This study explored the impact of numbers used in instructional tasks on the construction and generalization of multiplicative reasoning by fourth grade students designated as having learning difficulties or disabilities in mathematics (SLDs). In particular, this study addressed the following research questions: (1) In what ways do SLDs' conception of number as a composite unit afford or constrain transition to multiplicative reasoning? (2) Which specific numbers, used in instructional and/or assessment tasks, may support or interfere with SLDs' progression from additive reasoning to multiplicative Double Counting (mDC)? Results suggested that in early participatory stages, using numbers with multiples familiar to the students, such as 2 and 5, promoted multiplicative solution paths (e.g., counting by fives while simultaneously keeping track of how many fives they have counted). This use of familiar numbers allowed for students' reflection on their multiplicative thinking. Introduction of more difficult numbers--any number for which the child was yet to master multiples--tended to limit the multiplicative thinking and move students back to more known (additive) solution paths. In later participatory stages, the introduction of more difficult numbers promoted the progression within mDC. [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.]