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This paper proposes an enhanced algorithm to estimate the differential code biases (DCB) on three frequencies of the BeiDou Navigation Satellite System (BDS) satellites. By forming ionospheric observables derived from uncombined precise point positioning and geometry-free linear combination of phase-smoothed range, satellite DCBs are determined together with ionospheric delay that is modeled at each individual station. Specifically, the DCB and ionospheric delay are estimated in a weighted least-squares estimator by considering the precision of ionospheric observables, and a misclosure constraint for different types of satellite DCBs is introduced. This algorithm was tested by GNSS data collected in November and December 2013 from 29 stations of Multi-GNSS Experiment (MGEX) and BeiDou Experimental Tracking Stations. Results show that the proposed algorithm is able to precisely estimate BDS satellite DCBs, where the mean value of day-to-day scattering is about 0.19 ns and the RMS of the difference with respect to MGEX DCB products is about 0.24 ns. In order to make comparison, an existing algorithm based on IGG: Institute of Geodesy and Geophysics, China (IGGDCB), is also used to process the same dataset. Results show that, the DCB difference between results from the enhanced algorithm and the DCB products from Center for Orbit Determination in Europe (CODE) and MGEX is reduced in average by 46 % for GPS satellites and 14 % for BDS satellites, when compared with DCB difference between the results of IGGDCB algorithm and the DCB products from CODE and MGEX. In addition, we find the day-to-day scattering of BDS IGSO satellites is obviously lower than that of GEO and MEO satellites, and a significant bias exists in daily DCB values of GEO satellites comparing with MGEX DCB product. This proposed algorithm also provides a new approach to estimate the satellite DCBs of multiple GNSS systems. [ABSTRACT FROM AUTHOR]

This paper explores written calculation methods for division used by pupils in England (n = 276) and the Netherlands (n = 259) at two points in the same school year. Informal strategies are analysed and progression identified towards more structured procedures that result from different teaching approaches. Comparison of the methods used by year 5 (Group 6) pupils in the two countries shows greater success in the Dutch approach, which is based on careful progression from informal strategies to more structured and efficient procedures. This success is particularly notable for the girls in the sample. For the English pupils, whose written solutions largely involved the traditional algorithm, the discontinuity between the formal computation procedure and informal solution strategies presents difficulties. [ABSTRACT FROM AUTHOR]