Adaptive tutoring systems often model student knowledge in ways that break away from a "one size fits all" approach to learning. Nonetheless, the strengths of these systems can often be limited, as knowledge representations are not easily interpreted by teachers, which make these systems difficult to integrate into pedagogical practices. Fortunately, as researchers, we can still take advantage of the AI in these systems to extend our innovations and address problems of practice. As such, the goal of the present work is to leverage multidimensional representations of knowledge that these systems provide to explore innovations in educational measurement, pedagogical techniques, and practice. I explore these in three studies outlined below. In Study 1 I explore "Innovations in educational measurement" by adopting an alternative perspective to measuring student mathematical ability. In this study I invite the reader to re-conceptualize mathematical ability as a multidimensional construct, which runs counter to long-established tradition in academic measurement and pedagogical practice. In doing so, I compare the variation observed in students' mathematical ability when ability is measured using different metrics that vary in dimensionality. Findings suggest that under a multidimensional view, students (including those who may be traditionally seen as "low-ability") often possess relative strengths when compared to their peers, thus suggesting that categorizations such as low- and high-ability, which are typically used in practice, may be an over simplification. In Study 2 I explore "Innovations in pedagogical techniques" as I present three novel algorithms for grouping students that leverage existing technological AI innovations that model student knowledge across hundreds of mathematical skills. These methods attempt to better align the personalization of a tutoring system with teachers' instructional practices. I evaluate each of the three methods against two alternative baseline methods--one that groups students randomly and one that groups students based on a unidimensional course score. Findings demonstrate that these novel methods, which adopt a multidimensional view of ability, were more capable than the baseline methods at grouping students with similar strengths and weaknesses on a fine-grained skill level. In Study 3 I explore "Innovations in practice" in a research-practice partnership (RPP) with curriculum specialists at a local urban school district in Southern California. Implementation strategies, including curriculum and grouping recommendations were provided to teachers for a summer intervention program. In the spirit of a design-based implementation partnership, strategies and recommendations were formed to meet the needs of partners, while simultaneously attempting to address known problems of practice when implementing a blended learning design in the classroom. In this first cycle of iteration, these attempts were examined through teacher surveys as well as student login and learning data in a tutoring system. Ultimately, these data were used to examine the fidelity of implementation so that findings may inform future iterations of this ongoing partnership. [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.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]