App-Based Manipulatives and Explicit Instruction to Support Division with Remainders

ABSTRACT

In theory, both virtual manipulatives and explicit instruction are viable options to support students with disabilities as they learn mathematics. This study explored the effect of a treatment package—an app-based virtual manipulative (Cuisenaire® Rods) in conjunction with explicit instruction—on students’ acquisition and generalization of solving problems involving division of whole numbers with remainders. Three middle school students with disabilities participated in this multiple baseline, multiple probe across participants single case design study. Each of the students acquired the mathematical behavior of being able to solve division with remainders problems. In other words, a functional relation existed between the intervention package of explicit instruction and the Cuisenaire® Rods app-based manipulative and students’ accuracy in solving division with remainders problems. Yet, two students failed to generalize the skill without the explicit instruction and use of the app-based manipulative.     

Comparison of computed tomography and chest radiography in the detection of rib fractures in abused infants

PURPOSE: Chest radiographs (CXR) are the standard method for evaluating rib fractures in abused infants. Computed tomography (CT) is a sensitive method to detect rib fractures. The purpose of this study was to compare CT and CXR in the evaluation of rib fractures in abused infants. METHODS: This retrospective study included all 12 abused infants identified from 1999 to 2004 who had rib fractures and both CXR and CT (8 abdomen CTs, 4 chest CTs). CT exams had been performed for clinical indications, and were obtained within one day of the CXR. Studies were reviewed by two pediatric radiologists to determine the number, locations, and approximate ages of the rib fractures. A total of 225 ribs were completely (192) or partially (33) seen by CT, and the matched ribs on CXR were used for the analysis. RESULTS: The mean patient age was 2.5 months (1.2-5.6), with seven females and five males. While 131 fractures were visualized by CT, only 79 were seen by CXR (p<.001). One patient had fractures only seen by CT. There were significantly (p<.05) more early subacute (24 vs. 4), subacute (47 vs. 26), and old fractures (4 vs. 0) seen by CT than by CXR. Anterior (42 vs. 11), anterolateral (21 vs. 12), posterolateral (9 vs. 3) and posterior (39 vs. 24) fractures were better seen by CT than by CXR (p<.01). Bilateral fractures were detected more often by CT (11) than by CXR (6). CONCLUSIONS: While this study group is small, these findings suggest that CT is better than CXR in visualizing rib fractures in abused infants.     

Time and response matching with topographically different responses

Four pigeons were exposed to several nonindependent concurrent variable-interval schedules of reinforcement. One schedule component required a keypecking response; the other component required a treadlepressing response. The birds matched the ratio of their behavior (as measured by responses and time) between the two topographically different responses to the ratio of reinforcement in those two components. When additional foods not contingent on a keypeck or treadle-press were then added, the birds matched time spent in the components to total rates of food delivered in those components; response matching was somewhat disrupted. The matching law, developed under concurrent variable-interval schedules requiring similar responses, can thus account for choice behavior involving topographically different responses.