This study evaluated the influence of the frequency of reading and writing habits (RWH) associated with education on the performance of adults in brief neuropsychological tasks. A sample of 489 Brazilian subjects, composed of 71% women, aged 21-80 years, with 2-23 years of formal education, was evaluated by the Brazilian Brief Neuropsychological…

This document shows the use of the calculator to assist in solving different divisions of students in fourth grade of elementary school, through the interaction in its components (divisor, dividend, quotient and remainder). Worksheets were used with a constructivist approach, which provided the student self-assessment tests. The teacher's role was…

This study examined if solving arithmetic problems hinders undergraduates' accuracy on algebra problems. The hypothesis was that solving arithmetic problems would hinder accuracy because it activates an operational view of equations, even in educated adults who have years of experience with algebra. In three experiments, undergraduates (N = 184)…

Despite the emphasis that children should have a robust sense of number and a thorough understanding of fraction (National Mathematics Advisory Panel, 2008), many students continue to struggle with these concepts. Booker Diagnostic Assessment Framework (Booker, 2011) can inform decision about teaching that improves students' learning outcomes.…

The familiar process of synthetic division is extended to much more complicated divisors and turns out, surprisingly, not to be as difficult as one might imagine.

We describe a method to extract roots of a reducible quintic over the real field, which makes use of a simple division. A procedure to synthesize such quintics is given and a numerical example is solved to extract the roots of quintic with the proposed method.

The role of a teacher is different from that in traditional mathematics instruction when the implementation of a lesson is based on students' ideas. The author's experience teaching the same lesson (of the latter format) to two different classes of pre-service teachers in an elementary mathematics methods course is described. Since whole-class…

The purpose of this study was to determine whether there are different growth trajectories of arithmetic strategies and whether these trajectories result in different achievement outcomes. Longitudinal data were collected on 240 students who began the study as 2nd graders. In the 1st year of the study, the 2nd-grade students were assessed on…

The aim of this paper is to investigate the role that auxiliary means (manipulatives such as cubes and representations such as number line) play for kindergartners in working out mathematical tasks. Our assumption was that manipulatives such as cubes would be used by kindergartners easily and successfully whereas the number line would be used by…

This study builds on two lines of research that have so far developed largely separately: the use of additive methods to solve proportional word problems and the use of proportional methods to solve additive word problems. We investigated the development with age of both kinds of erroneous solution methods. We gave a test containing missing-value…

Dot enumeration (DE) and number comparison (NC) abilities are considered markers of core number competence. Differences in DE/NC reaction time (RT) signatures are thought to distinguish between typical and atypical number development. Whether a child's DE and NC signatures change or remain stable over time, relative to other developmental…

The arithmetic mean is a fundamental statistical concept. Unfortunately, social science students rarely develop an intuitive understanding of the mean and rely on the formula to describe or define it. According to constructivist pedagogy, educators that have access to a variety of conceptualizations of a particular concept are better equipped to…

Patterns of problem-solving among 5-to-7 year-olds' were examined on a range of literacy (reading and spelling) and arithmetic-based (addition and subtraction) problem-solving tasks using verbal self-reports to monitor strategy choice. The results showed higher levels of variability in the children's strategy choice across Years 1 and 2 on the…

Some years ago, Hatano differentiated between routine and adaptive expertise and made a strong plea for the development and implementation of learning environments that aim at the latter type of expertise and not just the former. In this contribution we reflect on one aspect of adaptivity, namely the adaptive use of solution strategies in…

Three experiments used dual-task suppression methodology to study the use of inner speech and visuospatial resources for mediating central executive performance by children with autism (CWA) and group-matched typically developing (TD) controls. Expt 1 revealed that CWA did not recruit inner speech to facilitate arithmetic task-switching…