Problem-solving, collaboration, and adaptability to in-person and virtual environments are critical for success today. Therefore, brick-and-mortar and online instructional models have shifted to ensure that K-12 students are prepared with these skills for 21st-century challenges. Grounded in systems theory, the study examined the inputs, processing, and output components that affect student learning of high school geometry in a fully online teaching environment. The study quantitatively evaluated the impact of problem-based learning and collaboration on student success (system outputs -- i.e., student grades and completion time). Course version served as the independent variable: Version A was the traditional geometry course, while Version B was enhanced with problem-based learning and collaboration activities. The sample consisted of 5,486 student records generated using propensity score matching: 53% females and 47% males, 53% public-school students, and approximately two-thirds non-honors course enrollment type. The average age of students was 15.53 years old, and the modal enrollment grade level was Grade 10. The independent samples t-test results indicated that students in the problem-based learning course earned lower semester grades compared to students in the traditional course -- first semester: p < 0.001; second semester: p < 0.001. The effect sizes for these differences, as measured by Cohen's d, were 0.38 (first semester) and 0.41 (second semester), indicating a small-medium effect. Moreover, several variables predicted students' final grades: student age, number of weeks a student took to complete a semester, course enrollment type, course semester, and course version (R[superscript 2] = 0.301). Future research should replicate the current study and integrate a qualitative component to ensure future redesign of the geometry course focuses on collaboration and problem-solving to match instructional and assessment approaches. [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.]