Kronecker Coefficients For Some Near-Rectangular Partitions

We give formulae for computing Kronecker coefficients occurring in the expansion of $s_{\mu}*s_{\nu}$, where both $\mu$ and $\nu$ are nearly rectangular, and have smallest parts equal to either 1 or 2. In particular, we study $s_{(n,n-1,1)}*s_{(n,n)}$, $s_{(n-1,n-1,1)}*s_{(n,n-1)}$, $s_{(n-1,n-1,2)}*s_{(n,n)}$, $s_{(n-1,n-1,1,1)}*s_{(n,n)}$ and $s_{(n,n,1)}*s_{(n,n,1)}$. Our approach relies on the interplay between manipulation of symmetric functions and the representation theory of the symmetric group, mainly employing the Pieri rule and a useful identity of Littlewood. As a consequence of these formulae, we also derive an expression enumerating certain standard Young tableaux of bounded height, in terms of the Motzkin and Catalan numbers

Anticipatory adjustments to being picked up in infancy

Anticipation of the actions of others is often used as a measure of action understanding in infancy. In contrast to studies of action understanding which set infants up as observers of actions directed elsewhere, in the present study we explored anticipatory postural adjustments made by infants to one of the most common adult actions directed to them - picking them up. We observed infant behavioural changes and recorded their postural shifts on a pressure mat in three phases: (i) a prior Chat phase, (ii) from the onset of Approach of the mother's arms, and (iii) from the onset of Contact. In Study 1, eighteen 3-month-old infants showed systematic global postural changes during Approach and Contact, but not during Chat. There was an increase in specific adjustments of the arms (widening or raising) and legs (stiffening and extending or tucking up) during Approach and a decrease in thrashing/general movements during Contact. Shifts in postural stability were evident immediately after onset of Approach and more slowly after Contact, with no regular shifts during Chat. In Study 2 we followed ten infants at 2, 3 and 4 months of age. Anticipatory behavioural adjustments during Approach were present at all ages, but with greater differentiation from a prior Chat phase only at 3 and 4 months. Global postural shifts were also more phase differentiated in older infants. Moreover, there was significantly greater gaze to the mother's hands during Approach at 4 months. Early anticipatory adjustments to being picked up suggest that infants' awareness of actions directed to the self may occur earlier than of those directed elsewhere, and thus enable infants' active participation in joint actions from early in life

Teachers’ perceptions of lessons using computer assisted language learning

The present study was designed to investigate the teachers’ perceptions of CALL lessons. The objectives of this study are to find out the problems faced by the teachers when conducting CALL lessons, to identify the perceptions teachers have on such lessons and also to investigate teachers’ perceptions of the effectiveness of the lessons using CALL on students. Questionnaires were distributed to 16 teachers who are currently teaching English at secondary schools in Johor Bahru. The data collected were analyzed using qualitative data. The problems identified in using CALL lessons were problems with facilities and problems with teachers’ attitudes. However, teachers had positive perceptions of CALL lessons as it helps teachers to attract students’ attention in the classroom and CALL lessons promote enhanced language acquisition