The six core competencies of mathematics in vocational schools are becoming increasingly important in mathematics learning. The reverse teaching design of vocational school mathematics, which focuses on core competencies, precisely grasps the internal logic of knowledge from a holistic perspective, and designs it on a unit by unit basis. The design process is to infer the starting point from the endpoint. Therefore, how to use reverse thinking in teaching design research in vocational school mathematics teaching under the background of core competencies will be the main content of this article.

The journey towards better healthcare sustainability in Asian nations demands a comprehensive investigation into the impact of urban governance, poverty, and female literacy on infant mortality rates. This study undertakes a rigorous exploration of these key factors to pave the way for evidence-based policy interventions, utilizing data from a panel of six selected Asian countries: Pakistan, China, India, Indonesia, Malaysia, and the Philippines, spanning the years 2001 to 2020. The findings reveal that adequate sanitation facilities, higher female literacy rates, and sustained economic growth contribute to a reduction in infant mortality. Conversely, increased poverty levels and limited women’s autonomy exacerbate the infant mortality rates observed in these countries. The Granger causality analysis validates the reciprocal relationship between urban sanitation (and poverty) and infant mortality rates. Furthermore, the study establishes a causal relationship where female literacy rates Granger-cause infant mortality rates, and conversely, infant mortality rates Granger-cause women’s autonomy in these countries. The variance decomposition analysis indicates that sustained economic growth, improved female literacy rates, and enhanced women’s empowerment will likely impact infant mortality rates in the coming decade. Consequently, in low-income regions where numerous children face potentially hazardous circumstances, it is imperative to allocate resources towards establishing and maintaining accessible fundamental knowledge regarding sanitation services, as this will aid in reducing infant mortality rates.

With the advent of the era of globalized economy, more attention should be paid to the training mode of comprehensive English literacy in colleges and universities in teaching. Therefore, how to cultivate and improve students' higher-level teaching methods in the context of ecolinguistics, so as to improve the quality of English teaching, is the current focus of English teaching in colleges and universities. By summarizing the basic concepts of ecolinguistics, this paper studies effective measures to improve the quality of linguistics teaching in colleges and universities, and comprehensively improves the quality and efficiency of English language teaching in colleges and universities under the background of ecolinguistics.

This paper aims to explore the impact of V-Girls APP on the improvement of female college students' Health literacy and its mechanism. Using a questionnaire survey method, the survey subjects were female students from a certain university. The results showed that using the V-Girls app can significantly improve the health knowledge level, health behavior habits, and mental health status of female college students. Further analysis reveals that the impact mechanisms of V-Girls APP mainly include cognitive mechanisms, social support mechanisms, and behavioral guidance mechanisms. The results of this study provide new ways and ideas for improving female college students' Health literacy.