Initial note: There is a difference between:
Each will have its place and appropriate circumstances. A diagnosis has to take note of the lack of an agreed definition, though the USA does have the DSM-V version. I consider this to be an appropriate definition.
There is also the nature of dyscalculics. Key researchers have described them as heterogeneous, that is, there is not one profile. This is compounded by the nature of maths itself. It is a subject with many facets which challenge a range of abilities and skills. However, that does not mean a thorough diagnosis of the components of maths difficulties and their cumulative severity is not possible.
Of course, many people who seek a diagnosis of a problem want to know not only what that problem is, but what can be done to address it, so for me, a diagnosis should lead to and include advice on addressing the issues. As with dyslexia, this will not be a cure, but advice on how to deal with as many issues as possible and how to cope with the others. Always beware of the snake oil purveyors. For a broad and balanced approach to identifying and diagnosing maths difficulties which looks at many of the factors involved, refer to 'More Trouble with Maths: A complete manual to Identifying and diagnosing mathematical difficulties' 2nd edition, (Chinn, 2017). The tests and procedures are not restricted to psychologists.
At this time with the general understanding of dyscalculia, there are few people who specialise in diagnosing dyscalculia, partly due to lack of experience and appropriate training. There will be a connection between why the diagnosis is needed and the qualifications necessary for the person who carries out the diagnosis. For example, to have a diagnosis that will help access the Disabled Students Allowance or accommodation for examinations the assessor will need to have an APC, an Assessment Practising Certificate (for more information see www.patoss-dyslexia.org/SupportAdvice/.../DSAInformationforStudents). A more informal diagnosis may be enough for a school to provide appropriate intervention, though something far more comprehensive may be needed to access funding and/or an Education and Health Care Plan (EHC).
A list of psychologists is available from the British Psychological Society (www.bps.org.uk). The psychologist should also have current HCPC (Health and Care Professions Council) registration. Assessments can also be carried out by an appropriately qualified specialist dyscalculia teacher with an APC. Usually the teacher will hold an AMBDA. The British Dyslexia Association (www.bdadyslexia.org.uk) can award an AMBDA to people who have completed comprehensive training, for example, Edge Hill University's PGCert-dyscalculia (www.edgehill.ac.uk/courses/education-dyscalculia)
For children, the first step is likely to be a realisation that the child is not making appropriate progress in maths compared to their peers. This may be a consequence of classroom observation and perceptions or poor performance in examinations and tests. Usually teachers and parents are comparing performance in maths with that in other subjects. It is that contrast in performance coupled with the persistence of the difficulties that is often leads to the first suspicions of a specific learning difficulty.
For adults, it is often the challenges that come from a promotion or a change of job that expose the difficulties that have been previously concealed. Adults (and indeed children) can become very skilled at disguising their dyscalculia. Society's norms collude to some extent in that it is socially acceptable to confess that you are 'not good' at maths, but not that you are 'not good' at reading and spelling. (I have never understood the irresistible compulsion some good spellers have to correct an incorrect spelling).
Diagnosis will focus on identifying the levels of mathematical knowledge, usually in arithmetical tasks, such as recall of times table facts. This may be coupled with examining key factors such as short term and working memories, mathematical vocabulary and speed of processing. The following sections give more detail.
A screener may the next step after informal recognition of classroom or workplace concerns. They have a purpose, but obviously are not a full diagnosis. Comparing a screener and a diagnosis:
So, a screener should flag up a potential problem. It will not attempt to offer advice on addressing the problem. That would be a subsequent process. Some of the screeners available are:
It is the nature of a screener to focus on what the authors consider to be key issues. For example, the GL screener has a focus on subitising (quickly recognising and quantifying small numbers of randomly organised dots) and numerical stroop (knowing which digit symbol represents the bigger value number despite relative font sizes as in 2 and 7). They will often look at basic arithmetic skills such as place value and basic fact recall.