Middle-schoolers' misconceptions in discretized nonsymbolic proportional reasoning explain fraction biases better than their continuous reasoning: Evidence from correlation and cluster analyses.

Early emerging nonsymbolic proportional skills have been posited as a foundational ability for later fraction learning. A positive relation between nonsymbolic and symbolic proportional reasoning has been reported, as well as successful nonsymbolic training and intervention programs enhancing fraction magnitude skills. However, little is known about the mechanisms underlying this relationship. Of particular interest are nonsymbolic representations, which can be in continuous formats that may emphasize proportional relations and in discretized formats that may prompt erroneous whole-number strategies and hamper access to fraction magnitudes. We assessed the proportional comparison skills of 159 middle-school students (mean age = 12.54 years, 43% females, 55% males, 2% other or prefer not to say) across three types of representations: (a) continuous, unsegmented bars, (b) discretized, segmented bars that allowed counting strategies, and (c) symbolic fractions. Using both correlational and cluster approaches, we also examined their relations to symbolic fraction comparison ability. Within each stimulus type, we varied proportional distance, and in the discretized and symbolic stimuli, we also manipulated whole-number congruency. We found that fraction distance across all formats modulated middle-schoolers' performance; however, whole-number information affected discretized and symbolic comparison performance. Further, continuous and discretized nonsymbolic performance was related to fraction comparison ability; however, discretized skills explained variance above and beyond the contributions of continuous skills. Finally, our cluster analyses revealed three nonsymbolic comparison profiles: students who chose the bars with the largest number of segments (whole-number bias), chance-level performers, and high performers. Crucially, students with a whole-number bias profile showed this bias in their fraction skills and failed to show any symbolic distance modulation. Together, our results indicate that the relation between nonsymbolic and symbolic proportional skills may be determined by the (mis)conceptions based on discretized representations, rather than understandings of proportional magnitudes, suggesting that interventions focusing on competence with discretized representations may show dividends for fraction understanding.

Understanding Interest and Self-Efficacy in the Reading and Writing of Students with Persisting Specific Learning Disabilities during Middle Childhood and Early Adolescence.

Three methodological approaches were applied to understand the role of interest and self-efficacy in reading and/or writing in students without and with persisting specific learning disabilities (SLDs] in literacy. For each approach students in grades 4 to 9 completed a survey in which they rated 10 reading items and 10 writing items on a Scale 1 to 5; all items were the same but domain varied. The first approach applied Principal Component Analysis with Varimax Rotation to a sample that varied in specific kinds of literacy achievement. The second approach applied bidirectional multiple regressions in a sample of students with diagnosed SLDs-WL to (a) predict literacy achievement from ratings on interest and self-efficacy survey items; and (b) predict ratings on interest and self-efficacy survey items from literacy achievement. The third approach correlated ratings on the surveys with BOLD activation on an fMRI word reading/spelling task in a brain region associated with approach/avoidance and affect in a sample with diagnosed SLDs-WL. The first approach identified two components for the reading items (each correlated differently with reading skills) and two components for the writing items (each correlated differently with writing skills), but the components were not the same for both domains. Multiple regressions supported predicting interest and self-efficacy ratings from current reading achievement, rather than predicting reading achievement from interest and self-efficacy ratings, but also bidirectional relationships between interest or self-efficacy in writing and writing achievement. The third approach found negative correlations with amygdala connectivity for 2 reading items, but 5 positive and 2 negative correlations with amygdala connectivity for writing items; negative correlations may reflect avoidance and positive correlations approach. Collectively results show the relevance and domain-specificity of interest and self-efficacy in reading and writing for students with persisting SLDs in literacy.