Things worth reading for fun: April 2013

The original meaning of the Greek word diagnosis: evaluate, distinguish, decide. Diagnostic constant education. The teacher or the estimated daily instruction starts, see what problems arise, consider why a task fails and decides the best explanation is adjusted. A diagnostic process involves more than make a diagnosis. It begins with the signaling capacity of the teacher, followed by the collection and organization of information on the progress of the group as a whole and for each child, testing and interpretation of results, the classification and error analysis, but also to monitor the extent of instructions and support. In 90% of cases resolved as teachers blockages and problems. However, they are sometimes very stubborn and show that it can be well controlled. In these moments, seek advice from a supervisor (internal or external) and expands the diagnostic process itself on. Gradually the knowledge that the necessary customization and more specialized, using different theories. The number of players teacher, trainee counselor, teacher, school counselor, and possibly a diagnostician (Hons). It is important to work together and are completed by qualified personnel.

Diagnosis may involve several steps, such as signage, recognition, reporting, and display boards. They complement each other and, depending on the severity of the problems are reinforced. As the problems are more serious, more personalized diagnosis and focused individual.

Signaling and recognition bring a difficulty to map and lead to a description of what happens: the recognition of the diagnosis ("what"). Preferably using tools developed good. "Mathematical problem" and "dyscalculia" are descriptive terms and explain nothing. When recognition is sometimes a division into different types of problems / disorders of calculation. In addition, other problems still occur and disorders (comorbidity). The distinction between them is called differential diagnosis. This involves not only cognitive, but also emotional and behavioral problems (eg, ADHD and anxiety). Identifying problems is always related to the context of education offered and continues to learn. Recognition also left the group of students that anyone can be useful to compare (considering age, cognitive and sensory).

Sometimes it may be desirable - for example, choosing the best way - the statement of a problem, namely the explanatory diagnosis ("what") For an explanation of using different and complementary theories .. This attention to factors of education (eg, teaching, teachers) individual factors (such as the development of logical thinking, intelligence and learning ability, language development, skills phonological memory and information processing, neuropsychological functioning). The literature suggests that to some extent the innate sense of quantity, not from specific genetic arithmetic and mathematics. Environmental influences and individual characteristics interact to cause problems.

To get an idea of how to recognize the diagnosis is made, the different stages of this process is explained below.

Signaling, analysis reports and the formulation of the request
You can identify a more or less formal. They complement each other. An informal way of signaling occurs mainly from continuous observation and study how students meet the challenges of good and bad results. The answer is not only informative, but also followed the thinking and working. The teacher in this phase usually looking not understand the instructions and gaps in the knowledge of students as teaching signals for adaptation. Occupational requirement is that the teacher understands the principles and teaching in the learning of mathematics. Examples of questions that teachers should ask themselves are:

    What kind of knowledge you? Students may have problems with the performance of the different steps of calculation (as in the implementation of the divisions cruise dozen jumps on the number line), but also made uniform availability arithmetic (simple example, memory and memory and scoreboards, or the use of terms such as denominator).

    What is the quality of knowledge in accounting? It makes a difference if a student has a calculation can be performed by a specific model (eg rekenrek), or you can imagine the proposal process and to "think" to run. Another example is the extent to which knowledge is automatic: very slow and prone to errors quickly and without problems.

    What kind of training is needed? Ideally suited to teaching students the different stages of the knowledge gained, preferably from explicit instruction using input from students, at least give more direct information on the provision of information to integrate isolated previously acquired knowledge / skills and applied in new situations.

Formal process is the use of keys compared to the standard or predefined criteria possible. For example, the concept of Test-Revised number Utrecht before the age of 4, 4-7, 5 years (CGU R, Van Luit and Rijt L ', 2009) and the Math key 1, 2 and 3 groups 3 t / m 8 (Cito). The keys have the advantage that they are effective and targeted comparative. Official supervision of students and early detection of problems is less dependent on the experience of many teachers, without the addition of knowledge and learning solution superfluous. Keys must be possible to meet the psychometric requirements.

Examples of requests for assistance in the final phase of the signal analysis and complaints can be established:

    Recognition questions:

        Does this student have dyscalculia?

        How serious is the problem of math?

        Are there additional problems (co-morbidity)?

        What are the strengths of this student?

    Questions to the statement:

        Why this simple math problem so persistent?

        Why automation behind understanding?

        What is the explanation of many procedural errors?

        Computational problems exacerbated by the teaching of this method?

    Questions to show:

        How is this problem to better meet the math?

        Method ... is adapted to this problem?

        Is there a reference for additional help?

        What is the target of intervention possible for the rest of the year?

Problem
The result of a problem is the identification and designation of a problem in descriptive terms. With a relatively simple and less persistent than has essentially a limited extent and content analysis of behavior calculation in mathematics or repair. An example of an outcome (descriptive) is as follows: "The problem of calculation for the procedural aspect of the reproduction."

As shown in the most complete and the most persistent, there are more steps, allows a content analysis of the most complete and the result of a decision on the issue of student leadership any calculation with respect to overall performance. An example is as follows: "This student has dyscalculia In what follows, we will discuss two versions of the problem. An organization calculation / classification specific behaviors and designation / classification of the whole problem of calculation.

Problem analysis and planning, description and classification of behaviors specific calculation

The problem may be related to the organization and description of specific examples of computational problems such as computational mathematics in everyday situations. With enough examples (!) You get a view of the unstable elements of the problem of calculation. Then, you may notice that the sums unduly history solved systematically result often too low or desirable digit subtraction (with numbers <100) to another whenever the smallest unit (or ten) of the main unit ( or ten) is subtracted.

For these two reasons, it is useful to map aspects stable.

Firstly, the errors are not always in the same way that happens. Students who have difficulty with a component, choose sometimes one, sometimes the other strategy, sometimes right. The dissolution behavior may change. This may or may not go well, not as it shows that there is a reasonable order with errors due to inattention or sloppy work, but he does not know how to approach. With very few concrete examples of behavior problems is a model in which the problems can not be identified or is another example of falsely recognized value. The material used in this phase is diverse: the results of tests or monitoring progress, written work in class, homework, oral answers.

The second reason to look (relatively) stable model is all possible help to give. More or less stable, because the problems are more systematic support that they are unpredictable.

The organization and description of behavioral problems as a concrete classification error. Ideally we would like this function (empirically validated) systems where misclassification errors / problems can be organized in a limited number of descriptive categories. This is, without reference to a representative supposed explanation of these problems. The statements may vary, not only because different processes can lead to the same behavior, but also because the prospect (theoretical) from which to consider the behavior is affected.

An example of a descriptive category is: read errors and write multi-digit numbers (for example, says '32 'instead of '23' and type '213 'instead of '231').

A descriptive category does not indicate why it fails. In the example, states can be:

    the student has an understanding of the system of official position, but always forget the rules of procedure in order pronunciation and notation;

    the student has no knowledge of the system of official position, even if it uses in spontaneous speech or in large quantities.

To determine which of these interpretations - or maybe more - is correct, we need more data. It is also important to identify what is going well and everything is controlled. This not only gives an idea of what the most likely explanation is that it excludes, but also provides clues to give help.

Suppose that there are many errors in the method of FIG "including" is increasing, but the multiplication tables up to 10 - declarative knowledge - well known and smoothly. They do not help and treated separately. We must consider the best way to proceed is based on questions such as: what sequence of steps is used, what is the average score in the results, when, on the contrary, do not forget to add, there is a set fixed point or change the type of a task?

In the literature, there is little attention to the purely descriptive classification systems, but the description and explanation (or interpretation) or as naturally related tasks considered representative of a child - and thus implicitly: - explanatory process. The question arises whether such a system is purely descriptive and no theory is fact. Strictly speaking, then go to a list of categories of types of responses () and / or employment types of exercises cluster analysis (stimuli). In our opinion, this is not very useful, especially because of the endless possibilities in the field of computational mathematics. Successful appears to come from a limited number of custom tasks chosen representative "and solve problems in the case of obvious gaps or systematic errors (classification) to identify the underlying reasons might be (analysis). These assumptions are additional keys, from the task level, preferably in direct contact and work with the student. What are the tasks of this type of problem can be considered representative, is a practice that is very different. For example, in a realistic pedagogy different situations involving older children learn to apply the change in amounts due to the main story of the band 6 or probability learning in formal secondary education. But in each of these three possible cases, a call is made on declarative knowledge and / or procedure that is specific to the selected tasks. When the review is completed by the observation of metacognitive knowledge and skills. Diagnostic analysis following classification, it is also a transition problem in a specific mission statement which may provide clues for further assistance.

In reviewing the specific tasks of explanation is - according to the principles of the doctrine of the diagnostic ability - To provide assistance and explanations. Provide assistance and explanations in a diagnostic test is one of the principles of learning aptitude test. In Kwantiwijzer for teachers (or "the Kwantiwijzer 'Van den Berg et al, 1992) - a diagnostic tool to identify the strengths and weaknesses of students in the act of quantities - has been developed to date of field and subtracted from 100, the application of the theory of psychology action. The tool also gives clues about where education is involved. individual research is process-oriented and quality, focusing on the directory. The Kwantiwijzer combines different techniques:

    observation of the entire observable behavior, including the use of these procedures sometimes barely visible, not effective and transparent (counting fingers, counting teeth);

    ask how something is made, and the (not recommended) for questions;

    discuss how the child, judging by the comments, the researcher conducted (see);

    series of tasks of a similar difficulty, having a lower or higher;

    provide and providing material support;

    guidance on key attributes and relationships in the problem;

    structure the method of solution;

    with the child to solve a similar task - refer directly to the method;

    warn against errors and the use of questions to help you get started.

Usually cause the search Kwantiwijzer computational problems, but evidence on teaching teachers. For process analysis computational problems is the diagnostic test of Kwantiwijzer a very useful tool. Valuable are the detailed steps that good content beyond explicit signaling. Other resources used in practice is limited in this regard, such as the calculation of diagnostic and research in Flanders Kortrijk test or calculation EPA2000.

These principles also apply to other areas in the field to be defined in the form of a conversation "diagnosis". Four techniques are particularly suitable case optionally followed by signaling errors in a test:

1. Note:
The student is observed when performing arithmetic. There is a good overview of how the student approaches the task (is moving ahead immediately if open), which makes the use of materials or fingers to come to a conclusion, it could mean "hidden "actions (eg fingers" secretly under the table or move the account radiator ribs).

2. Questions:
There are several ways to get the child to ask questions. The most common are children to think aloud during problem solving. Alternatively, the student will have the answer to the question of how he arrived at this answer. Generally provides a lack of clarity, the teacher must questions ("How did you do that?" What number did you use? "" Is there anything else you think? ").

3. Range of tasks:
When the student tasks drop test specified can not solve, you can in the process of diagnostic substitution exercises that offer a bit easier than the main task. Then discuss how students solve these alternative tasks. Otherwise, even the simplest tasks offer. Manage the main task relisted and whether the student can explain the relationship between the alternative states and the main task.

4. Help develop gradually:
Here are five levels of support can be distinguished. To be able to describe these levels, it is assumed in the following example.

Alex, a student of 13 years, the first year of secondary education, seems unable to correctly cite the following actions to resolve "Sjaak the empty bottles in the supermarket kind. Account 154 bottles in boxes do. In each box. 12 How many bottles boxes need him "at the following levels may, depending on what Alex did with the help of development:
Installation structure (A): the task structure is applied by cutting sentences bulk informative statement.

     Sjaak bottles in boxes do.
     It has 154 bottles.
     In each case of 12 bottles.
    How many boxes Sjaak mandatory for all jars?

Is it not good, then the second level of support is provided:
(B) the complexity of the structure and presentation of cut: Cut Loose the challenge remains informative sentences and the difficulty of the task simplified mathematical disagreeing, but 12 to 10.

    Sjaak has 154 bottles.
    Clean them in boxes.
    In all cases of 10 bottles.
    How many boxes Sjaak need?

If it does not work with Alex, the level of the third tranche of aid;
(C) verbal support: By asking questions about the work can be verified or Alex will understand what the job is about:

    How many bottles did Sjaak?
    What would I do with these bottles?

. What does a "drawer"?

. How many bottles as possible in a drawer?

. How many boxes are what you need?

. How do you calculate the best?

If anything using auxiliary verbal performance, then you can go to the fourth level of assistance;

(D) provide material support: In young children, it is actually a tangible solution, and older children and use tasks more complex to provide a solution that fits the schema student directory solution:

154

-100 (10 boxes)

   54

- 50 (5 cases)

     4 (4 bottles, it is also necessary cases)

A total of 10 5 1 -> 16 required fields

Giving material aid does not work, the fifth level of aid;

(E) Modeling: This means that the master strategy comes as the attention of the student. Then do it with student work more independently. If the teacher thinks the student in the process, allows students to solve these tasks independently.

The five levels of care to say something about the educational needs of children. It is clear that the more help a student needs assessment phase calculation more - especially - the support you need in the teaching of mathematics. This is usually support both the specific instruction of a specific program.

Problem analysis and recognition, classification and designation of a mathematics disorder

In the above problem, the function is to organize and describe the specific problem behaviors grouped: the misclassification, developed by a teacher, counselor or teacher in remediation. But in the diagnostic cycle can also refer to a problem of classification and designation of computer problems at all - assuming low gravity - in the range of developmental problems, including learning disabilities. In this case, we speak of an identification of a disorder diagnosis and recognition. In the case of dyscalculia is the psychological answer function is not automated touch declarative knowledge. Dyscalculia is disorder. Disorder may be more or less severe, more or less persistent. Each, however, low severity or persistence. By analogy with the view that for the identification of dyslexia was made by the health is considered persistence (resistance) of dyscalculia disorder as an important indicator of the severity. Resistance to interference, such as remedial courses, is an important criterion for the persistence of failure to learn to speak. In assessing the gravity we will return later. The identification of developmental toxicity based on the basis of descriptive problems that are met. The most common system in this context is the Diagnostic and Statistical Manual of Mental Disorders (DSM), the game is about the definition of dyscalculia also included. One is the condition the learning of mathematics (or dyscalculia), reading for example as a result of disorders (or dyslexia). The latest version of the DSM-IV-TR ™ (APA, 2000). Using the same criteria (rather limited and global) is a disorder of mathematics reasonably objective and easy to identify. One criterion is that the perceived problems are more severe than on the basis of intellectual ability is expected. Despite the fall of an intelligence test that seems obvious - and there may be legitimate reasons for that, in fact, do - not always necessary. After all, on the basis of performance in other cognitive domains or by observing the quality of mental development is a valid statement possible about the intellectual abilities compared to the current level of calculation. Note that the recognition criteria not spoken in a normal or average intelligence. Students with mathematics disorder may also reduce or above average intelligence. DSM classification problems is based on a consensus between the major groups (international) clinical experts who shared their experiences. They agree that the disorders described as such occur. When you assign a general disorder must meet the positives and negatives. A positive result indicates for example the amount and / or behavior that occurs, a negative criterion, for example, that such behavior can not be part of another disorder that is more complete. Therefore, it is unnecessary in the case of severe mental retardation as mathematics disorder can be distinguished. In the case of mathematics disorder, there is a lack of automation of knowledge, objectively determinable performance at a low level (too) without appropriate systematic (recovery) to help have the desired effect. The level of automation performance (speed and accuracy) is measured with an appropriate comparison group, similar training and similar intellectual and sensory capacities. This means that mathematics disorder can occur at different levels of education, different levels of intellectual ability, and may be associated with sensory disabilities. No lower limit for the duration of formal education must be followed, but it is obvious that this is so is that the systematic and planned aid has had a chance to succeed. A rule of thumb is to leave six months. There may be a reason for shorter or longer to keep.

The assessment of the severity

For behavioral problem to classify the severity of a minimum. However, there are varying degrees of severity, both individually and behavior of the disease in its entirety. An indication of the severity, is regarded as the degree of resistance to additional support, as evidenced by the performance objectively determinable too low. Standardized tests and questionnaires are an important tool, especially when it is repeated decline. A well known example is the citation of the students. Another source of information on the gravity is the ratio between what works and what does not. There is more to formulate criteria such as the length of the problems, the number of situations in which the person concerned negative experiences occur, insofar as restrictions son (in education, occupation, social functioning) and amount of stress experienced.

Statement Analysis
Identify problems can lead directly to an appropriate approach them. Therefore, all school days and test results of practice recovery and direct observation often provide clues to modify instruction. The same is true for misclassification. Suppose a student operations with fractions with the same name are not applied consistently, which will affect the content of the help. In many cases, the relationship between the problem and the need for support is not as clear. One possibility to overcome the coupling of misclassification errors for the analysis and testing provide assistance (diagnosis). This creates a transition between the analysis of the problem statement for specific tasks. However, it is sometimes necessary broadens and extends the diagnostic conditions not only cause problems explain how to maintain or amplified, but also have an impact on the selection or definition of further processing, for example, has comorbidity. The term "explanation" psychodiagnostic - more general application in the social sciences - both in the (large) to cause or condition of Appeal, perpetuate, strengthen or condition related problem. Knowledge of the conditions from the explanatory scientific theory and research. Instead explanatory conditions are the same are also known as risk factors. Some of them are (still) influenced and adapted to the provision of assistance, others less or not (such as inheritance). The explanatory value of a state is the combination of the theoretical and empirical evidence also of practical interest to the identified problem. The empirical basis is generally associated with a fixed relationship between the problems and conditions can be expressed as follows:. "Up to 25% of the variance in mathematics performance is explained by the general level of intelligence," or "The difficulties for the automatic control of multiplication occurs in 60% of children with dyslexia. Measure also an empirical relationship is generally applicable in the particular case remains uncertain. For this reason, the level of task analysis problem is essential. Or, for example, general intelligence, case by case, a likely explanation is either and therefore treatment should be taken depends on how the mathematical problem actually occurs. Mathematical problems can, but need not be manifested by a lack of understanding.

To detect conditions of literature useful for the diagnosis indicates two research directions: a fault condition and condition problems. The search condition problem connecting directly to the previous step in the evaluation process: the problem that leads to a problem identified and named. Ideally manuals can specify what types of problems can be linked to a testable (alternative) explanations. Problems in the field of computer science and mathematics have so far, however, such statements. Most often, the literature is not classified according to the types of problems, but the types of explanatory theory, and in the first part of this book is.

Regarding the problems of conditions has the disadvantage that only one type of condition that is central explanatory many different (sub) theories and research variants difficult.
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