it is often assumed that traditional instruments such as standard tests etc is to be used. However, in some of the work we have done with adult leARNERS, WE HAVE FOUND THAT FUNCTIONAL assessment which assessses the ability to use the relevant skills in a functional sense can be very productive. In this context, for example, numeracy skills are tested in the context of the spheres of life where such skills are utilised. There is no reason why that cannot happen for younger learners. I hasten to add that this is probably more effective for 'assessment for learning' rather than the summative assessment which is aimed at certification. If the focus is the latter, there are a range of assessment tools out there, but I am conscious that they will vary from region to region. As i am Uk based, the tools in use here might not be too relevant for you.
Even though this is will be a diagnostic assessment, we could definitely include some functional assessment as part of the assessment. Thus we could have some questions that show basic fact recall and calculation of pairs of single digit problems, as well as some contextual questions that involve similar calculations.
If you do have an assessment tool that you think is worthwhile, I would be happy to see if some of it fits our needs.
In our development and research work we have used Wright et al.s Maths Recovery programme items extensively to assess young learners progression in foundational numeracy tasks. Their work is extensive (4 books) and through. Much of our work is based on using the 1-1 interview and the LFIN to profile progress.
I have attached a paper below but you can also see my doctoral thesis for a lot more detail (also attached)
Thesis Learners’ numeracy progression and the role of mediation in ...
Conference Paper Identifying Stages of Numeracy Proficiency to Enable Remedia...