Academic literature on the topic 'Mathematical ability Sex differences Case studies'

AbstractSeveral hundred thousand intellectually talented 12-to 13-year-olds have been tested nationwide over the past 16 years with the mathematics and verbal sections of the Scholastic Aptitude Test (SAT). Although no sex differences in verbal ability have been found, there have been consistent sex differences favoring males in mathematical reasoning ability, as measured by the mathematics section of the SAT (SAT-M). These differences are most pronounced at the highest levels of mathematical reasoning, they are stable over time, and they are observed in other countries as well. The sex difference in mathematical reasoning ability can predict subsequent sex differences in achievement in mathematics and science and is therefore of practical importance. To date a primarily environmental explanation for the difference in ability has not received support from the numerous studies conducted over many years by the staff of Study of Mathematically Precocious Youth (SMPY) and others. We have studied some of the classical environmental hypotheses: attitudes toward mathematics, perceived usefulness of mathematics, confidence, expectations/ encouragement from parents and others, sex-typing, and differential course-taking. In addition, several physiological correlates of extremely high mathematical reasoning ability have been identified (left-handedness, allergies, myopia, and perhaps bilateral representation of cognitive functions and prenatal hormonal exposure). It is therefore proposed that the sex difference in SAT-M scores among intellectually talented students, which may be related to greater male variability, results from both environmental and biological factors.

Abstract. Sex differences in mathematical ability were examined in a nation-wide sample of 32,346 Jordanian 4th graders (age 9–10 year) on a 40-item mathematics test. Overall, boys were found to perform slightly worse ( d = −0.12) but had slightly more variation in scores ( SD = 1.02 and SD = 0.98 for boys and girls, respectively). However, when results were disaggregated by school type, single-sex versus coed (i.e., coeducational), boys were found to perform better than girls in coed schools ( d = 0.27) but worse across single-sex schools ( d = −0.37). Two-parameter item response theory analysis showed that item difficulty was similar across sexes in the full sample. Item loadings exhibited substantial departure from measurement invariance with respect to boys and girls at single-sex schools, though. For boys and girls at coed schools, both the item difficulty and item loading correlations were highly similar, evincing that measurement invariance largely held in this case. Partially consistent with findings from other countries, a correlation between item difficulty and male advantage was observed, r = .57, such that the relative male advantage increased with increased item difficulty. Complicating interpretation, this association did not replicate within coed schools. Item content, Bloom’s cognitive taxonomy category, and item position showed no relation to sex differences.

The study investigated the reported regressive performances of students in spatial reasoning concepts with a view to promote early spatial reasoning of lower primary school pupils across ability levels and sex. Non-equivalent experimental research design was employed. A hundred and five (105) pupils in four intact classes were exposed to six weeks intervention and subsequently post-tested. Data collected were analyzed using Analysis of Covariance. The study found significant effect of treatment on the performance of study participants in the ICT-integrated Think-Pair-Share treatment group. No significant interactive effect of ability was found though, the pupils of low-ability group benefitted more from the intervention (M = 12.32, 11.07; SD = 2.86, 2.98). There was no significant different of intervention between boys and girls across strategies and abilities. The study concluded that, while ICT-integrated learning strategies could improve output in spatial concepts of pupils at the primary school level, performances on the basis of sex-groups and ability groups have no significant interaction effect on the learners of spatial reasoning. Keywords: performance, spatial reasoning, treatment, strategies, ability group, think-pair-share, concrete-representation-abstract, learners’-self-controlled.INTRODUCTIONEarly graft of mathematic ability has been ascertained to predict later mathematical achievement and related endeavors in life [6]. Hence, the promotion of early mathematic competency is of critical importance. Established link between spatial ability and mathematics in early childhood by neuropsychological and brain imaging studies and behavioral evidences potent that math performance can be improved with spatial reasoning. Nigeria’s experience in local, national and international examinations show dwindling performances of examinees traceable to substantiated inefficient score in spatial reasoning items consistently featured [5, 1] in such standardized examinations. This was interpreted to mean that, children understanding of space pattern is necessary and demanded by the curriculum. The advent of information and communication technology (ICT) eulogized as potentially powerful and enabling tool for education change and reform is hereby engaged in learning delivery for comparative analysis of performance in learning spatial concepts among primary school pupils. METHODOLOGYNon-equivalent pretest, posttest and control group research design was adopted. The population consisted of 357,533 pupils’ enrolled in 1, 378 primary schools in Osun State (Daily Independent, 2013) characterized with male and female learners of varied academic abilities. Study sample was eked out using purposive and multi-stage sampling techniques. Primary III class was purposively selected based on the learners' age (6 – 8 years) limit in early childhood. Four schools with 105 intact class pupils were multi-stage sampled in the three major towns of the state considering available facilities for the study. Research instruments included Spatial Reasoning for Children (SpatReC), an interactive, multimedia package designed using C-Sharp (C#) programming language and follows the taxonomy based on Benjamin Blooms’ principles as revised by Anderson and Krathwohl in [8]; and Spatial Reasoning Test (SRT) used for pretest and posttest. Instruments, in a previous study [1] were adjudged validity and reliable. Learners in their intact classes were randomly assigned to study conditions namely; the three experimental groups and the one control group; three levels of cognitive ability groups - high, medium and low; and two sex groups - male and female. The intervention took forty minutes of Mathematics periods for three days in a week and six weeks in each of the schools excluding tests. ANALYSIS:Tests for significant interaction effect of treatment on groups were conducted. Result shows the test of equality of means to be significantly equal (t = 2.003, p - 0.05) in favor of equal variance assumed. The study’s subjects were thus adjudged to be reliably homogeneous (Table 1).Table 1: Test for Difference in the Participating group’s Post-test Scorest-test for Equality of MeanstdfSig.(2-tailed)Mean DifferenceStd. Error Difference95% Confidence Interval of the DifferenceLowerUpperEqual variances assumed2.003103.0481.253.626.0122.494Furthermore, the post-test scores of the research participants were subjected to a test of difference via analysis of covariance using their experimental groups as the differentiating variable and the pre-test scores as the covariate to remove the possible effect of previous learning and other confounds. The result showed significant difference in the post-test scores (F = 2.934, p - .05). It also showed from the table that, the R-squared value was 0.080 and the Adjusted R squared value stood at 0.053. This can be interpreted to mean that the maximum variance in the post test score is quite small. So other possible factors which might explain the difference in the post test scores and interact with the effectiveness of the learning strategies were sought after (Table 2).Table 2:Post-Test of Difference of Treatments Tests of Between-Subjects Effects - Dependent Variable: post test scoreSourceType III Sumof SquaresDfMean SquareFSig.Corrected Model96.677a332.2262.934.037Intercept34388.204134388.2043131.034.000GRP96.677332.2262.934.037R Squared = .080 (Adjusted R Squared = .053)The source of difference was located between the CRTL group and the CRA group (Table 3). It can be concluded that there exists significant difference among the learning strategies in improving performances.Table 3: Multiple Comparisons Post hoc TestDependent Variable: post-test score Tukey HSD(I) Treatment(J) TreatmentMean Difference(I-J)Std. ErrorSig.95% Confidence IntervalLower BoundUpper BoundCTRLTPS.413.924.970-2.002.83LSC.514.960.950-1.993.02CRA2.514*.960.049.015.02* The mean difference is significant at the 0.05 level.Would there be any interactive effect of intervention between various academic ability pupils by virtue of learning strategies? To answer this question, the post-test scores of the research participants were subjected to a test of difference via analysis of covariance. Result shown in Table 4 revealed that there is no significant interaction effect of experimental groupings and ability levels on the post-test scores (F = 1.440, p > .05). In this stance therefore, the research question is answerable in the negative.Table 4: Test of Difference of Treatment and Ability in Post-test Tests of Between-Subjects Effects Dependent Variable: post test scoreSourceType III Sum of SquaresDfMean SquareFSig.Corrected Model113.502a716.2151.440.198Intercept28102.188128102.1882495.206.000GRP * ability113.502716.2151.440.198a. R Squared = .094 (Adjusted R Squared = .029)Lastly, could any difference in performance result from variation in sexes? Despite the slight differences in group sizes, no significant difference in the performance on the basis of sex-groups (value = 0.186, > 0.05) was found. It as well showed that, there was no significant interaction found between groups and sex in describing performance of pupils in spatial reasoning (F = 0.030, p > 0.05) (Table5).Table 5: Test of Difference on Post-test in Treatment / Sex Groups DescriptivePost test scoreNMeanStd. DeviationStd. Error95% Confidence Interval for MeanMin.Max.dffsigLower BoundUpper BoundMale4118.153.190.49817.1419.1511281.030.862Female6418.273.560.44517.3819.151226103Total10518.223.405.33217.5618.881128104DISCUSSION - CONCLUSION:The application of ICT unto learning strategies was with a view to improve performance in spatial concepts in pupils of low and high ability at the primary school level. Notable results included significant effect of treatment on performance at the removal of possible effect of previous learning and other confounds. This discovery agrees with [3] whose study established that particular intervention in the experimental group might increase learner’s motivation and in turn lead to higher achievement levels for learners in the experimental group than for those in the control group. [2, 4] also found particular learning strategies - conceptual learning strategy and online tool substantially increasing math performance growth in separate studies. Ability levels’ effect on academic achievement as investigated indicated no significance in the post-test scores even after controlling for the previous learning through the pre-test. This result was at variance to [7] study on game-based learning (GBL) which found that, many students with low confidence toward learning mathematics can be restored and improve their confidence toward mathematics. Conclusively, performances on the basis of sex-groups and ability groups have no significant interaction found between ICT-integrated strategy learners of spatial reasoning. REFERENCES Adeleke, A. G. (2015) Comparative Effectiveness of ICT-Integrated Learners’-Self-Controlled, Concrete-Representational-and Think-Pair-Share Strategies in Enhancing Spatial reasoning Skills of Primary School Pupils in Osun State. A Doctoral Dissertation Submitted to Postgraduate College, Obafemi Awolowo University, Ile-Ife, Nigeria. Adeleke, M. A. (2007) Strategic Improvement of Mathematical Problem-solving Performance of Secondary School Students using Procedural and Conceptual Learning Strategies. Educational Research and Review Vol. 2 (9), pp.259-263. Alrabai, F. (2014) The Effects of Teachers’ In-Class Motivational Intervention on Learners’ EFL Achievement. Applied Linguistics. 2014 Oxford University Press.Haelermans, C. - Ghysels, J. (2014) The Effect of an Individualized Online Practice Tool on Math Performance - Evidence from a Randomized Field Experiment.Jegede, P. O., Adelodun, O. A. - Okoli, B. C. (1998) Evaluation of Test Characteristics of UME Mathematics Items in the Context of Bloom’s Taxonomic Categories. Journal of Creativity in Teaching for the Acquisition and Dissemination of Effective Learning (CITADEL) Vol.3 (6) pp.233-241.Krajewski, K - Schneider, W. (2009) Early development of quantity to number-word linkage as a precursor of mathematical school achievement and mathematical difficulties: Findings from a four-year longitudinal study. Learning and Instruction, 19(6), 513-526. Ku, O., Chen, S.-Y., Wu, D.-H., Lao, A.-C.-C., - Chan, T.-W. (2014). The Effects of Game-Based Learning on Mathematical Confidence and Performance: High Ability vs. Low Ability. Educational Technology - Society, 17 (3), 65–78.Wilson, L. O. (2013) Understanding the New Version of Bloom’s Taxonomy - A succinct discussion of the revisions of Bloom’s classic cognitive taxonomy by Anderson and Krathwohl and how to use them effectively. Available at http://www4.uwsp.edu/education/ lwilson/curric/newtaxonomy.htm

Coinfection of vector species can provide more insight into the complex relationship between zoonotic pathogens and its host. Ixodes scapularis (Say) or the deer-tick in particular is an important species in North America because of its exceptional ability as a vector that can transmit zoonotic diseases such as Lyme and Cat Scratch Disease (CSD). In recent years, many studies have suggested a possible link between the coinfection of Borrelia burgdorferi, the causative agent of Lyme, with other tick-borne bacteria such as Bartonella spp., the causative agent of CSD, as partly responsible for the symptoms associated with Chronic Lyme Disease or Post-Treatment Lyme Disease Syndrome. This study investigates the prevalence of Bartonella spp. and Borrelia burgdorferi in Ixodes scapularis using Polymerase Chain Reaction (PCR) assay to potentially find a link between the two of the most common tick-borne pathogens found in Nova Scotia. Standard PCR using primers targeted at the two bacterial species were conducted on 157 I. scapularis ticks collected in Nova Scotia. Overall, we found high prevalence for both bacteria at 75.16% for Bartonella spp. and 47.13% for B. burgdorferi with no significant differences between the sex of the ticks. Interestingly, all the ticks positive for B. burgdorferi were also positive for Bartonella spp. which implies that the coinfection rate between B. burgdorferi and Bartonella spp. is 47.13%. We report one of the highest coinfection rates for B. burgdorferi and Bartonella spp. in I. scapularis, consistent with the current trends of increasing tick presence in North America.

This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. Previously, we have worked with both kinds of fuzzy systems in different types of benchmark problems and it has been found that the use of fuzzy logic in combination with the differential evolution algorithm gives good results. In some of the studies, it is clearly shown that, when compared to other algorithms, our methodology turns out to be statistically better. In this case, the mutation parameter is dynamically moved during the evolution process by using shadowed and general type-2 fuzzy systems. The main contribution of this work is the ability to determine, through experimentation in a benchmark control problem, which of the two kinds of the used fuzzy systems has better results when combined with the differential evolution algorithm. This is because there are no similar works to our proposal in which shadowed and general type 2 fuzzy systems are used and compared. Moreover, to validate the performance of both fuzzy systems, a noise level is used in the controller, which simulates the disturbances that may exist in the real world and is thus able to validate statistically if there are significant differences between shadowed and general type 2 fuzzy systems.

The manufacture of alloys in solid state has many differences with the conventional melting (casting) process. In the case of high energy milling or mechanical alloying, phase transformations of the raw materials are promoted by a large amount of energy that is introduced by impact with the grinding medium; there is no melting, but the microstructural changes go from microstructural refinement to amorphization in solid state. This work studies the behavior of pure metals (Cu and Ni), and different binary alloys (Cu-Ni and Cu-Zr), under the same milling/mechanical alloying conditions. After high-energy milling, X ray diffraction (XRD) patterns were analyzed to determine changes in the lattice parameter and find both microstrain and crystallite sizes, which were first calculated using the Williamson-Hall (W-H) method and then compared with the transmission electron microscope (TEM) images. Calculations showed a relatively appropriate approach to observations with TEM; however, in general, TEM observations detect heterogeneities, which are not considered for the W-H method. As for results, in the set of pure metals, we show that pure nickel undergoes more microstrain deformations, and is more abrasive than copper (and copper alloys). In binary systems, there was a complete solid solution in the Cu-Ni system and a glass-forming ability for the Cu-Zr, as a function of the Zr content. Mathematical methods cannot be applied when the systems have amorphization because there are no equations representing this process during milling. A general conclusion suggests that, under the same milling conditions, results are very different due to the significant impact of the composition: nickel easily forms a solid solution, while with a higher zirconium content there is a higher degree of glassforming ability.

A retrospective case control study was undertaken at the molecular biology department of a private center for reproductive medicine in order to determine whether any correlation exists between mitochondrial DNA (mtDNA) content of cleavage-stage preimplantation embryos and their developmental potential. A total of 69 couples underwent IVF treatment (averaged women age: 36.5, SD 4.9) and produced a total of 314 embryos. A single blastomere was biopsied from each embryo at the cleavage stage (day-3 post-fertilization) subjected to low-pass next generation sequencing (NGS), for the purpose of detecting aneuploidy. For each sample, the number of mtDNA reads obtained after analysis using NGS was divided by the number of reads attributable to the nuclear genome. The mtDNA copy number amount was found to be higher in aneuploid embryos than in those that were euploid (mean mtDNA ratio ± SD: 6.3 ± 7.5 versus 7.1 ± 5.8, p < 0.004; U Mann–Whitney test), whereas no statistically significant differences in mtDNA content were seen in relation to embryo morphology (6.6 ± 4.8 vs. 8.5 ± 13.6, p 0.09), sex (6.6 ± 4.1 vs. 6.2 ± 6.8, p 0.16), maternal age (6.9 ± 7.8 vs. 6.7 ± 4.5, p 0.14) or its ability to implant (7.4 ± 6.6 vs. 5.1 ± 4.6, p 0.18). The mtDNA content cannot serve as a useful biomarker at this point in development. However, further studies investigating both quantitative and qualitative aspects of mtDNA are still required to fully evaluate the relationship between mitochondrial DNA and human reproduction.

The results of studies of indicators of nitrogen metabolism in the blood serum of the descendants of four bulls at the age of 12-13 months are presented. The studies were conducted in the South of Western Siberia at Vaganovo OJSC on the livestock population of Holstein breed. The creatinine concentration in the blood serum samples of the sons was determined using a set of reagents from Vector-Best (Russia). In the regions of animal breeding, constant monitoring of water, soil, feed, animal organs and tissues is carried out. It was established that in the areas in which the studied breeds were bred, the content of macro- and microelements did not exceed the MPC. The level of serum creatinine in the examined animals on average for all groups of sons was 308.2 ± 24.1 μmol / L, which exceeds the generally accepted values of this indicator. However, taking into account age and sex and breed characteristics, taking into account data on the overall health of the animals examined, information on the ecological well-being of the breeding zone, the results can be considered as reference values for healthy Holstein bulls in Western Siberia. It was shown that in the blood serum of the sons of some fathers, the creatinine content was 1.7 times higher (364.2 ± 52.7 μmol / L) than in the descendants of other manufacturers (p> 0.95). A group of half-siblings was found, which were characterized by a low hereditary predisposition to creatinine content. Discovered differences in the creatinine content in the blood serum of sons reflect the differentiation of bulls and indicate genetically determined features of the functioning of the homeostasis system. In this case, most likely, there is a different ability of descendants to adapt to environmental and climatic conditions.

El objetivo del presente estudio fue conocer el efecto agudo de dos tipos diferentes de descansos activos (baja y alta intensidad), llevados a cabo entre dos clases, sobre varias variables cognitivas como la memoria, atención-concentración, cálculo matemático, razonamiento lingüístico y creatividad en jóvenes de Educación Secundaria. Participaron 136 adolescentes de 12.92 ± 0.43 años. Se emplearon 3 grupos de estudio: 1) Grupo de control (GC) que permaneció sentado dentro de la clase; 2) Grupo experimental 1 (GE1) que realizó 1 descanso activo de 4 minutos a baja intensidad; y 3) Grupo experimental 2 (GE2) que llevó a cabo ejercicios de alta intensidad. Para analizar los efectos de los diferentes tipos de descansos se empleó ANCOVA de medidas repetidas 3 Grupo (GC, GE1, GE2) x 2 Tiempo (pre, post). Se empleó como covariables la edad, sexo y estudios de la madre. Los resultados mostraron que los descansos activos mejoraron la memoria posterior de los participantes (p<0.001). Los descansos activos de baja intensidad presentaron un efecto de mejora similar en la atención y concentración (21 y 25%, p<0.001). Se observaron mejoras en el cálculo matemático tras ambos tipos de descansos activos, sin embargo, las diferencias no han llegado a ser significativas. Los adolescentes no mostraron mejoras en la capacidad lingüística ni en la creatividad. Se sugiere la inclusión de descansos activos, preferiblemente a baja intensidad, para obtener beneficios a corto plazo en la atención, concentración y cálculo matemático en jóvenes de educación secundaria. Abstract. The objective of this study was to know the acute effect of two different types of active breaks (low and high intensity), carried out between two classes, on several cognitive variables such as memory, attention-concentration, mathematical calculation, linguistic reasoning and creativity in high school youth. 136 adolescents of 12.92 ± 0.43 years participated. Three study groups were used: 1) Control group (CG) that remained seated within the class; 2) Experimental group 1 (EG1) that made 1 active break of 4 minutes at low intensity; and 3) Experimental group 2 (EG2) that carried out high intensity exercises. To analyze the effects of the different types of breaks, ANCOVA was used with repeated measures 3 Group (CG, EG1, EG2) x 2 Time (pre, post). Age, sex and studies of the mother were used as covariates. The results showed that active rest improved the participants' later memory (p <0.001). The low intensity active breaks had a similar improvement effect in attention and concentration (21 and 25%, p <0.001). Improvements in the mathematical calculation were observed after both types of active breaks, however, the differences have not become significant. The adolescents showed no improvement in linguistic ability or creativity. It is suggested the inclusion of active breaks, preferably at low intensity, to obtain short-term benefits in the attention, concentration and mathematical calculation in secondary school youth.

Abstract A test apparatus is designed to carry out dynamic and static fluid-loss tests of fracturing fluids. This test apparatus simulates the pressure difference, temperature, rate of shear, duration of shear, and fluid-flow pattern expected under fracture conditions. For a typical crosslinked fracturing fluid, experimental results indicate that fluid loss values can be a function of temperature, pressure differential, rate of shear, and degree of non-Newtonian behavior of the fracturing fluid. A mathematical development demonstrates that the fracturing-fluid coefficient and filter-cake coefficient can be obtained only if the individual pressure drops can be measured during a typical fluid-loss test. Introduction In a hydraulic fracturing treatment, the development of fracture length and width is strongly dependent on a number of key fluid and formation parameters. One of the most important of these parameters is the rate at which the fracturing fluid leaks, off into the created fracture faces. This parameter, identified as fluid loss, also influences the time required for the fracture to heal after the stimulation treatment has been terminated. This in turn will influence the final distribution of proppant in the fracture and will dictate when the well can be reopened and the cleanup process started. Historically, tests to measure fluid loss have been carried out primarily under what is characterized as static conditions. In such tests, the fracturing fluid is forced through filter paper or through a thin core wafer under a pressure gradient, and the flow rate at the effluent side is determined. Of course, the use of filter paper cannot account for reservoir formation permeability and porosity; therefore, the fluid-loss characteristics derived from such tests should be viewed as only gross approximations. The static core-wafer test on the other hand, reflects to some extent the interaction of the formation and fracturing-fluid properties. However, one important fluid property is altogether ignored in such static core-wafer tests. This is the effect of shear rate in the fracture on the rheology (viscosity) of fracturing fluid and subsequent effects of viscosity on the fluid loss through the formation rock. In the past, several attempts were made to overcome the drawbacks of static core-wafer tests by adopting dynamic fluid-loss tests. Although these dynamic tests were a definite improvement over the static versions, each had drawbacks or limitations that could influence test results. In some of the studies, the shearing area was annular rather than planar as encountered in the fracture. In other cases, the fluid being tested did not experience a representative shear rate for a sufficiently long period of time. An additional problem arose because most studies were performed at moderate differential pressures and temperatures. The final drawback in several of the studies was that the fluid flow and leakoff patterns did not realistically simulate those occurring in the field. In the first part of this paper, we emphasize the design of a dynamic fluid-loss test apparatus that possesses none of these drawbacks. In the second part of the paper, test results with this apparatus are presented for three different fluid systems. These systems areglycerol, a non-wall-building Newtonian fluid,a polymer gel solution that is slightly wall-building and non-Newtonian, anda crosslinked fracturing system that is highly non-Newtonian in nature and possesses the ability to build a wall (filter cake) on the fracture face (see Table 1). The fluids were subjected to both static and dynamic test procedures. In the third part of the paper, results of experiments carried out with crosslinked fracturing fluid for different core lengths, pressure differences, temperatures, and shear rates are compared and the significance of the difference of fluid loss is emphasized. Experimental Equipment and Procedure The major components of the experimental apparatus shown in Fig. 1 are a fluid-loss cell, circulation pump, heat exchanger, system pressurization accumulators, and a fluid-loss recording device. The construction material throughout most of the system is 316 stainless steel. The fluid loss is measured through a cylindrical core sample, 1.5 in. [3.81 cm] in diameter, mounted in the fluid-loss cell. Heat-shrink tubing is fitted around the circumference of the core and a confining pressure is maintained to prevent channeling. Fracturing fluid is circulated through a rectangular channel across one end of the core. SPEJ P. 482^

Law, Helen.
"August 2010."
Thesis (M.Phil.)--Chinese University of Hong Kong, 2010.
Includes bibliographical references (leaves 78-84).
Abstracts in English and Chinese.
ABSTRACT --- p.i
ACKNOWLEDGEMENTS --- p.v
LIST OF TABLES AND FIGURES --- p.viii
Chapter CHAPTER ONE --- INTRODUCTION --- p.1
Chapter 1.1 --- Background of Study --- p.1
Chapter 1.2 --- Research Problems and Objectives --- p.3
Chapter 1.3 --- Layout of Thesis --- p.5
Chapter CHAPTER TWO --- LITERATURE REVIEW --- p.6
Chapter 2.1 --- Explaining the Gender Gap in Math Achievement: A Brief Overview of Previous Studies --- p.6
Chapter 2.2 --- Gender Stratification Hypothesis --- p.9
Chapter 2.3 --- Role of Parents --- p.11
Chapter 2.4 --- Role of Single-Sex Schooling --- p.12
Chapter 2.5 --- Focus of this Study --- p.16
Chapter CHAPTER THREE --- ROLE OF FAMILY BACKGROUND AND SINGLE-SEX SCHOOLING IN THE GENDER GAP IN MATH TEST SCORES IN SIXTEEN COUNTRIES --- p.18
Chapter 3.1 --- Hypotheses --- p.18
Chapter 3.2 --- Data and Method --- p.19
Chapter 3.3 --- Results --- p.23
Chapter 3.4 --- Discussion --- p.40
Chapter CHAPTER FOUR --- THE GENDER GAP IN MATH TEST SCORES IN ALL COUNTRIES PARTICIPATING IN PISA 2006 --- p.50
Chapter 4.1 --- Data and Method --- p.51
Chapter 4.2 --- Results --- p.57
Chapter 4.3 --- Discussion --- p.63
Chapter CHAPTER FIVE --- CONCLUSION --- p.67
Chapter 5.1 --- Summary of Findings --- p.67
Chapter 5.2 --- Theoretical Implications --- p.69
Chapter 5.3 --- Empirical Implications --- p.70
Chapter 5.4 --- Limitations and Suggestions for Future Research --- p.71
APPENDIX A: Description of dependent variables and student-level independent variables --- p.75
APPENDIX B: Description of school-level independent variables --- p.76
REFERENCES --- p.78

This chapter evaluates the contribution of behavioral genetics to the understanding of mathematical development. Quantitative genetic methods are introduced first and are followed by a review of the existing literature on the relative contribution of genes and environments to variation in mathematical ability at different ages and in different populations. The etiology of any observed sex differences in mathematics is also discussed. The chapter reviews literature on multivariate twin research into the etiological links between mathematics and other areas of cognition and achievement; between mathematical ability and disability; and between mathematical achievement and mathematical motivation. In the molecular genetic section, the few molecular genetic studies that have specifically explored mathematical abilities are presented. The chapter concludes by outlining future directions of behavioral genetic research into mathematical learning and potential implications of this research.

Numbers are the most powerful adjective in the human language, being that they are descriptive and quantifiable. Humans can harness that power with our eyes and our innate ability to see shape patterns. Virtual worlds afford us this opportunity without the physical world hindrances of materials, space, time, or gravity. Explore how language, decimal-centricity, and symbols with their processes have clouded the view of numbers, their shapes, and the discovery of metapatterns: visually recognizable algebraic expressions and equations. The experiences shared in the case study within reveal the need of a working virtual world environment for educational training, prototyping, and studio image capturing. Common Core Standards for Mathematics aspire to bring the student into the understanding of the “why”. In the virtual reality of Second Life, the metaphor of seeing the forest before the trees is realized with our example and number patterns: from the earliest subitizing, to multi-digit, multi-base number recognition, to metapatterns, to deriving polynomial equations through differences.

For individuals, cognitive ability is often an important reference for predicting education level, academic achievement, and work ability. In many cases, people usually work or study in a group situation with co-actors. For example, many students study together in a classroom, or workers work together in a workstation. People in a group interact and influence each other, which means they become each other’s social presence. Some studies found that the cognitive ability of group members affected the overall performance of the group. Therefore, it is also necessary to consider the individual cognitive ability factors in the research of social facilitation effects. We are curious about whether group members’ difference in cognitive abilities would moderate the effect of social presence on his task performance when they complete tasks in a group situation. In other words, we are interested in the effects of social presence on the intensity or direction of social facilitation exerting on people with different cognitive abilities when completing cognitive tasks.This paper investigated the effects of individual cognitive ability, social presence and task difficulty on the performance of mathematical calculations and recognition memory tasks. The mathematical calculation tasks and memory tasks are two kinds of typical cognitive tasks that people often need to deal with in work or study. Moreover, the extant studies verified that the social facilitation effect existed in those tasks. Hence, this study selected them as experimental tasks respectively. A three-factor mixed design experiment was conducted. The Cognitive Ability factor had two levels: low and high, which were distinguished by the score of the Cognitive Ability scale. The difficulty factor had two levels: easy and hard. The social presence factor had two levels: alone and group. In the alone condition, the participant did the task alone in a room. In the group condition, two participants conducted the experiment face-to-face in the room at the same time. There were 4 experimental conditions of two within-subject factors (2 difficulty × 2 social presence). Every participant needed to finish a trial of easy tasks and a trial of hard tasks in both alone and group conditions. The trials were randomly and balanced assigned in a counterbalanced design to the 8 trials across the experiment used. Thirty-six participants participated in this study. The response time and accuracy rate were used to assess the task performance. The results indicated that, although cognitive ability had a significant main effect on the performances, the interaction effect between cognitive ability and social presence on task performance was not significant. There existed a two-way interaction effect between social presence and task difficulty on response time of both tasks. The findings provide useful information for work organization and task allocation in a group work.