Problem Solving the Hungarian Way

Lajos Pósa (pronounced Posha) is one of the most prominent mathematics educators in Hungary.The authors introduce readers to the Pósa method for teaching mathematics, an approach consistent withexploratory methods promoted in the United States. The authors present two scenarios (with extensions)that were posed during the workshop, both with different strategies and goals

Diet and Energy-Sensing Inputs Affect TorC1-Mediated Axon Misrouting but Not TorC2-Directed Synapse Growth in a Drosophila Model of Tuberous Sclerosis

The Target of Rapamycin (TOR) growth regulatory system is influenced by a number of different inputs, including growth factor signaling, nutrient availability, and cellular energy levels. While the effects of TOR on cell and organismal growth have been well characterized, this pathway also has profound effects on neural development and behavior. Hyperactivation of the TOR pathway by mutations in the upstream TOR inhibitors TSC1 (tuberous sclerosis complex 1) or TSC2 promotes benign tumors and neurological and behavioral deficits, a syndrome known as tuberous sclerosis (TS). In Drosophila, neuron-specific overexpression of Rheb, the direct downstream target inhibited by Tsc1/Tsc2, produced significant synapse overgrowth, axon misrouting, and phototaxis deficits. To understand how misregulation of Tor signaling affects neural and behavioral development, we examined the influence of growth factor, nutrient, and energy sensing inputs on these neurodevelopmental phenotypes. Neural expression of Pi3K, a principal mediator of growth factor inputs to Tor, caused synapse overgrowth similar to Rheb, but did not disrupt axon guidance or phototaxis. Dietary restriction rescued Rheb-mediated behavioral and axon guidance deficits, as did overexpression of AMPK, a component of the cellular energy sensing pathway, but neither was able to rescue synapse overgrowth. While axon guidance and behavioral phenotypes were affected by altering the function of a Tor complex 1 (TorC1) component, Raptor, or a TORC1 downstream element (S6k), synapse overgrowth was only suppressed by reducing the function of Tor complex 2 (TorC2) components (Rictor, Sin1). These findings demonstrate that different inputs to Tor signaling have distinct activities in nervous system development, and that Tor provides an important connection between nutrient-energy sensing systems and patterning of the nervous system

Problem Solving the Hungarian Way (Part 2) (pp. 9--15)

Lajos Posa (pronounced Posha) is one of the most prominent mathematics educators in Hungary. The authors introduce readers to the Posa's technique of developing numerous methods as a means to foster student mathematical understanding. The authors illustrate the approach through exploration of multiple solution strategies for the 1000 square task