This study sought to understand how students activate number sense in determining the position of fractions on a number line and identify how the natural number bias and number sense influences students' thinking processes. The study utilized the Cognitive Task Analysis (CTA), involving four fifth-grade elementary students as the research…

Purpose: Previous studies examining the inter-relations between serial and discrete naming with reading have found that the ability to efficiently process multiple items presented in a sequence (indexed by serial naming) is a unique predictor of word- and text-reading fluency. However, conclusions have been tempered by the concurrent nature of the…

The development of math reasoning and 3-d mental rotation skills are intertwined. However, it is currently not understood how these cognitive processes develop and interact longitudinally at the within-person level -- either within or across genders. In this study, 553 students (52% girls) were assessed from fifth to seventh grades on 3-d mental…

Learning of the mathematical number line has been hypothesized to be dependent on an inherent sense of approximate quantity. Children's number line placements are predicted to conform to the underlying properties of this system; specifically, placements are exaggerated for small numerals and compressed for larger ones. Alternative hypotheses…

Many people have serious difficulties in understanding rational numbers, limiting their ability to interpret and make use of them in modern daily life. This also leads to later difficulties in learning more advanced mathematical content. In this study, novel tasks are used to measure 263 late primary school students' spontaneous focusing on…

We identify and document 3 cognitive obstacles, 3 cognitive affordances, and 1 type of integer understanding that can function as either an obstacle or affordance for learners while they extend their numeric domains from whole numbers to include negative integers. In particular, we highlight 2 key subsets of integer reasoning: understanding or…

Two investigations of fifth graders' strategies for locating whole numbers on number lines revealed patterns in students' coordination of numeric and linear units. In Study 1, we investigated the effects of context on students' placements of three numbers on an open number line. For one group ("n"?=?24), the line was presented in a…

The purpose of the present study was to explore the 3rd-grade cognitive predictors of 5th-grade computational skill with rational numbers and how those are similar to and different from the cognitive predictors of whole-number computational skill. Students (n=688) were assessed on incoming whole-number calculation skill, language, nonverbal…

The purpose of the present study was to reveal the developmental pathway from third grade cognitive competencies to sixth grade conceptual and procedural fraction knowledge through the intervening whole numerical skills at fifth grade. The study used empirical data that come from 536 students in nine schools across two Delaware public school…

The comparison distance effect (CDE), whereby discriminating between two numbers that are far apart is easier than discriminating between two numbers that are close, has been considered as an important indicator of how people represent magnitudes internally. However, the underlying mechanism of this CDE is still unclear. We tried to shed further…

The main purpose of this study is to determine the strategies of using the generalizing patterns of the primary fifth grade students. The practice of this research is conducted on twelve students, which have high, middle and low success levels. Task-based interviews and students journals are used as the tools for data collection. For the analysis…

Children (n = 122) and adults (n = 200) with dyslexia completed rapid automatic naming (RAN) letters, rapid automatic switching (RAS) letters and numbers, executive function (inhibition, verbal fluency), and phonological working memory tasks. Typically developing 3rd (n = 117) and 5th (n = 103) graders completed the RAS task. Instead of analyzing…

Although equal sharing problems appear to support the development of fractions as multiplicative structures, very little work has examined how children's informal solutions reflect this possibility. The primary goal of this study was to analyze children's coordination of two quantities (number of people sharing and number of things being shared)…