This dissertation includes three essays: one essay focuses on the effect of teacher preparation programs on teacher knowledge while the other two focus on test-takers' response times on test items. Essay One addresses the problem of how opportunities to learn in teacher preparation programs influence future elementary mathematics teachers' knowledge. This essay used data collected for the Teacher Education and Development Study in Mathematics (TEDS-M). TEDS-M measured the mathematics content knowledge (MCK) and the mathematics pedagogical content knowledge (MPCK) of future teachers in their final year in teacher preparation programs. The purpose of this essay is to explore whether elementary teaching candidates' MCK and MPCK are associated with their opportunities to learn in mathematics courses, mathematics methods courses, general pedagogy courses, and student teaching in five countries. The results showed that opportunities to learn in some teacher preparation components are more important than in other components and that there are more associations in high-performance countries than in low-performance countries. Essay Two addresses the problem of how to detect item pre-knowledge using item responses and response time data. Item-knowledge is indicated by an unexpected short response time and unexpected correct response. This essay used a hierarchical framework proposed by other researchers for predicting expected response and response times. Large residuals between the expected responses and the observed responses indicate aberrance. Two samples are used for detecting item pre-knowledge. The first sample is from the early stage of the operational test and is used for item calibration. The second sample is from the late stage of the operational test, which may feature item pre-knowledge. The purpose of this essay is to explore whether there are item pre-knowledge and compromised items in the second sample using the parameters estimated from the first sample. The results showed two items (out of 111) potentially exposed, and two candidates (out of 1,172) showing some indication of pre-knowledge on multiple items. Essay Three addresses the problem of how to improve ability estimation or shorten a test using response times as collateral information. Response times can provide useful information about ability based on the correlation between person ability and person speed. The purpose of this essay is to explore whether incorporating a response time model into a CAT procedure will improve the correlation between true ability and estimated ability and classification accuracy by simulation studies. At the same time, the test length for the examinees whose ability is near the cut score is usually very long in variable length adaptive tests that have stopping rules related to decision making. Another purpose of this essay is to investigate whether using response times as collateral information can shorten the test length for these examinees while maintaining the same level of accuracy. The results from this study showed that using response times as collateral information does not improve ability estimation for this large-scale licensure examination using the specified estimation procedure which was designed to support a CAT procedure. [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://www.proquest.com/en-US/products/dissertations/individuals.shtml.]