Abstract
<p>The effectiveness of two instructional interventions was investigated in the context of teaching Arithmetic Combinations (ACs) of multiplication and division to students with Learning Disabilities (LD) or Mild Intellectual Disability (MID). The intervention for the control group (LD = 20, MID = 10) was based on principles of effective instruction, while the intervention for the experimental group (LD = 19, MID = 4) combined the intervention for the control group and an alternative grouping and presentation scheme of ACs. Correlations between cognitive and learning characteristics of the two disability categories and participants’ performance in ACs learning were also investigated. Intra-group comparisons showed that post-intervention performance of both groups (control and experimental) was significantly higher than their pre-intervention performance. However, inter-group comparisons revealed that there was no significant difference between the results obtained through the two interventions. Students with LD outperformed their counterparts with MID. Differences of the two disability categories in domains such as speed of information processing and counting skills correlated with performance. Results are discussed in reference to the organization of effective intervention programs for supporting students with LD or MID in their effort to learn arithmetic combinations of multiplication and division.</p>
Highlights
The multiplications of two one-digit numbers (e.g., 6 x 9 = 54) and the divisions created when using the products of these multiplications as dividends and the factors as dividers (e.g., 54 : 9 = 6) are the arithmetic combinations of multiplication and division respectively (Agaliotis, 2011)
Considering that appropriate implementation of any complex task depends on the fluent use of individual structural components, it becomes obvious that students should be able to recall Arithmetic Combinations (ACs) as quickly and accurately as possible, in order to deal successfully with demanding mathematical tasks including ACs as one of their components (Baroody, Bajwa, & Eiland, 2009; Crawford, 2003)
Results of comparisons between students with Learning Disabilities (LD) (n = 39) and students with Mild Intellectual Disability (MID) (n = 14) showed that there was no significant difference in pre- intervention fluency in the use of multiplication ACs (U = 263,5, z = -.193, p = .847), while the difference between the two groups in the fluency in division ACs was marginally not significant (U = 184.0, z = -1.901, p = .057), with students with LD having higher mean scores (Table 5)
Summary
Arithmetic Combinations (ACs) are components of complex mathematical tasks (e.g., use of algorithms in the context of word problem-solving). Considering that appropriate implementation of any complex task depends on the fluent use of individual structural components, it becomes obvious that students should be able to recall ACs as quickly and accurately as possible, in order to deal successfully with demanding mathematical tasks including ACs as one of their components (Baroody, Bajwa, & Eiland, 2009; Crawford, 2003). Students with Learning Disabilities (LD) and students with Mild Intellectual Disability (MID) often have significant difficulties in learning and directly recalling the ACs, until the end of primary school or even later in life (Bouck, Bassette, Taber-Doughty, Flanagan, & Szwed, 2009; Geary, Hoard, & Nugent, 2012; Gersten, Jordan, & Flojo, 2005). Clarification of these issues would offer important information for organizing appropriate interventions for students of both categories of educational needs
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