The Effect of Funnix Math on Pre-kindergarten Student\u27s Achievement in Mathematics

It is imperative that mathematics education in the United States be effective and comprehensive in nature. Mathematical skills are a necessary component to functional and independent living. Much debate has aroused over which instructional methodologies to adopt, but the research clearly supports the use of explicit instruction. Direct Instruction is an expository approach to learning, which encompasses critical design principles that enable it to be sequential and thorough. Funnix Math is the newest program, which utilizes this methodology. The present study investigates the efficacy of Funnix Math on the pre-kindergarten population. The results of this study contradict previous research on the Direct Instruction model

Water activity in lamellar stacks of lipid bilayers: "Hydration forces" revisited

Water activity and its relationship with interactions stabilising lamellar stacks of mixed lipid bilayers in their fluid state are investigated by means of osmotic pressure measurements coupled with small-angle x-ray scattering. The (electrically-neutral) bilayers are composed of a mixture in various proportions of lecithin, a zwitterionic phospholipid, and Simulsol, a non-ionic cosurfactant with an ethoxylated polar head. For highly dehydrated samples the osmotic pressure profile always exhibits the "classical" exponential decay as hydration increases but, depending on Simulsol to lecithin ratio, it becomes either of the "bound" or "unbound" types for more water-swollen systems. A simple thermodynamic model is used for interpreting the results without resorting to the celebrated but elusive "hydration forces"Comment: 24 pages, 12 figures. Accepted for publication in The European Physical Journal

The Formation and Properties of Thin Lipid Membranes from HK and LK Sheep Red Cell Lipids

Lipids were obtained from high potassium (HK) and low potassium (LK) sheep red cells by sequential extraction of the erythrocytes with isopropanol-chloroform, chloroform-methanol-0.1 M KCl, and chloroform. The extract contained cholesterol and phospholipid in a molar ratio of 0.8:1.0, and less than 1% protein contaminant. Stable thin lipid membranes separating two aqueous compartments were formed from an erythrocyte lipid-hydrocarbon solution, and had an electrical resistance of ∼108 ohm-cm2 and a capacitance of 0.38–0.4 µf/cm2. From the capacitance values, membrane thickness was estimated to be 46–132 A, depending on the assumed value for the dielectric constant (2.0–4.5). Membrane voltage was recorded in the presence of ionic (NaCl and/or KCl) concentration gradients in the solutions bathing the membrane. The permeability of the membrane to Na+, K+, and Cl- (expressed as the transference number, Tion) was computed from the steady-state membrane voltage and the activity ratio of the ions in the compartments bathing the membrane. TNa and TK were approximately equal (∼0.8) and considerably greater than TCl (∼0.2). The ionic transference numbers were independent of temperature, the hydrocarbon solvent, the osmolarity of the solutions bathing the membranes, and the cholesterol content of the membranes, over the range 21–38°C. The high degree of membrane cation selectivity was tentatively attributed to the negatively charged phospholipids (phosphatidylethanolamine and phosphatidylserine) present in the lipid extract