete, A., & Roeyers, H. (2005). Cognitive building blocks in mathematical problem solving in

grade 3.British Journal of Educational Pychology, 75, 119-138. Desoete, A., Roeyers, H., Buysse, A., & De Clercq, A. (2002). Dynamic assessment of

metacognitive skills in young children with mathematics learning disabilities. In D. Van der Aalsvoort, W.C.M. Resing & A.J.J.M. Ruijssenaars (Eds.), Learning Potential Assessment and Cognitive Training (pp 307-333). JAI Press Inc/Elsevier Science Ltd.: England .

Desoete, A., Roeyers, H. & De Clercq, A. (2004). Children with mathematics learning disabilities in Belgium. Journal of learning disabilities, 37, 50-61.

Desoete, A., Roeyers, H.,& De Clercq, A. (2002). Assessment of off-line metacognitive skills in young children with mathematics learning disabilities. FOCUS. On Learning problems in mathematics, 24 (2) ,53-69

De Vos, T. (1992). Tempo Test Rekenen. Handleiding [Arithmetic Number Facts test. Manual]. Berkhout: Nijmegen.Donceel, J. and Ghesquière, P. (1998). De impact van leerstoornissen op de opvoeding in het

gezin. [Impact of learning disabilities on family education] In Ghesquière, P. and Ruijsenaars, A.J.J.M (Red.). Ernstige leer- en gedragsproblemen op school: Bijdragen uit onderzoek en praktijk [Severe learning and behavoiral disabilities in school: contibutions from research and practice] (pp. 151-166). Leuven / Amersfoort: Acco.

Dowker, A. (2004). What works for children with mathematical difficulties. Research Report No 554.University of Oxford: UK. Edwards, A. (1984). Computational estimation for numeracy. Educational Studies in Mathematics, 15, 59-73Faraone, S. V., Biederman, J., Lehman, B. K., Keenan, K., Norman, D., Seidman, L. J., Kolodny, R., Kraus, I., Perrin, J. and Chen,

W. J. (1993). Evidence for the independent familial transmission of attention deficit hyperactivity disorder and learning disabilities: results from a family genetic study. American Journal of Psychiatry, 150, 891-895

Feuerstein, R., Rand, Y,& Hoffman, M.B. (1979) . The Dynamic Assessment of Retarded Performers : The Learning Potential Assessment Device. Theory, Instruments, and Techniques. University Press: Baltimore.

21

Fuchs, L. S. and Fuchs, D. (2002). Mathematical problem-solving profiles of students with mathematics disabilities with and without comorbid reading disabilities. Journal of learning disabilities, 35, 563-57

Fuson, K.C., Richards, J.,& Briars, D.J. (1982). The acquisition and elaboration of the number word sequence. In C.J. Brainerd (Ed.), Children’s logical and mathematical cognition: Progress in cognitive development research (pp. 33-92). New York: Springler-Verlag.

Fuson, K.C., Wearne, D., Hiebert, J., Murray, H.G., Human, P.G., Olivier, A.I., Carpenter, T.P.,& Fennema, E. (1997). Children’s conceptual structures for multidigit numbers and methods of multidigit addition and subtraction. Journal of research in Mathematics Education, 28, 130-162.

Gadeyne, E., Ghesquière, P. and Onghena, P. (2004). Psychosocial functioning of young children with learning problems. Journal of Child Psychology and Psychiatry, 45, 510-521.

Gallistel, C.R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44, 43-74.Geary, D. C. (2004). Mathematics and learning disabilities. Journal of learning disabilities, 37, 4-15. Gersten, R. and Chard, D. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical disabilities.

Journal of Special Education, 33, 18-28.Ghesquière, P. and Ruijssenaars, A. (1994). Vlaamse normen voor studietoetsen Rekenen en technisch lezen lager onderwijs

[Flemish standards for study evaluatin or mathematics and technical reading in primary school]. Leuven: KUL-CSBO.Ginsburg, H. P. (1997). Mathematics learning disabilities: a view from developmental psychology. Journal of learning disabilities, 30,

20-33.Greenham, S. (1999). Learning disabilities and psychosocial adjustment: a critical review. Child neuropsychology, 5, 171-196. Gross-Tsur, V., Manor, O. and Shalev, R. S. (1996). Developmental dyscalculia: prevalence and demographic features.

Developmental Medicine and Child Neurology, 38, 25-33.Gross-Tsur, V., Shalev, R. S., Manor, O., Amir, N. (1995). Developmental right hemisphere syndrome: clinical spectrum of the

nonverbal learning disability. Journal of Learning Disabilities, 28, 80-86.Haüber, O. (1995). Untersuchungen zur Häufigkeit von isolierten und kombinierten Rechenströrungen in einer repräsentativen

Stichprobe von Schülern 3. Klassen. Disertation thesis submitted to the Charité Medical School, Humboldt-University, Berlin.Hécaen, H. (1962). Clinical symptomatology in right and left hemispheric lesions. In Mountcastle, V. B. (Ed .), Inerhemispheric

relatins and cerebral dominance (pp. 215-243). Baltimore: Johns Hopkins.Hécaen, H., Angelergues, R. and Houillier, S. (1961). Les variétés cliniques des acalculies au cours des lésions rétrorolandiques :

Apprroche statistique du problème [The clinical varieties of the acalculies in retrorolandic lesions : A statistical approach to the problem]. Revue Neurologique, 105, 85-103.

Hegarty, M., & Kozhevnikov, M. (1999). Types of visual-spatial representations and mathematical problem solving. Journal of Educational Psychology, 91, 684-689.

22

Hein, J. (1999). The specific disorder of arithmetical skills. Disertation thesis submitted to the Charité Medical School, Humboldt-University, Berlin.

Kamphaus, R. W., Petosky, M. D. and Rowe, E. W. (2000). Current trends in psychological testing of children. Professional Psychology: Research and Practice, 31, 155-164.)

Kavale, K. A. and Forness, S. R. (2000). What definitions of learning disability say and don’t say. A critical analysis. Journal of learning disabilities, 33, 239-256.

Keeler, M.L., & Swanson, H.L. (2001). Does strategy knowledge influence working memory in children with mathematical disabilities ? Journal of Learning Disabilities, 34, 418-434.

Klauer, K. J. (1992). In Mathematik mehr leistungsschwache Madchen, im Lesen und Rechschreiben mehr leistungsschwache Junden? Zeitschift fur Entwicklungspsychologie und Padagogische Psychologie, 26, 48-65.

Kosc, L. (1974). Developmental dyscalculia. Journal of Learning Disabilities, 7, 46-59.Kort, W., Schittekatte, M., Compaan, E. L., Bosmans, M., Bleichrodt, N., Vermeir, G., Resing, W. & Verhaeghe, P. (2002).

Handleiding WISC-IIINL [Manual of the WISC-IIINL]. The Psychological Corporation. NIP Dienstencentrum: Londen, Amsterdam. Levine, M.D. (1999). Developmental variation and learning disorders. Cambridge, MA: Educators Publishing Service.Lewis, C., Hitch, G. J., Walker, P. (1994). The prevalence of specific arithmetic difficulties and specific reading difficulties in 9- to 10-

year old boys and girls. Journal of Child Psychology and Psychiatry, 35, 283-292. Light, G. J. & DeFries, J. C. (1995). Comorbidity for reading and mathematics disabilities: Genetic and environmental etiologies.

Journal of Learning Disabilities, 28, 96-106.Logie, R.H., & Gilhooly, K. (1998). Working memory and thinking. Current issues in thinking and reasoning. Hour: Psychology

Press.Manor, O., Shalev, R. S., Joseph, A. & Gross-Tsur, V. (2000). Arithmetic skills in kindergarten children with developmental

language disorders. European Journal of Paediatric Neurology, 5, 71-77.Mazzocco, M. M. M. (2001). Math learning disability and math LD subtypes: Evidence from studies of Turner syndrome, Fragile X

syndrome and Neurofibromatosis type 1. Journal of learning disabilities, 34, 520-533.McCloskey, M. (1992). Cognitive mechanisms in numerical processing: evidence from acquired dyscalculia. Cognition, 44, 107-157.McCloskey, M., & Macaruso, P. (1995). Representing and using numerical information. American Psychologist, 50, 351-363.McGlaughlin, S.M., Knoop, A.J., & Holliday, G.A. (2205). Differentiating students with mathematics difficulty in college: mathematics

disabilities vs. no diagnosis, Learning Disability Quarterly, 28, 223-232.Montague, M. (1998). Research on Metacognition in Special Education. In T.E. Scruggs & M.A. Mastropieri (Eds.), Advances in

learning and behavioural disabilities (pp.151-183). Greenwich: JAI Press Inc.Nabuzoka, D. and Smith, P. (1993). Sociometric status and social behavior of children with and without learning difficulties. Journal

of Child Psychology and Psychiatry and Allied Disciplines, 34, 1435-1448.

23

Njiokiktjien, C. (2004). Gedragsneurologie van het kind [Behavior Neurlogy of the child]. Amsterdam: Suyi Publications.Osman, B. B. (2000). Learning disabilities and the risk of psychiatric disorders in children and adolescents. In Greenhill, L. L. (Ed.),

Learning disabilities. Implications for psychiatric treatment. Washington, D.C: American Psychiatric Press, Inc.Ostad, S. A. (1998). Developmental differences in solving simple arithmetic word problems and simple number-fact problems: A

comparison of mathematically normal and mathematically disabled children. Mathematical Cognition, 4, 1-19.Prior, M., Smart, D., Sanson, A. and Oberklaid, F. (1999). Relationships between learning difficulties and psychological problems in

preadolescent children from a longitudinal sample. Journal of the American Academy of Child and Adolescent Psychiatry, 38, 429-436.

Reynolds, C. R. (1984). Critical measurement issues in learning disabilities. Journal of Special Education, 18, 451-476.Reys, R.E. (1984). Mental computation an Focussing on Mathematical Disabilities: A Search for Definition, Classification and Assessment d estimation: past, present and future.

Elementary School Journal, 84, 547-557Rittle-Johnson, B., Siegler, R.S., & Alibali, M.W. (2001). Developing conceptual understanding and procedural skill in mathematics:

An iterative process. Journal of Educational Psychology, 93, 346-362.Rourke, B. P. (1989). Nonverbal learning disabilities: The syndrome and the model. New York: Guilford Press.Rourke, B. P. (1993). Arithmetic disabilities, specific or otherwise: A neuropsychological perspective. Journal of learning disabilities,

26, 214-226. Rourke, B. P. (Ed.). (1995). Syndrome of nonverbal learning disabilities: Neurodevelopmental manifestations. New York: Guilford

Press.Rourke, B. P. and Conway, J. A. (1997). Disabilities of arithmetic and mathematical reasoning: perspectives from neurology and

neuropsychology. Journal of learning disabilities, 30, 34-46.Rourke, B. P. and Finlayson, M. A. (1978). Neuropsychological significance of variations in patterns of academic performance :

Verbal and visuo-spatial abilities. Journal of Abnomral Child Psychology, 6, 121-133. Rourke, B. P. and Fuerst, D. R. (1991). Learning disabilities and psychosocial functioning. A neuropsychological perspective. New

York: The Guilford Press.Rourke, B. and Fuerst, D. (1992). Psychosocial dimensions of learning disabilities subtypes: neuropsychological studies in the

Windsor Laboratory. School Psychology Review, 21, 361- 374.Rourke, B. P. and Fuerst, D. R. (1995). Cognitive processing, academic achievement, and psychosocial functioning: A

neuropsychological perspective. In. Cichetti, D. and Cohen, D. (Eds.), Manual of developmental psychopathology (Vol. 1, pp. 391-423). New York: Wiley.

Schachter, D., Pless, I. and Bruck, M. (1991). The prevalence and correlates of behavior problems in learning disabled children. Canadian Journal of Psychiatry – Revue Canadienne de Psychiatrie, 36, 323-331.

24

Schneider, W., & Pressley, M. (1997). Memory development between two and twenty (2nd ed.). Mahwah, NJ: Erlbaum.Schoen, H.L., & Zweng, M.L. (1986). Estimation and Mental Computation.Reston, VA:

NCTM.Semrund-Clikeman, M., Biederman, J., Sprich-Buckminster, S., Krifcher Lehman, B., Faraone, S. S. and Norman, D. (1992).

Comorbidity between ADDH and learning disability: a review and report in a clinically referred sample. Journal of American Academy of Child and Adolescent Psychiatry, 31, 439-448.

Seron, X., & Noel, M.P. (1995). Transcoding numbers from the Arabic code to the verbal one or vice versa: How many routes? Mathematical Cognition, 1, 215-243.

Shalev, R. (1998). Developmental dyscalculia. In: Perat, M. J. (Ed.). New Developments in Child Neurology (pp. 635-641). Bologna: Monduzii Editore.

Shalev, R. S. (2004). Developmental dyscalculia. Journal of Child Neurology, 19, 765-771.Shalev, R. S., auerbach, J. and Gross-Tsur, V. (1995). Developmental dyscalculia, behavioural and attentional aspects: A research

note. Journal of Child Psychology and Psychiatry, 36, 1261-1268.Shalev, R. S., Auerbach, J., Manor, O. and Gross-Tsur, V. (2000). Developmental dyscalculia: prevalence and prognosis. European

Child and Adolescent Psychiatry, 9, II59-II64.Shalev, R. S. and Gross-Tsur, V. (1993). Developmental dyscalculia and medical assessment. Journal of Learning Disabilities, 26,

134-137.Shalev, R. S. and Gross-Tsur, V. (2001). Developmental Dyscalculia. Pediatric Neurology, 24, 337-342.Shalev, R. S., Manor, O., Auerbach, J., Gross-Tsur, V. (1998). Persistence of developmental dyscaculia: What counts? Results

from a three year prospective follow-up study. Journal of Pediatrics, 133, 358-362.Shalev, R. S., Manor, O. and Gross-Tsur, V. (1997). Neuropsychological aspects of developmental dyscalculia. Mathematical

Cognition, 3, 105-120.Shalev, R., Manor, O., and Gros-Tsur, V. (2005). Developmental dyscalculia: a prospectieve six-year follow-up. Developmental

Medicine and Child Neurologie, 47, 121-125.Siegel, L. S. (1989). IQ is irrelevant to the definition of learning disabilities. Journal of Learning Disabilities, 22, 469-478.Stock, P., Desoete, A., & Roeyers, H. (2006). Focussing on Mathematical Disabilities: A Search for Definition, Classification and

Assessment. Soren V. Randall (Ed.). Learning Disabilities New Research. Nova Science Publishers.Sowder, J. (1992). Estimation and number sense. In D.A. Grouws ( Ed.), Handbook of Research on Arithmetics Teaching and

Learning. A Project of the National Council of Teachers of Arithmetics (pp. 371-387). New York: Simon & Schuster Macmillan.Sullivan, M.M. (2005). Teaching mathematics to college students with mathematics-related learning disabilities: report from the

classroom. Learning Disability Quarterly,28, 205-220.Swanson, H.L. (2000). Issues facing the field of learning disabilities. Learning Disability Quarterly, 23, 37-49.

25

Sweller, J. (1994). Cognitive Load Theory, learning difficulty and instructinal design. Learning and Instruction, 4, 295-312.Tsanasis, K., Fuerst, D. & Rourke, B. (1997). Psychosocial Dimensions of Learning Disabilities: External Validation and

Relationship with Age and Academic Functioning. Journal of Learning Disabilities, 30, 490-502.Van Nieuwenhoven, C., Grégoire, J. & Noël, M.-P. (2001). Le TEDI-MATH. Test Diagnostique des compétences de base en

mathématiques. Paris: ECPA.Veenman, M.V.J. (1998). Kennis en vaardigheden. Soorten kennis en vaardigheden die relevant zijn voor reken-wiskunde taken. In

H.W. Bakker-Renes & C.M. Fennis-Poort (Eds.), Hulp bij leerproblemen: rekenen-wiskunde (pp G0050/1-13). Alphen aan den Rijn: Samsom.

Verschaffel, L. (1999). Realistic mathematical modelling and problem solving in the upper elementary school: Analysis and improvement. In J.H.M. Hamers, J.E.H. Van Luit & B. Csapo (Eds.), Teaching and Learning Thinking Skills. Contexts of Learning (pp. 215-240). Lisse: Swets & Zeitlinger.

von Aster, M. G. (1993). Developmental and acquired dyscalculias in children. In Stachowiak, F. J. (Ed.). Developments in the Assesment and Rehabilitation of Braindamaged Patients. Tübingen: Narr.

von Aster, M. G. (1994). Developmental dyscalculia in children: review of the literature and clinical validation. Acta Paedopsychiatrica, 56, 169-178.

von Aster, M. (2000). Developmental cognitive neuropsychology of number processing and calculation: varieties of developmental dyscalculia. European Child and Adolescent Psychiatry, 9, II/41-II/57.

von Aster, M. G., Deloche, G., Dellatolas, G. and Meier, M. (1997). Zahlenverarbeitung und Rechnen bei schulkindern der 2 und 3 Klassenstufe: Eine vergleichende Studie franzosischsprachiger und deutschsprachiger Kinder. Zeitschift fur Entwicklungspsychologie und Padagogische Psychologie, 29, 151-166.

von Aster, M. and Weinhold, M. (2002). Zareki. Testverfahren zur Dyskalkulie. Swets: Lisse.World Health Organisation (2001). International Classification of the Functoning, Disability and Health (ICF). Geneva: WHO.

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Appendix AChecklist for dyscalculia

Checklist dyscalculia – relevant items

Date:Name:Date of birth:

PART 1

REASON FOR THE ASSESSMENTName 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?

Overall academic achievement; general grade

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Grade obtained for mathematicsGrade obtained for language

General Yes No Remarks1. 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: …

Yes No Remarks3. do you go to school on a regular basis If not, why not:

Yes No Remarks4. How would you describe your working habit

Motivated Attentive

Yes No Remarks5. How would you describe your working fluency

Slow Irregular Depending on what has to be studied

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Yes No Remarks6.How would you describe your relationship with other students

Nothing special to mention Afraid Being teased often

Yes No Remarks7.How would you describe your relationship with your teachers

Nothing special to mention Introvert Squared to fail

Yes No Remarks8 Are there problems at home Please add some information, if you answer yes:

Yes No Remarks9. How would you describe your mood

Nothing special to mention Irregular Depressed

10. Do you have problems with hearing/vision Yes No

Yes No Remarks11 Are you on medication? Add some information, if yes:

In which area do you have problems: Yes No

1. Are there problems with reading comprehension

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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/statisticsGood Normal Bad

Speed Insight Techniques Automatisaton

Other remarks:

Other questionsWhy 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?

What do you think about this approach?

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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 skillsGood Normal Bad

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 Understanding terminology(product, acute, vulgar..) Placing numbers on a number line

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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 2ACTUAL 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?

Do you have problems concentrating on tasks?

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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 EXAMPLESGetting in fights, being angry, oppositional behaviourIntrovert, quiet, sad, afraid, defeatist attitudeHyperactive, restless, impulsiveProblems with peers, family and friendsProblems with adults, teachers and parentsOther problems

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 Remarks1. Do you have good contact with your mother 2. Do you have good contact with your father?

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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)

Yes No RemarksDo you have problems with eating/sleeping? Do you drink alcohol? Do you use drugs?

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?

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Appendix B

CDR

Complete the following detailsFirst name

Surname

Course/Subject

School/Department

Organization/Institution

Make these exercises without calculator. You get 40 minutes. Success!

Write the numbers on the ….NR1 LXVII …………….NR2 1 set of eggs ………eggsNR3 4 pare of books ……books.

Write in words on the ….NR4 1309,03 .......................NR5 date of birth 12.08.1958 .......................

Put the correct sign ( <, > or = ) on the….

S1 610 m … 61000 mm

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S2 14.25 hour … 5 before half past 2 in the afternoonS3 900 ml … 9 lS4 4 x (12,7 – 0,9) … 30 + 20S5 906 … 9,06

1000

Put in order, start with the smallest numberK1 2 5 0,5 0,2

5 2K2 8,52 95,02 85,2 9,25

Put the correct number on the K3 56700 56800 56900 …K4 1230,7 1230,8 1230,9 …K5 432,17 432,18 432,19 …

Solve the exerciseP1 1263 + 861 + 73 + 445 = ………..P2 30563,7 - 137,95 = ………..P3 7,25 x 11 = ………..P4 27681 : 90 = ……….P5 72 : 9 = ……….

10

L1 283 more than -71 is …L2 One-half of 3/5 is …L3 … is 3 hundreds less than 4125,15L4 The biggest mean divisor of 27, 6 and 12 is …L5 One-half of 140 has as double … M1 1250,8 is 4 tens more than …M2 2458,26 is 3 hundreds more than …

36

M3 270,6 is six times …M4 Four times 180 is one-half of … M5 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? ….

37

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 2498 + 3495? Choose between: 2500+3500 2400+3500 2500+3400 2400+3400

N2 1003,14 - 598,23 ?Choose between:1000-500 10031-6002 100014-59823 1000-600

N3 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

N4 18:15 is nearest to ? Choose between : 6 pm 15:00 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

38

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.

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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.

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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.

Students do not need to rely on mental computation; they can always use a calculator.

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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.

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