Examining the representation and understanding of large magnitudes using the hierarchical alignment model of analogical reasoning

Understanding scale is fundamental in science education, but scale comprehension is difficult. One reason difficulties may arise is a disconnect between the linear scale of magnitude and how scale information is cognitively represented. An intervention was designed to foster a linear representation of magnitude, based on the theory that people represent magnitude information in a hierarchically organized structure. The intervention extends principles from the progressive alignment model of analogical reasoning to include hierarchical alignment. Half the students in an undergraduate introductory-level geology class were given multiple opportunities to progressively align time to a constant spatial scale in a linear representation, and locate all previous scales relative to the current scale. The other half of the class received the same content and practice aligning time to space. The intervention group demonstrated a more accurate sense of the relative durations of geological events and a reduction in the magnitude of temporal location errors relative to the control group. These findings suggest that the hierarchical and progressive alignment of geologic time is an effective way to reduce magnitude-based errors in understanding geologic time. These findings are consistent with the category adjustment model, and suggest commonalities between number and time magnitude representation Educational implications are discussed.