Reading popular mathematics from equations or words: Comparison of analysis of covariance and hierarchical linear modeling

Understanding mathematical reasoning is challenging. No conclusive evidence exists on which external representation is more beneficial to comprehension: equation or words. This study involved 299 high school students and examined the effects of external representations and participants’ abilities on reading comprehension of popular mathematics. Because students were nested within schools, analysis of covariance (ANCOVA) and hierarchical linear modeling (HLM) were performed, and their results were compared. The materials included three popular mathematics and comprehension tests, all of which were in the domain of geometry. The main difference between the equation version and the verbal version was the method of representation used in key sentences (only one, five, and five sentences differed in each of the three passages, respectively). The other sentences, illustrations, and tests were the same in both versions. Students were randomly assigned into groups for each of the two versions and completed the reading comprehension tests, reading comprehension screening tests, and math prior knowledge tests. The ANCOVA results demonstrated that the equation readers outperformed the verbal readers and that the high-ability readers performed better than the low-ability ones, but the results did not indicate any interaction between version and ability. After the exclusion of the effects of school-average math ability, the HLM results found that low-ability equation readers demonstrated a nonsignificant difference in performance compared with high-ability verbal readers. The benefits of using equations were discussed by comparing the linguistic features of the two external representations. Furthermore, the results were compared with previous research in terms of passage domain, cognitive load, focus of measurement, and participant characteristics.