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Invention activities are Productive Failure activities in which students attempt (and often fail) to invent methods that capture deep properties of a construct before being taught expert solutions. The current study evaluates the effect of scaffolding on the invention processes and outcomes, given that students are not expected to succeed in their inquiry and that all students receive subsequent instruction. While socio-cognitive theories of learning advocate for scaffolding in inquiry activities, reducing students' agency, and possibly their failure rate, may be counter-productive in this context. Two Invention activities related to data analysis concepts were given to 87 undergraduate students in a first-year physics lab course using an interactive learning environment. Guided Invention students outperformed Unguided Invention students on measures of conceptual understanding of the structures of the constructs in an assessment two months after the learning period. There was no effect, however, on measures of procedural knowledge or conceptual understanding of the overall goals of the constructs. In addition, Guided Invention students were more likely to invent multiple methods during the Invention process. These results suggest that the domain-general scaffolding in Invention activities, when followed by instruction, can help students encode deep features of the domain and build on their failures during Productive Failure. These results further suggest not all failures are equally productive, and that some forms of support help students learn form their failed attempts.

A ring resonator based 4 channel wavelength division multiplexing (WDM) receiver with polarization diversity is demonstrated at 10 Gb/s per channel. By forming a waveguide loop between the two output ports of a polarization splitter-rotator (PSR), the input signals in the quasi-transverse-electric (quasi-TE) and the quasi-transverse-magnetic (quasi-TM) polarizations can be demultiplexed by the same set of ring resonator filters, thus reducing the number of required channel control circuits by half compared to methods which process the two polarizations individually. Large signal measurement results indicate that the design can tolerate a signal delay of up to 30% of the unit interval (UI) between the two polarizations, which implies that compensating for manufacturing variability with optical delay lines on chip is not necessary for a robust operation. The inter-channel crosstalk is found negligible down to 0.4nm (50 GHz) spacing, at which point the adjacent channel isolation is 17 dB, proving the design's compatibility for dense WDM application.