Using a compiled sample of 34 broad-line active galactic nuclei (AGNs) with measured H$\beta$ time lags from the reverberation mapping (RM) method and measured bulge stellar velocity dispersions $\sigma_*$, we calculate the virial factor $f$ by assuming that the RM AGNs intrinsically obey the same $M_{\rm BH}-\sigma_*$ relation as quiescent galaxies, where $M_{\rm BH}$ is the mass of the supermassive black hole (SMBH). Considering four tracers of the velocity of the broad-line regions (BLRs), i.e., the H$\beta$ line width or line dispersion from the mean or rms spectrum, there are four kinds of the factor $f$. Using the \hb Full-width at half-maximum (FWHM) to trace the BLRs velocity, we find significant correlations between the factor $f$ and some observational parameters, e.g., FWHM, the line dispersion. Using the line dispersion to trace the BLRs velocity, these relations disappear or become weaker. It implies the effect of inclination in BLRs geometry. It also suggests that the variable $f$ in $M_{\rm BH}$ estimated from luminosity and FWHM in a single-epoch spectrum is not negligible. Using a simple model of thick-disk BLRs, we also find that, as the tracer of the BLRs velocity, H$\beta$ FWHM has some dependence on the inclination, while the line dispersion $\sigma_{\rm H\beta }$ is insensitive to the inclination. Considering the calibrated FWHM-based factor $f$ from the mean spectrum, the scatter of the SMBH mass is 0.39 dex for our sample of 34 low redshift RM AGNs. For a high redshift sample of 30 SDSS RM AGNs with measured stellar velocity dispersions, we find that the SMBH mass scatter is larger than that for our sample of 34 low redshift RM AGNs. It implies the possibility of evolution of the $M_{\rm BH}-\sigma_*$ relation from high-redshift to low-redshift AGNs.
Abstract A lack of evidence bridging the chasm between professional learning practices and commonly used, publicly available resources such as YouTube videos, remains a long‐term challenge in both research and practice. The study introduced a YouTube video club for female early childhood teachers in Hong Kong ( N = 29) to view, analyse and discuss STEM teaching videos. The participants wrote reflections and discussed with peers to exchange views on teaching content and strategies. All participants completed pre‐ and post‐intervention surveys reporting their teaching beliefs, and five participants from the experimental group were invited for individual interviews. The questionnaire survey data were analysed using statistical analysis, while the interview data were analysed through inductive thematic analysis. The study, which was pre‐post quasi‐experimental, showed that the video club enhanced teachers' beliefs and attitudes towards professional practices in early childhood education. Qualitative analysis of teacher interviews revealed benefits and constraints of using YouTube videos for professional learning. The study transformed video clubs into a web‐mediated mode using YouTube, Google Classroom and Zoom. The results have implications for the design and implementation of video clubs in teacher learning programmes. Practitioner notes What is already known about this topic As the largest and most popular video‐sharing service, YouTube hosts a wide range of freely accessible video types that can be used for professional education in various disciplines. There are worldwide efforts to improve early childhood teachers' ability to teach STEM. Video recordings of classroom observations have been used in the context of video clubs since the 1990s to support teacher learning. What this paper adds We introduced the design of a YouTube video club focusing on STEM teaching, in which the participants were asked to view and analyse video excerpts, write reflection as guided by the facilitator and discuss with peers in groups to exchange views on the teaching content and strategies demonstrated in the video excerpts. We extended prior research on video clubs by transforming video clubs into a fully web‐mediated mode using the technologies of YouTube, Google Classroom and Zoom. This design‐based study evaluated the design of YouTube video club in terms of affording and constraining teachers' professional learning in STEM education. Implications for practice and/or policy Results of this study can inform the design of teacher learning programmes using YouTube videos. YouTube videos can be used in web‐mediated video clubs to enhance teachers' professional beliefs, as well as the pedagogical content knowledge in specific learning domains (eg, STEM). More enhancements should be made to optimize the design of YouTube video club.
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