This document presents three main strategies that form two closely related teaching methodologies: special techniques, peer responsibility, and joint projects. The first two strategies combine together to form the first teaching methodology, Special Techniques and Peer Responsibility Teaching Method (STAPRM), and all three strategies combine together to form the second teaching methodology, Special Techniques and Peer Responsibility Teaching Method with Joint Projects (STAPRMJ). Both STAPRM and STAPRMJ reduce anxiety and improve standards in any course in which they are used. They also maximize student participation and student interaction during the course as well as student-instructor interaction. This paper discusses the 23 techniques that form the Special Techniques, some of which form a new style of teaching developed to optimize time in the classroom and the structure and organization of peer responsibility. All the examples and discussions are related to mathematics courses; however, these teaching methodologies can also be used in many other disciplines. (KHR)