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If you are seeking a detailed and comprehensive fully standardised and normalised maths assessment, standardised on the UK population then the KeyMaths3 (UK version) might just be what you are looking for.

The KeyMaths3 UK is based upon the US version, except that it has been fully updated, expanded and standardised on the UK population in 2013. It is designed for use by Educational Psychologists and/or Specialist Teachers in a one-to-one diagnostic setting. It provides fully standardised scores and percentile ranking for assessing children and young people’s mathematical performance across the whole spectrum of mathematical agility, from age 4 years 6 months to 21 years 11 months.

The kit comes complete with Diagnostic Assessment manual, Response Forms, written test, and 2 easels. The easels are particularly self explanatory and provide an opportunity for observations to be recorded against responses.

The test is designed to be adaptive to the individual and is broken into 3 subsections:

- Basic Concepts
- Operations
- Applications

The test is designed to be adaptive in its administrative procedure to enable a more accurate measure of the individual’s mathematical performance. Each subsection has a number of subtests, which provide scaled scores. The scaled scores are summated to provide a standard score for each subsection. Hence either the complete test can be delivered or a complete subsection of the test can be delivered on its own. Each subsection is able to pin point with precision accuracy where any specific mathematical learning difficulty may lie.

Although it is possible to deliver one, or all three subsections, the start points of each subset are based upon the numeracy ceiling item result; it is therefore not possible to carry out a portion of the test without completing the numeracy subset first. The ceiling of each subset is obtained through 4 consecutive incorrect responses. A useful and detailed description of each subtest is provided within the manual to identify each mathematical concept being assessed.

As described by the title, this subsection assesses basic mathematical competency by measuring the conceptual ability required to perform at any level in maths. The following subtests are all assessed through the use of an easel:

- Numeracy
- Algebra
- Geometry
- Measurement
- Data, analysis and probability

Each subtest corresponds to the developmental progression as seen through the national curriculum and include a range of questions from basic number awareness, ordering fractions, standard form to ratio and solving equations. All tests are, in essence, mental arithmetic as there is no need for a calculator or for the examinee to make notes. The tests are self-explanatory and allow the examiner to judge the ability of the examinee by their responses to the questions. A full and comprehensive analysis of strengths and weaknesses and basic mathematical competence can therefore be obtained.

This subsection homes-in more specifically the four operations: addition, subtraction, multiplication and division through the use of a response booklet and consists of 3 subtests:

- Mental Calculation and Estimation
- Addition and Subtraction
- Multiplication and Division

As with any test, the examinee is required to work his or her way through the booklet answering the increasingly more complex mathematical questions, until the ceiling is reached, assessing and individual’s written and mental computation. The questions involve basic numerical and procedural analysis through to more complex algorithms, such as expand and simplify brackets, or solve to find x and y.

In addition to the written test, there is a further mental arithmetic and estimation test which is delivered through the use of an easel. The questions consist of basic numerical computation and hence facilitate the assessment of the examinee’s mental performance across a range of numerical operations. This subtest is designed to measure an individual’s ability to mentally compute answers to given maths problems across the range of the four operations thereby assessing the understanding of mathematical principles and the examinees ability to apply mathematical concepts. The quick approximation enables the examiner to determine whether the examinee is able to fully grasp numerical relationships and magnitude, rather than merely apply a rule to a given context.

This subsection is particularly useful for assessing the general understanding of an examinee; particularly when the performance of a simple arithmetical operation is placed beside a response placed within the context of a problem. If a pupil is able to calculate but not apply the mathematical concept across a range of concepts, this test will highlight where such generalisation difficulties may lie. It may also provide clues to further, more specific, learning difficulties such as working memory difficulties or a specific language impairment, where the examinee is not able to process multiple pieces of information within a multi-staged problem.

This useful, shorter subsection consists of two subtests and assesses an individual’s ability to apply conceptual knowledge and operational skills to solve maths problems. It consists of two subtests:

- Foundations of Problem Solving
- Applied Problem Solving

The first subtest assesses the examinee’s ability to problem-solve within the mathematical context by using riddles and problems. It is an important subtest as it assesses how the examinee would perform a task, by asking what strategies would be used, as opposed to seeking a correct or incorrect response. It therefore provides an indicator as to how well the basic concepts are understood, as opposed to learning the rule. The Applied Problem Solving subtest assesses numerical application in a more practical sense and real-world context. The use of a calculator is permitted, as the test assesses problem solving agility as opposed to the ability to compute; is the examinee able to determine which calculation is required to complete the problem? This subtest is therefore essential for assessing application and use of mathematical skills and knowledge.

I tested a number of students ranging from 9 to 16 and found the test not only simple and straightforward, but fun and engaging for the students. The tests are untimed and allowed the students to work at their own pace, which is a bonus for individuals who have a weak processing speed and tend to underperform during timed maths tests. The easels engaged the students with concentration difficulties and enabled pupils with auditory processing difficulties to engage with the mathematical concepts, providing an accurate picture of their actual numerical ability. However, as the tests are untimed, the older the examinee, the longer they seemed to take, and for some students, I assessed them in two stages as they took too long to assess accurately in one go.

Overall, this test provides an excellent diagnostic assessment of an individual’s mathematical ability across all strands, providing an accurate assessment of the individual’s strengths and weaknesses within the mathematical context. It would be especially useful for determining mathematical interventions to follow and would therefore save time by allowing the examiner to design intervention plans with are tailored to the specific needs of the individual.

**Pearl Barnes**

Specialist Teacher and Assessor, Past President of NASEN

MA(SEN), BSc(Hons), PGCE, PGCertEd, CPT3A

Pearl has a specialist interest in mathematical learning difficulties and the co-occurrence of other specific learning difficulties.

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