For our last Brown Bag of the semester, Dr. Jessica Namkung presented her research regarding students' learning of fractions. She presented two studies, and a discussion followed regarding students' fraction knowledge.
One study investigated the cognitive mechanisms underlying students' fraction and whole-number learning. Dr. Namkung chose to focus on specific cognitive factors used for calculations including working memory, processing speed, phonological reasoning, nonverbal reasoning, language, incoming calculation, and attentive behavior. She then examined these predictors to determine if there was a difference in which underlying mechanisms are present for fraction learning compared to whole-number learning. Dr. Namkung used factor analysis to determine that the significant predictors of fraction learning are language, processing speed, and attentive behavior. Significant predictors of whole-number learning were found to be processing speed, attentive behavior, and incoming calculation. In conclusion, both attentive behavior and processing speed are common predictors. Some implications for instruction include training students on using the predictors, teaching more mathematical strategies that allow for students to compensate for slow processing speed in order to increase efficiency, explicitly teaching vocabulary, and requiring students to explain their understanding of terms.
The second study examined the abundance of fraction difficulties that exist among students. According to Dr. Namkung, whole-number bias is a common occurrence in students' understanding of fractions, and this reasoning has an effect on students' understanding of fraction magnitudes. Dr. Namkung examined fourth graders considered to have adequate whole-number knowledge and fourth graders with deficits in whole-number knowledge. She found that students with adequate whole-number knowledge performed better on fraction problems than students with less severe whole-number knowledge deficits, and students with less severe whole-number knowledge deficits performed better than students with more severe whole-number knowledge deficits. Significant differences were shown for all groups. In conclusion, this study found that if a student has difficulties with whole-numbers then the student is likely to also have difficulties understanding fractions, and more research needs to be conducted to determine why this relationship exists.