This study analyzed the variation in teachers' mathematical educational values between distance and traditional face-to-face teaching. Enabled by the unique circumstances of the COVID-19 pandemic, the research explored the impact of remote teaching on primary and secondary mathematics education in Hong Kong. An online survey, completed by 109 practicing mathematics teachers, assessed their pre-existing educational values and their adaptability to the shift towards distance teaching, as well as their teaching practices. Findings indicated that despite the multitude of digital teaching tools, the implementation of most mathematical educational values was more restricted in distance teaching. Rationalism and Control were prioritized, reflecting the challenges of assessing student progress remotely. Among the 13 values identified, Fun and Engagement, along with Thinking and Problem-solving, Achievement, and Reasoning, were significantly diminished, highlighting the shortcomings of one-way and superficial concept-based teaching. The study concludes that distance teaching, when completely isolated from traditional methods, may not offer the benefits suggested in the literature, impacting student engagement, motivation, and higher-order thinking. This necessitates a unique curriculum development model to effectively incorporate blended and self-directed learning.