Gender differences in children’s math self-concept in the first years of elementary school

In the course of elementary school children start to develop an academic self-concept reflecting their motivation, thoughts, and feelings about a specific domain. For the domain of mathematics, gender differences can emerge which are characterized by a less pronounced math self-concept for girls. However, studies are rather sparse regarding the early years of elementary school education, hence, the point in time when such gender differences emerge yet remains a matter of debate. In our study, we found that the math self-concept of elementary school children (n = 81) declined from first to second grade. While no differences in math achievement were observed between girls and boys, it became apparent that girls’ math self-concept was already less pronounced than the math self-concept of boys in the first years of elementary school. Our findings emphasize the importance of considering such gender differences even at the beginning of school education

Who Wants to Have a Career in Science or Math? Exploring Adolescents’ Future Aspirations by Gender and Race/Ethnicity

Our study utilizes data from a national cohort of eighth-grade students to consider how different gender and racial/ethnic subgroups compare to White males in their likelihood to aspire toward a science or math occupation and examine the roles that self-concept, enjoyment, and achievement may play in shaping disparities at this early point in occupational trajectories. We find that the importance of enjoyment, self-concept, and achievement in explaining disparities in science career aspirations relative to White males varies according to the female subgroup considered, such that no singular story applies to females across different racial/ethnic backgrounds. For math, White and Hispanic females remain approximately half as likely as White males to aspire to a math occupation regardless of all indicators we consider. Finally, Black and Hispanic adolescent boys have generally comparable aspirations toward future careers in science and math as their White male peers, despite notably large differences in achievement. We discuss implications of our results for future research on equity

New classes of nonlinearly self-adjoint evolution equations of third- and fifth-order

In a recent communication Nail Ibragimov introduced the concept of nonlinearly self-adjoint differential equation [N. H. Ibragimov, Nonlinear self-adjointness and conservation laws, J. Phys. A: Math. Theor., vol. 44, 432002, 8 pp., (2011)]. In the present communication a nonlinear self-adjoint classification of a general class of fifth-order evolution equation with time dependent coefficients is presented. As a result five subclasses of nonlinearly self-adjoint equations of fifth-order and four subclasses of nonlinearly self-adjoint equations of third-order are obtained. From the Ibragimov's theorem on conservation laws [N. H. Ibragimov, A new conservation theorem, J. Math. Anal. Appl., vol. 333, 311--328, (2007)] conservation laws for some of these equations are established

The murky distinction between self-concept and self-efficacy: beware of lurking jingle-jangle fallacies

This study extends the classic constructive dialogue/debate between self-concept and self-efficacy researchers (Marsh, Roche, Pajares & Miller, 1997) regarding the distinctions between these two constructs. The study is a substantive-methodological synergy, bringing together new substantive, theoretical and statistical models, and developing new tests of the classic jingle-jangle fallacy. We demonstrate that in a representative sample of 3,350 students from math classes in 43 German schools, generalized math self-efficacy and math outcome expectancies were indistinguishable from math self-concept, but were distinct from test-related and functional measures of self-efficacy. This is consistent with the jingle-jangle fallacies that are proposed. On the basis of pre-test-variables, we demonstrate negative frame-of-reference effects in social (big-fish-little-pond effect) and dimensional (internal/external frame-of-reference effect) comparisons for three self-concept-like constructs in each of the first four years of secondary school. In contrast, none of the frame-of-reference effects were significantly negative for either of the two self-efficacy-like constructs in any of the four years of testing. After controlling for pre-test variables, each of the three self-concept-like constructs (math self-concept, outcome expectancy, and generalized math self-efficacy) in each of the four years of secondary school was more strongly related to post-test outcomes (school grades, test scores, future aspirations) than were the corresponding two self-efficacy-like factors. Extending discussion by Marsh et al. (1997) we clarify distinctions between self-efficacy and self-concept; the role of evaluation, worthiness, and outcome expectancy in self-efficacy measures; and complications in generalized and global measures of self-efficacy

Effects of Movement, Growth Mindset and Math Talks on Math Anxiety

Mathematical anxiety is prevalent in our schools. This research provides insight into how mathematical anxiety develops and how it affects students throughout their lives. This study focuses on the mathematical anxiety and mathematical self-concept of five second grade classes at an economically disadvantaged school in rural North Texas. The study looked to see if adding the interventions of movement, mathematical growth mindset and math talks to a classroom would improve the mathematical self-concept of the children in the classrooms which participated. The study contained three classrooms of students who participated in the interventions and two classrooms which were used as a control group. All five second grade classrooms completed a pre and post-intervention survey of mathematical self-concepts. The three main categories measured by the survey were math self-concept, comfort using different mathematical strategies and comfort level with discussing and using math concepts in front of peers. The children received mathematical movement lessons on Mondays, growth mindset journaling and discussions on Tuesdays and mental math number talks on Wednesdays. After the four-week study, the results showed an overall gain in positive responses for the three categories, which were measured for this study in the intervention group. The control group did not show as much of a positive gain as the intervention group did, and in some cases actually went down in positive responses

Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT-symmetric quantum mechanics.Comment: version accepted for publication in J. Math. Phys.: criterion excluding basis property (Proposition 6) added, unbounded time-evolution discussed, new reference

An integrated model of academic self-concept development: academic self-concept, grades, test scores, and tracking over six years

Our newly proposed Integrated Academic Self-concept Model integrates three major theories of academic self-concept formation and developmental perspectives into a unified conceptual and methodological framework. Relations among math self-concept (MSC), school grades, test scores, and school-level contextual effects over six years, from the end of primary school through the first five years of secondary school (a representative sample of 3,370 German students, 42 secondary schools, 50% males, Mn age = 11.75) support the: 1. Internal/external frame of reference model: math school grades had positive effects on MSC, but the effects of German grades were negative; 2. Reciprocal effects (longitudinal panel) model: MSC was predictive of and predicted by math test scores and school grades; 3. Big-fish-little-pond effect: the effects on MSC were negative for school-average achievement based on four indicators (primary school grades in math and German; school-track prior to the start of secondary school; math test scores in the first year of secondary school). Results in all three theoretical models were consistent across the five secondary school years: this supports the prediction of developmental equilibrium. This integration highlights the robustness of support over the potentially volatile early-to-middle adolescent period, the interconnectedness and complementarity of three ASC models, their counter-balancing strengths and weaknesses, and new theoretical, developmental, and substantive implications at their intersections

La relación entre el autoconcepto matemático, la ansiedad ante las matemáticas y la motivación de logro en adolescentes de 12 a 14 años

Abstract:This study examines the relation between math self-concept, test and math anxiety, achievement motivation, and math achievement in typically developing 12 to 14-year-old adolescents (N = 108) from a school for secondary education in the Netherlands. Data was obtained using a math speed test, achievement motivation test, and the math experience questionnaire. A significant positive correlation was found between math self-concept and math achievement in all four math domains (measurement, relations, numbers, and scale), as well as automatized math skills. Furthermore, there was a significant negative correlation between math anxiety and math achievement in the math domain “scale”. Math anxiety was not a mediator in the correlation between math self-concept and math achievement. There was no correlation between achievement motivation, test anxiety, and math achievement. Regression analyses indicated that math self-concept was the only variable that accounted for a significant unique proportion of variance in math scores. Together, these results suggest that stimulating positive feelings and beliefs of students in their own competence in math may lead to better math achievement. La relación entre el autoconcepto matemático, la ansiedad ante las matemáticas y la motivación de logro en adolescentes de 12 a 14 años Resumen: En este estudio se examinó la relación entre el auto concepto matemático, la ansiedad ante los exámenes en matemáticas, la motivación de logro y el rendimiento matemático en adolescentes de desarrollo estándar (N = 108) de 12 a 14 años de un centro de educación secundaria en Holanda. Los datos fueron obtenidos a partir de una prueba de velocidad de resolución matemática, un test de motivación de logro y un cuestionario sobre su experiencia con las matemáticas. Se encontró una correlación positiva entre el auto concepto matemático y los resultados en matemáticas en los cuatro dominios evaluados (medidas, relaciones, numeración y escalas), así como con las habilidades matemáticas automatizadas. Igualmente se encontraron correlaciones negativas significativas entre la ansiedad ante las matemáticas y los resultados en esta materia para las tareas de escalas. La ansiedad matemática no resultó ser un mediador en la correlación entre auto concepto matemático y los resultados en matemáticas. Tampoco se encontró correlación entre motivación de logro, la ansiedad ante los exámenes y los resultados en matemáticas. El análisis de regresión indicó que el autoconcepto matemático fue la única variable que explicaba una proporción significativa de la varianza en los resultados en matemáticas. Teniendo en cuenta estos datos, se sugiere que la estimulación de creencias y sentimientos positivos de los estudiantes sobre su propia competencia en matemáticas, puede mejorar el rendimiento en esta materia.</jats:p

An eMath Teacher TOOL for ACTIVE LEARNING FLEURY'S ALGORITHM

An eMathTeacher [Sánchez-Torrubia 2007a] is an eLearning on line self assessment tool that help students to active learning math algorithms by themselves, correcting their mistakes and providing them with clues to find the right solution. The tool presented in this paper is an example of this new concept on Computer Aided Instruction (CAI) resources and has been implemented as a Java applet and designed as an auxiliary instrument for both classroom teaching and individual practicing of Fleury’s algorithm. This tool, included within a set of eMathTeacher tools, has been designed as educational complement of Graph Algorithm active learning for first course students. Its characteristics of visualization, simplicity and interactivity, make this tutorial a great value pedagogical instrument