Testing a learner using a general grade level maths test that results in a single maths mark or percentage might tell us that a learner is struggling, but it doesn’t tell us what they are struggling **with**. Even a test on a specific topic of work needs to be able to inform on exactly what the problem is.

Transformative assessment needs to be **diagnostic**.

Look at this Fraction Test. Is it diagnostic? Notice that it tests adding common fractions and mixed numbers, subtracting common fractions and mixed numbers and multiplying common fractions and mixed numbers. While you could certainly use learners’ individual responses to specific questions in a diagnostic way, the overall learner result can only tell you generally how the learner works with fractions. It is time-consuming to analyse each learner’s individual question response.

There is a way to work around this. Firstly assessment that specifically designed to be diagnostic must test only one concept in a test item. If you test more than one concept then you don’t know which of the two components the cause of the problem is.

Look at these test items:

The first tests adding like fractions – those with the same denominators. The second tests adding unlike fraction but where one denominator is a multiple of the other. The third tests adding unlike fractions, which requires finding a common denominator (which is a common multiple of 5 and 7). The fourth tests understanding of adding mixed numbers through the relationship between whole numbers and common fractions. These four simple items can be administered at the start of a lesson and self-marked. The teacher can guide learners to analyse their responses to the questions and how these reveal their understanding of adding fractions. This self-analysis is a crucial

part of transformative assessment which is transparent in the sharing of its purpose with the learners.

Craig Barton, an ex-maths teacher in the U.K. is a global expert in diagnostic assessment.

He recommends:

- closed questions rather than open for diagnostic questions, in fact, he chooses a multiple-choice format to start each lesson;
- one correct response for each item and each incorrect distractor identifying a specific common mistake or misconception but no explanations must be necessary from the learner and it must not be possible to answer correctly if the learner is holding a misconception; and
- only testing one concept clearly and unambiguously in one item.

Mr Barton, as he is known, maintains an online resource of thousands of diagnostic questions for maths teachers to access and use in their classrooms either with technology or without – and it is a free resource.

**On Formative Assessment in Math – How Diagnostic Questions Can Help –**by Craig Barton

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