Three experiments were conducted to explore the ability of school-age children to transfer solutions to analogous problems. This research addressed the issue of how the variability of procedural features in source examples facilitates the induction of a general problem schema and, thus, promotes subsequent transfer. Children were asked to solve a series of problems analogous to Luchins's (1942) classic water jar problems. All the problems shared a common isomorphic structure and a general solution but required either similar or different specific procedures. Children who experienced problems with variant procedural features were more likely than those who experienced problems with invariant procedural features to construct a general problem schema and to solve novel problems requiring unfamiliar procedures. This research sheds light on the cognitive mechanisms involved in strategy generalization and analogical problem solving.When encountering novel problems, children, like adults, sometimes use either familiar examples or general solution principles to solve them (e.g.,

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With the advance of the research on acoustic metamaterials, the limits of passive metamaterials have been observed, which prompts the studies concerning actively tunable metamaterials with adjustable characteristic frequency bands. In this work, we present a tunable acoustic metamaterial with doublenegativity composed of periodical membranes and side holes, in which the double-negativity pass band can be controlled by an external direct-current voltage. The tension and stiffness of the periodically arranged membranes are actively controlled by electromagnets producing additional stresses, and thus, the transmission and phase velocity of the metamaterial can be adjusted by the driving voltage of the electromagnets. It is demonstrated that a tiny direct-current voltage of 6V can arise a shift of double-negativity pass band by 40% bandwidth, which exhibits that it is an easily controlled and highly tunable acoustic metamaterial, and furthermore, the metamaterial marginally causes electromagnetic interference to the surroundings.Currently, acoustic metamaterials are extensively studied owing to unprecedented characteristics, which exhibit application potentials in various fields [1][2][3][4][5][6] . However, with the development of acoustic metamaterials, the limitations of passive metamaterials have been observed. First, the characteristic frequency bands related to extraordinary acoustic performance are restricted into narrow bands induced by resonance. In addition, since the unique characteristics of metamaterials are created by artificial structures, they cannot be freely changed once the metamaterials are fabricated. Therefore, tunable acoustic metamaterials with adjustable characteristic frequency bands are urgently required treading on the heels of their counterparts in electromagnetics and optics [7][8][9][10] . Different mechanisms were adopted to realize tunable metamaterials. First, tunable features arose from nonlinear effects in acoustic metamaterials, in which the constitutive parameters could be changed with the intensities of input acoustic fields, and they were considered to be self-modulation metamaterials [11][12][13] . On the other hand, actively tunable metamaterials, which could be controlled by an external source other than input acoustic fields, were presented. As an example, by mechanically changing the volumes of Helmholtz resonators in a metamaterial, the resonant frequency was adjusted, which could change the corresponding characteristic frequency bands 11,14 . A similar method on the analogy of the split-ring resonators in electromagnetic metamaterials was introduced into acoustic metamaterials, in which the resonant frequency of a split hollow sphere was tuned by filling water into the sphere to change the volume 15 . Similarly, the equivalent sound speed could be changed by filling a fluid into the intermediate gaps of a metamaterial 16 . Generally, an external electric signal is preferred as the control signal in tuning the performance of a metamaterial. Piezoelectric materials, which...

Insulating against low-frequency sound (below 500 Hz) remains challenging despite the progress that has been achieved in sound insulation and absorption. In this work, an acoustic metamaterial based on membrane-coated perforated plates is presented for achieving sound insulation in a low-frequency range, even covering the lower audio frequency limit, 20 Hz. Theoretical analysis and finite element simulations demonstrate that this metamaterial can effectively block acoustic waves over a wide low-frequency band regardless of incident angles. Two mechanisms, non-resonance and monopolar resonance, operate in the metamaterial, resulting in a more powerful sound insulation ability than that achieved using periodically arranged multi-layer solid plates.