Two -way direction of influence in mother-infant interaction as denoted by concurrent reciprocal learning processes

This series of 5 single-subject studies used the operant conditioning paradigm to investigate, within the two-way influence process, how (a) contingent infant attention can reinforce maternal verbal behaviors during a period of mother-infant interaction and under subsequent experimental manipulation. Differential reinforcement was used to determine if it is possible that an infant attending to the mother (denoted by head-turns towards the image of the mother plus eye contact) increases (reinforces) the mother's verbal response (to a cue from the infant) upon which the infant behavior is contingent. There was also (b) an evaluation during the contrived parent-infant interaction for concurrent operant learning of infant vocal behavior via contingent verbal responding (reinforcement) implemented by the mother. Further, it was noted (c) whether or not the mother reported being aware that her responses were influenced by the infant's behavior. Findings showed: the operant conditioning of the maternal verbal behaviors were reinforced by contingent infant attention; and the operant conditioning of infant vocalizations was reinforced by contingent maternal verbal behaviors. No parent reported (1) being aware of the increase in their verbal response reinforced during operant conditioning of parental behavior nor a decrease in those responses during the DRA reversal phase, or (2) noticing a contingency between infant's and mother's response. By binomial 1-tail tests, the verbal-behavior patterns of the 5 mothers were conditioned by infant reinforcement (p < 0.02) and, concurrently, the vocal-response patterns of the 5 infants were conditioned by maternal reinforcement (p < 0.02). A program of systematic empirical research on the determinants of concurrent conditioning within mother-child interaction may provide a way to evaluate the differential effectiveness of interventions aimed at improving parent-child interactions. The work conducted in the present study is one step in this direction. ^

Rank and k-nullity of contact manifolds

We prove that the dimension of the 1-nullity distribution N(1) on a closed Sasakian manifold M of rankl is at least equal to 2l−1 provided that M has an isolated closed characteristic. The result is then used to provide some examples of k-contact manifolds which are not Sasakian. On a closed, 2n+1-dimensional Sasakian manifold of positive bisectional curvature, we show that either the dimension of N(1) is less than or equal to n+1 or N(1) is the entire tangent bundle TM. In the latter case, the Sasakian manifold Mis isometric to a quotient of the Euclidean sphere under a finite group of isometries. We also point out some interactions between k-nullity, Weinstein conjecture, and minimal unit vector fields.

The effect of reciprocal mapping on high-risk sixth-grade students' social studies achievement

Reading deficits in students in Grades 4 to 12 are evident in American schools. Informational text is particularly difficult for students. This quasi-experimental study (N=138) investigated sixth-grade students' achievement in social studies using the Reciprocal Mapping instructional routine, compared to sixth-grade students' achievement taught with a traditional approach. The Reciprocal Mapping instructional routine incorporated explicit instruction in text structure using graphic organizers. Students created their own graphic organizers and used them to write about social studies content. The comparison group used a traditional approach, students' reading the textbook and answering questions. Students for this study included sixth-graders in the seven sixth-grade classrooms in two public schools in a small, rural south Florida school district. A focus of this study was to determine the helpfulness of the intervention for at-risk readers. To determine students considered to be at-risk, the researcher used data from the reading portion of the Florida Comprehensive Assessment Test (FCAT), 2011-2012, that considers Level 1 and 2 as at-risk readers. The quasi-experimental study used a pretest-posttest control group design, with students assigned to treatment groups by class. Two teachers at the two rural sites were trained on the Reciprocal Mapping instructional routine and taught students in both the experimental and control groups for an equivalent amount of time over a 5-week period. Results of the 3 x 2 factorial ANCOVA found a significant positive difference favoring the experimental group's social studies achievement as compared to that of the comparison group as measured by the pre/post unit test from the social studies series (McGraw-Hill, 2013), when controlling for initial differences in students' reading FCAT scores. Interactions for high-risk struggling readers were investigated using the significance level p < .05. Due to no significant interaction the main effects of treatment were interpreted. The pretest was used as a covariate and the multivariate analysis was found to be significant. Therefore, analysis of covariance was run on each of the dependent variable as a follow-up. Reciprocal Mapping was found to be significant in posttest scores, independent of gender and level of risk, and while holding the pretest scores constant. Findings showed there was a significant difference in the performance of the high-risk reading students taught with the Reciprocal Mapping intervention who scored statistically better than students in the control group. Further study findings showed that teacher fidelity of implementation of the treatment had a statistically significant relationship in predicting posttest scores when controlling for pretest scores. Study results indicated that improving students' use of text structure through the Reciprocal Mapping instructional routine positively supported sixth-grade students' social studies achievement.