A lack of mathematics facility prevents many students from pursuing majors in science, technology, engineering, and mathematics. Research revealed that teaching methodology is crucial for success in any course. This dissertation focuses on learners' experiences in a flipped instructional model and a customized direct instructional model. Although the flipped instruction model is gaining popularity among teachers of secondary and post-secondary schools due to permeating access to the internet and digital technology, especially during the recent global COVID-19 pandemic, the flipped teaching method is faced with resistance from both instructors and students. The COVID-19 global pandemic has inspired the education community to rethink the way we teach college courses by promoting active learning strategies for equitable learning, including all variants of blended learning or hybrid instruction. This study investigates the prospects of pedagogical methods (flipped instructional model vs direct instructional model) on college students' course satisfaction, mastery learning, and long-term academic achievement. In total, 90 undergraduate students participated in the study; 33 students were taught precalculus using flipped instruction, and 57 received direct instruction. The sequential explanatory mixed methods design (Creswell & Clark, 2007; Teddlie & Tashakkori, 2009) was used to determine predictive abilities of the instructional methods on learning and achievement, and course satisfaction, after controlling for the learner's cognitive and affective background characteristics. The dissertation further explores students' perceptions of the factors affecting their motivation to learn and succeed in Precalculus regardless of the type of teaching method they received. This study considered the effects of undergraduates' mindsets and motivation beliefs, teacher and teaching qualities, experiential behavior of the student, the curriculum, and other factors on their academic performances in introductory college mathematics by collecting, analyzing, and interpreting data from self-reporting surveys, semi-structured interviews, analytical memos of classroom observations, Precalculus and Calculus1 grades, course evaluation, and artifacts of educational activities. The findings indicated that the flipped instructional model supports short-term learning achievement, while the direct instructional model instruction facilitates learning retention. Course satisfaction ratings were comparable. The study also identified three types of mindsets (i.e., a fixed, a growth, or a mixed mindset) and fourteen factors that impacted achievement in the course. This study found that the quality of the learning space, course organization and structure, student's aptitude based on his/her background knowledge, mindsets, motivation beliefs, and teacher's expertise and relationship with the students impacted learning in a course. The ability to harmonize the identified factors affecting student motivation to learn is the culmination of effective learning and success. For example, this dissertation study revealed that mindset beliefs were not diametrical as reported in the literature; rather a student might hold a fixed mindset belief on a topic and become enthusiastic and cognitively engaged on the next. The study's findings provide educators and researchers with evidence to evaluate the implications of students' perceptions of factors affecting their motivation to learn and to succeed in introductory mathematics. The attainment of desired learning outcomes is possible if educators spend time creating quality educational activities that can stimulate the learners' interest to learn, then provide necessary cues to boost their motivation for continued cognitive engagement and participation, as well as guide and support the students to accomplish their desired achievement goals. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]