Equation structure and the meaning of the equal sign: The impact of task selection in eliciting elementary students’ understandings

This paper reports results from a written assessment given to 290 third-, fourth-, and fifth-grade students prior to any instructional intervention. We share and discuss students’ responses to items addressing their understanding of equation structure and the meaning of the equal sign. We found that many students held an operational conception of the equal sign and had difficulty recognizing underlying structure in arithmetic equations. Some students, however, were able to recognize underlying structure on particular tasks. Our findings can inform early algebra efforts by highlighting the prevalence of the operational view and by identifying tasks that have the potential to help students begin to think about equations in a structural way at the very beginning of their early algebra experiences.     

Wheels within wheels

A simple means of representing the structure of all strongly connected directed graphs is developed and applied to a certain problem involving the construction of “toll booths”.     

Optimal measurement points for program frequency counts

A procedure recently devised by A. Nahapetian, for reducing the number of measurements needed to determine all the execution frequencies in a computer program, is shown to be optimal, by interpreting the procedure in a new way.Research supported by Norges Almenvitenskapelige Forskningsråd and the U.S. Office of Naval Research. Reproduction in whole or in part is permitted for any purposes of the U. S. Government.     

A short proof of Darboux's lemma

Elementary asymptotic methods suffice to establish asymptotic series for the coefficients of analytic functions with algebraic singularities.     

Investigating the vortex melting phenomenon in BSCCO crystals using magneto-optical imaging technique

Using a novel differential magneto-optical imaging technique we investigate the phenomenon of vortex lattice melting in crystals of Bi₂Sr₂CaCu₂O₈ (BSCCO). The images of melting reveal complex patterns in the formation and evolution of the vortex solid-liquid interface with varying field (H)/temperature (T). We believe that the complex melting patterns are due to a random distribution of material disorder/inhomogeneities across the sample, which create fluctuations in the local melting temperature or field value. To study the fluctuations in the local melting temperature/field, we have constructed maps of the melting landscape T _m(H, r), viz., the melting temperature (T _m) at a given location (r) in the sample at a given field (H). A study of these melting landscapes reveals an unexpected feature: the melting landscape is not fixed, but changes rather dramatically with varying field and temperature along the melting line. It is concluded that the changes in both the scale and shape of the landscape result from the competing contributions of different types of quenched disorder which have opposite effects on the local melting transition.     

Energy dependence of multiplicity in proton-nucleus collisions and models of multiparticle production

This is a continuation of our earlier investigation (Gurtuet al 1974Phys. Lett. 50 B 391) on multiparticle production in proton-nucleus collisions based on an exposure of emulsion stack to 200 GeV/c beam at the NAL. It is found that the ratioR _em = 〈n _s〉/〈n _ch〉, where 〈n _ch〉 is the charged particle multiplicity in pp-collisions, increases slowly from about 1 at 10 GeV/c to 1·6 at 68 GeV/c and attains a constant value of 1·71 ± 0·04 in the region 200 to 8000 GeV/c. Furthermore,R _em = 1·71 implies an effectiveA-dependence ofR _A =A ^0.18,i.e., a very weak dependence. Predictions ofR _em on various models are discussed and compared with the emulsion data. Data seem to favour models of hadron-nucleon collisions in which production of particles takes place through adouble step mechanism,e.g., diffractive excitation, hydrodynamical and energy flux cascade as opposed to models which envisage instantaneous production.     

Constructing Graphical Representations: Middle Schoolers' Intuitions and Developing Knowledge About Slope and Y‐intercept

Middle‐school students are expected to understand key components of graphs, such as slope and y‐intercept. However, constructing graphs is a skill that has received relatively little research attention. This study examined students' construction of graphs of linear functions, focusing specifically on the relative difficulties of graphing slope and y‐intercept. Sixth‐graders' responses prior to formal instruction in graphing reveal their intuitions about slope and y‐intercept, and seventh‐ and eighth‐graders' performance indicates how instruction shapes understanding. Students' performance in graphing slope and y‐intercept from verbally presented linear functions was assessed both for graphs with quantitative features and graphs with qualitative features. Students had more difficulty graphing y‐intercept than slope, particularly in graphs with qualitative features. Errors also differed between contexts. The findings suggest that it would be valuable for additional instructional time to be devoted to y‐intercept and to qualitative contexts.     

Discrete element modeling of a Mars Exploration Rover wheel in granular material

Three-dimensional discrete element method (DEM) simulations were developed for the Mars Exploration Rover (MER) mission to investigate: (1) rover wheel interactions with martian regolith; and (2) regolith deformation in a geotechnical triaxial strength cell (GTSC). These DEM models were developed to improve interpretations of laboratory and in situ rover data, and can simulate complicated regolith conditions. A DEM simulation was created of a laboratory experiment that involved a MER wheel digging into lunar regolith simulant. Sinkage and torques measured in the experiment were compared with those predicted numerically using simulated particles of increasing shape complexity (spheres, ellipsoids, and poly-ellipsoids). GTSC simulations, using the same model regolith used in the MER simulations, indicate a peak friction angle of approximately 37–38° compared to internal friction angles of 36.5–37.7° determined from the wheel digging experiments. Density of the DEM regolith was 1820 kg/m³ compared to 1660 kg/m³ for the lunar simulant used in the wheel digging experiment indicating that the number of grain contacts and grain contact resistance determined bulk strength in the DEM simulations, not density. An improved correspondence of DEM and actual test regolith densities is needed to simulate the evolution of regolith properties as density changes.     

Tri-partite complex for axonal transport drug delivery achieves pharmacological effect

Background

Targeted delivery of pharmaceutical agents into selected populations of CNS (Central Nervous System) neurons is an extremely compelling goal. Currently, systemic methods are generally used for delivery of pain medications, anti-virals for treatment of dermatomal infections, anti-spasmodics, and neuroprotectants. Systemic side effects or undesirable effects on parts of the CNS that are not involved in the pathology limit efficacy and limit clinical utility for many classes of pharmaceuticals. Axonal transport from the periphery offers a possible selective route, but there has been little progress towards design of agents that can accomplish targeted delivery via this intraneural route. To achieve this goal, we developed a tripartite molecular construction concept involving an axonal transport facilitator molecule, a polymer linker, and a large number of drug molecules conjugated to the linker, then sought to evaluate its neurobiology and pharmacological behavior.

Results

We developed chemical synthesis methodologies for assembling these tripartite complexes using a variety of axonal transport facilitators including nerve growth factor, wheat germ agglutinin, and synthetic facilitators derived from phage display work. Loading of up to 100 drug molecules per complex was achieved. Conjugation methods were used that allowed the drugs to be released in active form inside the cell body after transport. Intramuscular and intradermal injection proved effective for introducing pharmacologically effective doses into selected populations of CNS neurons. Pharmacological efficacy with gabapentin in a paw withdrawal latency model revealed a ten fold increase in half life and a 300 fold decrease in necessary dose relative to systemic administration for gabapentin when the drug was delivered by axonal transport using the tripartite vehicle.

Conclusion

Specific targeting of selected subpopulations of CNS neurons for drug delivery by axonal transport holds great promise. The data shown here provide a basic framework for the intraneural pharmacology of this tripartite complex. The pharmacologically efficacious drug delivery demonstrated here verify the fundamental feasibility of using axonal transport for targeted drug delivery.