Through a constructivist lens, this dissertation research (a case study) examines the problem of how elementary teachers' MKT might be related to their ways of implementing and adapting mathematical tasks to promote students' construction of multiplicative reasoning. In particular, this study addresses the following four research questions: 1. What schemes of multiplicative reasoning can be inferred to be a part of teachers' First Order Model (FOM) and thus a constituent of their MKT? 2. How might teachers interpret the conceptual linkage and progression in multiplicative reasoning schemes and thus include it in their MKT? 3. In what ways, if any, might teachers integrate their own FOM of multiplicative reasoning and the sense they make of student conceptual progression? 4. In what ways, if any, might teachers adapt tasks that have been used to promote their multiplicative reasoning during the AdPed PD program, and could their use of such tasks be linked with their integration in their MKT (#3 above)? Through the analysis of two teachers' teaching to promote their students' multiplicative reasoning schemes, findings indicate that both teachers have constructed an understanding of a concatenation of multiplicative schemes, which combines the conceptual understanding of mDC, SUC, and UDS (Tzur et al., 2013), as well as an understanding of a reversal of the conceptual progression order of those schemes. Further, analyses indicate that the teachers' understanding of the scheme concatenation impacts their inferences of students' assimilatory schemes, their adjustments of the learning goals they set for students along a learning progression spectrum, and eventually adaptation of tasks that they use to promote an intended learning transition. In Chapter 5 (Discussion), I discuss three major contributions of this study to the field: 1) an expansion of the UDS scheme to a richer scheme that includes the concatenation, 2) a theoretical expansion of MKT in relation to Student-Adaptive Pedagogy (Tzur, 2010, 2013) via linking the teachers' understanding of the concatenation to task design, and 3) implications for practice and future research. [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.]