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Our preliminary results suggest that directed actions in combination with pedagogical language promoted valid informal proofs, and that dynamic gestures played a key, mediating role.
Consistent with the predictions made by H4 and H5, players were significantly more likely to make dynamic gestures (H4) and more likely to generate correct insights and valid informal proofs (H5) after receiving verbal hints.
In support of H5, when coupling directed actions to pedagogical language, participants were more likely to produce favorable mathematics outcome measures, including expressing the insight (odds ratio = 3.1, d = 0.6, p < 0.001) and formulating a valid informal proof (odds ratio = 4.7, d = 0.9, p < 0.001).
One indicator is that pedagogical hints were found to influence insight performance directly, and to increase the production of dynamic gestures, which, as hypothesized earlier (H1), promotes mathematical insight and the formulation of valid informal proofs (H6) through a mechanism such as transduction.
Therefore, reliable and valid informal caregiver (proxy) ratings could be extremely useful in the field of dementia.
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Choose valid information.
The choice of an adequate recall period is especially important for the valid measurement of informal patient payments.
Thus, using mixing modes of data collection, specifically the introduction of a self-administrated part during a face-to-face interview, could be suitable for collecting valid data on informal patient payments.
Our review is expected to facilitate the development of future research designs for collecting valid and reliable data on informal patient payments.
959,997 respondents provided a valid answer to the question about informal caring, of whom 195,364 (20.4 %) reported that they were informal carers, with 64,416 (33.0 %) indicating that their caring commitments exceeded 20 hours per week.
However, we provide valid taxon names if possible and provisional informal names otherwise for all of the clusters in our dataset.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com