The effects of meta-cognitive instruction on third and sixth graders solving word problems

This study examined the differential effects of a meta-cognitive instruction, called IMPROVE, on third and sixth graders’ solution of word problems. In particular, the study focused on the solution of two kinds of word problems: with consistent and with inconsistent language. Participants were 194 Israeli students who studied in third (N = 110) and sixth (N = 84) grades. All students were administered pre- and post-tests constructed of 16 word problems with consistent and inconsistent language. About half of the students within each grade level were exposed to IMPROVE and the others studied under a ‘traditional’ teaching method. The findings indicate that at both grade levels the IMPROVE students significantly outperformed their counterparts in the control group, but third graders benefited from IMPROVE more than sixth graders. In addition, the study indicates that the gap in achievement between IMPROVE and control groups was larger on word problems with inconsistent language compared to word problems with consistent language. The theoretical and practical implications of the study are discussed.     

Chromosomal differentiation of populations of Lysapsus limellus limellus, L. l. bolivianus, and of Lysapsus caraya (Hylinae, Hylidae)

Cytogenetic analysis were done on specimens from two populations of Lysapsus limellus limellus, three of L. l. bolivianus and of one of Lysapsus caraya. All animals showed a diploid chromosomal number of 2n=24. The karyotypes of the two L. limellus subspecies were very similar, differing only by the larger amount of telomeric heterochromatin and a small pericentromeric C-band on the short arms of pair 2 in L. l. limellus specimens. The karyotype of L. caraya differed from those of the two L. limellus subspecies in terms of chromosomal morphology, C-banding pattern and location of the main NOR on chromosomes 7 and 6, respectively. The karyotype of the L. l. bolivianus population from Guajará-Mirim/RO differed from those of the other populations of the same subspecies in morphology and heterochromatin pattern of chromosomes 7 and 8. Additional NORs were detected by silver staining and confirmed by FISH in one of the homologues of pairs 1 and 8 in L. l. bolivianus and in pair 7 in L. caraya. These results suggest that a reassessment of the taxonomic status of L. limellus subspecies, especially of the L. l. bolivianus populations, may be necessary.     

Koszulity of splitting algebras associated with cell complexes

We associate to a good cell decomposition of a manifold M a quadratic algebra and show that the Koszulity of the algebra implies a restriction on the Euler characteristic of M. For a two-dimensional manifold M the algebra is Koszul if and only if the Euler characteristic of M is two.     

Hilbert series of algebras associated to directed graphs and order homology

We give a homological interpretation of the coefficients of the Hilbert series for an algebra associated with a directed graph and its dual algebra. This allows us to obtain necessary conditions for Koszulity of such algebras in terms of homological properties of the graphs. We use our results to construct algebras with a prescribed Hilbert series.     

On a class of algebras associated to directed graphs

To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Such algebras are related to factorizations of polynomials over noncommutative algebras. We also construct a basis for our algebras associated to layered graphs.