Learning events in the life of a community of mathematics educators

The paper examines some characteristics of learning events of a community of mathematics educators. Participation in the community entailed gaining familiarity with agreed upon conventions, goals, and forms of communication. The case discussed herein is an attempt to convey the complexities underlying learning in such a community through (re)negotiation of practices and goals. The notion ofreflective discourse is borrowed to describe a group discussion involving collective reflection that constituted an occasion for meaningful learning.     

Relations between Types of Reasoning and Computational Representations

This paper examines the idea that particular representations differentially support and enhance different cognitive processes, in particular different types of reasoning. Five case studies were conducted consisting of detailed observations of pairs of middle-school students interacting with a computer-based learning environment. The software environment, called NumberSpeed, deals with kinematics concepts by having students construct various motion scenarios by adjusting numerical motion parameters: position, velocity and acceleration. NumberSpeed provides feedback about the student-specified motion using two representations: the motion representation and the number-lists representation. Two distinct types of reasoning were recognized in students’ learning while interacting with NumberSpeed: (1) model-based reasoning and (2) constraint-based reasoning. These two types of reasoning are characterized in detail and their roles in problem-solving are analyzed. A cross-analysis between the types of reasoning and the use of particular NumberSpeed representations reveals a correlation between type of reasoning and representational choice. These findings are explained by analyzing the representations’ characteristics and the ways they may differentially support and enhance particular types of reasoning.     

Students' Verification Strategies for Combinatorial Problems

We focus on a major difficulty in solving combinatorial problems, namely, on the verification of a solution. Our study aimed at identifying undergraduate students' tendencies to verify their solutions, and the verification strategies that they employ when solving these problems. In addition, an attempt was made to evaluate the level of efficiency of the students' various verification strategies in terms of their contribution to reaching a correct solution. 14 undergraduate students, who had taken at least 1 course in combinatorics, participated in the study. None of the students had prior direct learning experience with combinatorial verification strategies. Data were collected through interviews with individual or pairs of participants as they solved, 1 by 1, 10 combinatorial problems. 5 types of verification strategies were identified, 2 of which were more frequent and more helpful than others. Students' verifications proved most efficient in terms of reaching a correct solution when they were informed that their solution was incorrect. Implications for teaching and learning combinatorics are discussed.     

Spectro Analytical,Computational and In Vitro Biological Studies of Novel Substituted Quinolone Hydrazone and it’s Metal Complexes

Some novel transition metal [Cu (II), Ni (II) and Co (II)] complexes of nalidixic acid hydrazone have been prepared and characterized by employing spectro-analytical techniques viz: elemental analysis, ¹H-NMR, Mass, UV–Vis, IR, TGA-DTA, SEM-EDX, ESR and Spectrophotometry studies. The HyperChem 7.5 software was used for geometry optimization of title compound in its molecular and ionic forms. Quantum mechanical parameters, contour maps of highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO) and corresponding binding energy values were computed using semi empirical single point PM3 method. The stoichiometric equilibrium studies of metal complexes carried out spectrophotometrically using Job’s continuous variation and mole ratio methods inferred formation of 1:2 (ML₂) metal complexes in respective systems. The title compound and its metal complexes screened for antibacterial and antifungal properties, exemplified improved activity in metal complexes. The studies of nuclease activity for the cleavage of CT- DNA and MTT assay for in vitro cytotoxic properties involving metal complexes exhibited high activity. In addition, the DNA binding properties of Cu (II), Ni (II) and Co (II) complexes investigated by electronic absorption and fluorescence measurements revealed their good binding ability and commended agreement of K_b values obtained from both the techniques. Molecular docking studies were also performed to find the binding affinity of synthesized compounds with DNA (PDB ID: 1N37) and “Thymidine phosphorylase from E.coli” (PDB ID: 4EAF) protein targets.     

Micropeptins from Microcystis sp. collected in Kabul Reservoir,Israel

Three new micropeptins, micropeptin KR1030, KR1002 and KR998 and the known microcyclamide GL546A were isolated from the extract of Microcystis sp. bloom material collected in Kabul Reservoir, Israel. The planar structures of the compounds were determined by homonuclear and inverse-heteronuclear 2D-NMR techniques as well as high-resolution mass spectrometry. The absolute configuration of the asymmetric centres of the amino acids was studied using Marfey's method for HPLC. The inhibitory activity of the compounds was determined for the serine proteases: trypsin, chymotrypsin and elastase.