Abstract:

Considerable parts of the population of students with mild disabilities face permanent difficulty in memorizing and/or using fluently the results of additions and subtractions involving two one-digit numbers, which are known as “number combinations” (NC). However, fluent use of NCs is regarded as a prerequisite knowledge and predictor factor of performance on a set of numeracy tasks including mental calculations, algorithms and math problems.

In early learning stages students develop counting strategies for finding NCs. Later on students develop complex mental strategies for finding NCs by combining existing concepts, known facts and skills. These strategies constitute an intermediate stage between the time-consuming and prone to mistakes counting strategies and the instant and errorless recall of answers.

The primary purpose of this study was to assess and compare four instructional design packages for teaching 60 addition and 60 subtraction NCs to a total of 123 students with mild disabilities, who attended Resource Rooms of primary schools in central Macedonia, Greece. The first instructional package was based on specific principles of effective teaching, such as the explicit instruction, the control of prerequisite knowledge, the use of the concrete-representational-abstract (CRA) knowledge representation, the systematic and sufficient practice and the positive feedback. The second instructional package combines the principles of the first one with the use of an alternative grouping of NCs that facilitates memorization (memorization strategy). The third instructional package includes the second one and, additionally, certain teaching strategies promoting precision and fluency in the use of NCs. Finally, the fourth instructional package comprises the third instructional package and also the separate and intense teaching of dimensions of number sense, such as counting and part-whole knowledge, which supposedly promote the basic conceptual prerequisites of NCs.

Each instructional design package was used for teaching NCs to separate groups of students with mild disabilities. According to the results there were significant within-groups differences and improvements between the initial and the final performance. In terms of between-groups differences it was found that the last one, which was taught through the instructional design package combining all provisions, significantly outperformed the group that was taught through an intervention based only on the principles of effective teaching specifically in addition NCs. The findings suggest that students with mild disabilities benefit most from intervention combining principles of effective instruction, explicit teaching of strategies and development of number sense. In reference to subtraction NCs there was no significant difference between groups. Finally, there was no significant difference between the groups regarding generalization and maintenance of addition and subtraction NCs. Results are discussed in reference to the necessary instructional measures for the organization of effective interventions for the support of students with mild disabilities in their effort to learn NCs.

Keywords:

Mild disabilities, effective teaching, number combinations, intervention.