In light of conceptual metaphor theory, historical mathematicians' and students' difficulty with negative numbers reveals that the collecting objects metaphor may be a cognitive obstacle to those first learning about negative numbers. Moreover, consistency of physical motions with targeted ideas is a factor of cognition. Thus, this pre-post-delayed post study randomly assigned 8 classes of initial learners to a collecting objects integer model (chip model) or a moving-along-a-path metaphor-based model (number line model) to learn integer arithmetic with the four primary operations during an eight-day mini-unit. The study investigated the questions: What do students demonstrate learning with each model and what, if any differences in learning are found between models? Findings did support theory that a motion-aligned model using a moving-along-a-path metaphor would likely support learning better than collecting objects. [For the complete proceedings, see ED583989.]