Traditionally, a specific learning disability (SLD) referred to a discrepancy of one to two standard deviations between intellectual functioning and academic functioning. However, the amount of discrepancy was arbitrary (1), older children were favoured (2), higher IQs were favoured (3) and it was failure-based (4). Currently, the definition holds that achievement in key academic areas is substantially below the age norm and in excess of sensory deficits, linguistic processes, attention and memory. The prevalence is 2 to 10%.

Response to intervention (RTI) refers to a tiered system in which a failure to respond to an intervention is the criterium for identification of specific learning disabilities. This indicates the need for more specific and intensive intervention. First, there is screening for risk (e.g. simple tests of basic pre-reading skills) and assessment of family history of reading and language difficulties. After this, there are several tiers:

1. Tier 1 intervention (i.e. trained classroom teachers).
   This includes assessment and possible modification of the language programme in a classroom to ensure that the instruction is addressing the individual needs of all the children in the classroom.
2. Tier 2 intervention (i.e. additional one-on-one instruction and small groups).
   This includes a small-group intervention for children whose literacy difficulties are not resolved by appropriate adjustments to the classroom instructional programme.
3. Tier 3 intervention (i.e. special education classroom).
   This includes a more intensive intervention (e.g. fewer children; daily one-to-one tutoring) for children who continue to perform poorly.

In the Netherlands, there are three different but similar tiers:

1. Tier 1
   This includes a high quality classroom instruction.
2. Tier 2
   This includes additional teaching in class by teacher or additional instruction by a reading specialist, either individually or in a small group.
3. Tier 3
   This includes the help of a dyslexia specialist outside of the school but children are not yet in special education.

A child moves to the next tier if the progress in a tier is inadequate. The three-tier model is the most common model of RTI and is defined by three sequentially ordered intervention strategies. It aims at early identification of at-risk children.

All tiers depend on continuous monitoring of student progress as this determines the eligibility for a given tier. It thus does not look at an IQ­-achievement discrepancy. A diagnostic classification depends on the outcomes of different interventions. The majority of children who identified as at-risk at first scored average after one or two semesters of tutoring (i.e. tier 1). This means that most struggling readers can become average-level readers if they are provided with effective intervention.

Almost all children identified as at-risk for long-term reading difficulties in first grade had the same characteristics:

• They lacked emergent literacy skills (e.g. phonological awareness; knowledge of the alphabet).
• They were exposed to a less optimal language programme.

This means that not dyslexia but poor education was the cause of their reading difficulties. For most beginning readers with reading difficulties, the problems were caused by experiential and instructional deficits and not by basic deficits in reading-related cognitive abilities.

RTI is better than IQ discrepancy and other psychometric measures in identifying children who are at-risk for long-term reading difficulties. IQ is not a good predictor for early identification. It does not predict differential response to intervention and does not differentiate atypical achievers from typical achievers with average IQ. IQ-achievement discrepancy should not be used as a predictor of dyslexia because:

• Dyslexia is characterized by a wide IQ range.
• IQ is not a strong predictor of intervention responses.
• Reading ability and IQ are continuous.
• Children at the low-end of the reading distribution need treatment regardless of diagnosis.
• Dyslexia is not diagnosed if it is secondary to other causes (e.g. low IQ; bad schooling).

False positives refer to children being falsely identified as being at-risk. This unduly taxes the school resources. False negatives refer to children being falsely identified as being not at-risk. This deprives the truly at-risk children of intervention. Sensitivity refers to a measure of the degree of accuracy in identifying reading disabled children. The standard is 90%. Specificity refers to the degree of accuracy in identifying non-reading disabled children. The tolerable minimum is between 85% and 90%.

Children at-risk for early and long-term reading difficulties can be efficiently identified at the beginning of kindergarten and this can leads to prevention of later difficulties. Only 16% of the children identified as at-risk at the beginning of kindergarten had reading difficulties by the end of second or third grade despite intervention (i.e. reading disability).

The same principles of RTI work for dyscalculia as well as dyslexia. Dyscalculia has several characteristics:

• There are limitations in mathematical understanding.
• There are deficits in the number sense.
• It impedes activities that involve problem solving or retrieving mathematical information.
• There are problems in the acquisition of the number sense (i.e. mental number line) because of a poor approximate number system (ANS).

The prevalence is 5% to 10% and it is highly heritable. There are two types of dyscalculia:

1. 1. 1. 1. Primary dyscalculia
            This refers to math deficits stemming from an impaired ability to acquire those skills.
         2. Secondary dyscalculia
            This refers to math deficits caused by external factors (e.g. poor teaching; low SES).

Children with the most severe math deficits exhibit cognitive deficits in very basic number processing while children with moderate impairments do not. The distinction may thus be one of severity.

Pure dyscalculia refers to dyscalculia driven by an impaired number sense and mathematical learning disabilities (MLD) refers to dyscalculia driven by endogenous factors (e.g. cognitive deficits) not related to numerical processing. There are distinct pathological profiles of pure DD and MLD. Studies often use broad selection criteria. Studies with stringent selection criteria found no differences between primary DD and typically developing children on working memory measures, demonstrating the different pathological profiles.

The skills required for successful mathematical performance change over the course of development. Some children may have a specific deficit at an early learning stage which disrupts the acquisition of later skills. Persistent deficits need to be identified for the diagnosis of DD. Primary DD may be driven by a core deficit of the number sense (i.e. most severe problems).

There are several behavioural markers of pure DD:

1. Impaired arithmetic fact retrieval
   Children with DD keep on using procedural approaches (e.g. counting) instead of using retrieval from memory.
2. Immature of inefficient problem-solving strategies
   Children with DD use a count all method to solve simple calculations instead of a count-min strategy.

The intraparietal sulcus (IPS) is involved in the processing of numerical magnitude representation. Children with dyscalculia demonstrate atypical brain activation during this. There is reduced modulation of the right IPS in children with DD during a non-symbolic numerical comparison task. They also show reduced activation of the IPS during mental arithmetic.

Typically developing children show a greater activation in the IPS for number pairs that were closer together compared to pairs that were separated by a larger numerical distance (i.e. distance effect). Children with dyscalculia do not show a distance effect in the IPS (i.e. no greater activation with greater distance).

Treatments which aim to target cognitive processes which are crucial for the development of math skills (e.g. Graphogame; the number race) are effective in improving number-comparison performance. However, there is no generalization to counting and arithmetic.