The Theoretical Framework that underpins the assessment of Reasoning and its importance in Mathematical learning is defined in international assessments such as PISA and TIMSS. Reasoning is understood as being part of Mathematical Literacy and defined broadly as using mathematical understanding to solve problems in complex contexts (TIMSS, 2011).

In the UAE students spanning a wide range of abilities, are assessed in the domain of Mathematics. The test construct is developed according to the national curriculum outcomes with local experts and proportionally represents the content taught in classrooms, with items from the mathematical sub-domains of Number, Patterns and Algebra, Measurement, Geometry and Statistics.

The assessments provide a wealth of diagnostic information which is reported back to all key stakeholders allowing observation of trends across cohorts; principals to observe patterns across the grade levels; teachers to identify issues at class and student levels; and finally and perhaps most importantly, parents to closely monitor their own child’s performance in Mathematics.

In conjunction with this framework, the items are also classified according to the cognitive domains of Knowing, Applying and Reasoning, derived from Bloom’s Taxonomy and used in international large scale assessments. These cognitive domains transcend the content domains and whilst these may not be explicitly taught, there is an expectation that items from each of the cognitive domains be evidenced in the assessment. 

Hierarchically ‘Reasoning’ has a greater cognitive load and it may be debated as to whether it items testing reasoning be included in large-scale assessments, testing students with limited experience in this realm.

As large-scale assessment moves closer to online adaptive testing, the question of the validity of the inclusion of Reasoning items in the early determining stages of testing where students may be disadvantaged due to the inclusion of such items is an issue worthy of investigation.

This paper reports an investigation of the impact and value of the inclusion of Reasoning items in large-scale testing of students in Mathematics. It attempts to justify the inclusion of Reasoning items in the calculation of ability estimates of all students, and challenges whether it is valid to include these types of items in such assessments. 

It examines the appropriateness of the inclusion of reasoning items in traditionally content-based instruments, and will compare the ability of students on Mathematical assessments with and without Reasoning items. It will further investigate whether any differences found are influenced by age or gender; and consider whether only students who demonstrate higher abilities be tested on such items.

   The primary source of data to be used will be from the national assessment of Abu Dhabi , EMSA 2014 and 2015 Mathematics. These sets of student data will be disaggregated by grade, Cycle and gender; then using IRT analysis techniques (Rasch 1960), further analysed for overall student ability and relative to items testing Knowledge and Applying; and Reasoning.

As the next phase of this large-scale testing program involves the migration to an online environment where the adaptive test design will rely on valid decisions made at key decision points in the live assessment, it is critical that key stakeholders be equipped with research findings such as this that will guide the process towards a refined and valid instrument with a more accurate measure of student ability in Mathematics.

• Masters, G.N. (1988). The Analysis of Partial Credit. Applied Measurement in Education, 1(4), 279-297. Copyright 1988, Laurence Erlbaum Associates, Inc. • TIMSS 2011 International Results in Mathematics, Ina V.S. Mullis, Michael O. Martin, Pierre Foy, and Alka Arora. Publisher: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College, Chestnut Hill, MA, USA and International Association for the Evaluation of Educational Achievement (IEA) • Wu, M.L., Adams, R.J., Wilson, M.R., Haldane, S.A. (2007). ACER ConQuest Version 2: Generalised item response modelling software [computer program]. Camberwell: Australian Council for Educational Research. • http://www.curriculum.wa.edu.au/ProgressMaps/Documents/Mathematics/Working%20Mathematically_1.doc This document is the Progress Maps for the Working Mathematically Strand of the Mathematics Curriculum in Western Australia.