Math anxiety negatively affects student learning and academic performance. Students with high math anxiety exhibit physical, mental, and emotional symptoms. As a result, they tend to avoid mathematics and mathematics-related situations, perform poorly, and exhibit deficiencies in working memory. Research studies have shown that inquiry-based learning (IBL) develops confidence, conceptual understanding, and self-efficacy. Using the hypothesis that IBL will remediate math anxiety, in this research study, I explored whether IBL decreases Calculus I students' math anxiety and how IBL compares to lecture-based instruction in this regard. I employed an explanatory sequential mixed methods design to investigate three scopes of research questions--quantitative, qualitative, and mixed--comparing the math anxiety of Calculus I students who experienced inquiry-based instruction and those who experienced lecture-based instruction. The quantitative question investigated the change in pre- to post-Mathematics Anxiety Rating Scale (MARS-S) scores. The qualitative questions guided me to explore students' perceptions and experiences of math anxiety while learning Calculus I. Finally, I examined the interactions between the quantitative and qualitative findings using the mixed methods question. This study included quantitative data from 15 IBL and 20 lecture-based students who responded to both pre- and post-MARS-S survey and qualitative data from student and instructor interviews and class observations. I analyzed the MARS-S scores of IBL and lecture-based groups and based on the change in their anxiety scores from pre- to post-tests, I selected and interviewed nine IBL and three lecture-based students for one-on-one, semi-structured interviews. I also collected data from eight class observations of each group, instructor interviews, and the artifacts from both types of classes. The average anxiety scores of the IBL group from pre- to post-MARS survey slightly decreased from 73 to 71.87 and the lecture-based group's slightly increased from 79 to 80.55. Student responses to the 30-item MARS-S show that both groups of students were anxious about pop quizzes, tests, and exams. The qualitative data revealed that some activities, such as optional and ungraded homework, the opportunity to work in groups, and the instructor's welcoming, caring, and amicable nature decreased IBL students' anxiety. On the other hand, the instructor's readiness to explain the material in class when students asked him to do so and his care for student success decreased lecture-based students' anxiety. However, the tests and exams and anticipating the instructor's call for a response increased anxiety among both groups of students. Based on the students' perceptions and experiences, I recommend that the instructors of Calculus I and other mathematics courses engage their students in group work, use formative assessment techniques, and show some flexibility in meeting with students. The findings also suggest that mathematics instructors should reduce the number of timed tests and engage students in numerous group assignments and projects. [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.]