My experience and knowledge in teaching and tutoring diverse populations at secondary, undergraduate, and graduate levels have led me to research how students learn mathematics and how to teach them effectively. This journey began by comparing teaching and learning mathematics in the US with teaching and learning mathematics in Armenia. It then delved into the pervasive issue of math anxiety and the reasons for its development, identifying a lack of skills in foundational mathematics by analyzing common mistakes students make and analyzing how students solve word problems. These lead to identifying the obstacles to learning mathematics, how to overcome the obstacles, the role of common sense in learning mathematics, and its detrimental effects on learning. Beyond this, I identified several other obstacles hindering students' mathematics progress. This thorough and comprehensive research process, which included a comparison of the pros and cons of various teaching modalities, was conducted with meticulous attention to detail, leading to the identification of a teaching modality that promises to be the most effective way of teaching. This modality has practical implications for educators, offering students a more rewarding experience in learning mathematics and instilling confidence in the validity of the findings.

Keywords: mathematics education, math anxiety, learning by rote, teaching methodology, hybrid mode, blended mode.