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Covariation and covariational reasoning are key themes in mathematics education research. Recently, these ideas have been expanded to include cases where more than two variables relate to each other, in what is termed multivariation. Building on the theoretical work that has identified different types of multivariation structures, this study explores students' reasoning about these structures. Our initial assumption that multivariational reasoning would be built on covariational reasoning appeared validated, and there were also several other aspects of reasoning employed in making sense of these structures. There were important similarities in reasoning about the different types of multivariation, as well as some nuances between them. [ABSTRACT FROM AUTHOR]

We report on results from 20 one-hour task-based interviews with 10 students enrolled in firstterm calculus. Each student participated in two interviews. The first interview included tasks designed to assess students’ ways of reasoning about fractions in static measurement scenarios (which did not involve varying quantities) and the second interview included tasks designed to assess students’ reasoning about scenarios involving quantities that co-vary. We discuss relationships between the ways students coordinated units in static situations and the ways students reasoned about co-varying quantities. The results contribute to the field’s understanding of the development of covariational reasoning and the role of constructing threelevels- of-units coordinating structures. [ABSTRACT FROM AUTHOR]

The method of experimental determination of the Fano factor in superconducting materials is based on usage of two sensor signals of a distributed readout imaging detector (DROID). In detector of this type a photon is absorbed in a superconducting layer with two superconducting tunnel junctions (STJs) at the ends. In this work it is shown, that the correlation between the two STJ signals depends on the fundamental combination of the Fano factor and the effective energy of quasiparticle formation in the superconducting material of DROID. The suggested formula for this fundamental combination depends on the energy of a primary particle, on the mean values of STJs’ signal amplitudes, and on the variances of the sum and the difference of the STJs’ signals. As this fundamental combination depends on the energy of a primary particle and on the particle interaction point, then it should depend on the local physical properties of the absorber. Independent determination of the effective energy of quasiparticle formation allows one to determine the value of the Fano factor. The important advantage of proposed method is its independence from the STJs’ electronic gains and noise. [ABSTRACT FROM AUTHOR]