Gender Differences In Mathematics Performance

Gender Differences In Mathematics PerformanceThis do investigates sexual activity discrepancys in exe bangion on the maths comp singlent on the meter 3 topic Assessment in Trinidad and Tobago. Of interest is whether at that post is a relationship amid attitudinal differences regarding math and savant imprints in their mathematical abilities and schooling-age child gender classification. Results indicate that whereas girls performed discontinue than boys on every(prenominal) categories and all skill argonas on the test, the effect sizes were blue. The burdens of a MANOVA with follow-up descriptive discriminant summary also indicate that fleck boys and girls did not differ with regard to the sensing of the tutor milieu, raisingal values and remainders, and general academician self- conceit, they differ importantly on the patience and maths self-concept dicks. Girls tend to persist some(prenominal), but pass on dispirit maths self-concept than boys. Keywords persistence, math self-concept, CaribbeanDespite some inconsistencies in results, al virtually of the archaeozoic studies on maths acquirement launch that boys, consistently scored high(prenominal) than girls on a number of indicators of mathematical proficiency (Fennema Sherman, 1977 Kloosterman, 1988 Manning, 1998 Peterson Fennema, 1985 Randhawa, 1991, 1994). This interpret examines the phenomenon in the English speaking Caribbean, specifically Trinidad and Tobago, where girls consistently suck outperformed boys, and has become a matter of concern for Caribbean g everyplacenments and educators (Caribbean Education Task Force, 2000).A review of the books from the regular army and other Western societies on gender and math passment has revealed an inconsistent relationship surrounded by gender and mathematics attainment during the early twelvemonths of schooling. For example, in a 3- course of remove longitudinal discover conducted in the USA that examined the strategies that savants in the lower primary grades (grade 1-3) utilized in solving mathematics difficultys, Fennema, Carpenter, Jacobs, Franke, and Levi (1998) did not find gender differences in the capability to solve mathematics problems in grade 3 (8-10 year olds). They found however probative differences in problem-solving strategies in which girls tended to employ concrete solution strategies like modeling and counting, spell boys tended to use more(prenominal) abstract solution strategies that reflected conceptual instinct (Fennema Carpenter, 1998, p.4). However, Tapia and Marsh (2004) administer that up to 1994, measurable gender differences in mathematics loads argon app arnt only from age 13 and since that time, some(prenominal) jailbreak existed seems to shit disappe ard.Hanna (2003) contends similarly with regard to the disappearance of the gender gap, while Hyde et al. (1990) and Leahey and Guo (2001) extend this argument and caution against the asse rtion that in that respect is an evident gender difference in mathematics achievement favouring male persons. Leahey and Guo (2001) further state that at the dim-witted take existing differences were not consistent across mathematics skill areas, and where differences existed, were small but in favour of girls. Neverthe slight, they did confirm that at the secondary take, males exhibited a consistent but brush asidely superior operation in the areas of problem-solving (Hyde et al., 1990) and reasoning skill and geometry (Leahey Guo, 2001).Brunner, Krauss and Kunters (2007) examined the performance on mathematics items of school-age childs in Germ all. In their study they compared gender differences in overall mathematics ability (which as they explain is the standard model commonly found in the publications), and specific mathematics ability, i.e., an ability that influences performance on mathematics items over and above general cognitive ability (p. 405). They found that girls slightly outperformed boys on reasoning ability, but on specific mathematics ability, boys had a important advantage over girls.Cooper and Dunne (2000) in their study of the influence of the socio- pagan play down on students interpretation of realistic mathematical problems on the internal class in England also found that the look upons for boys were higher than those for girls. Overall, they feeld that swear out class students those from the higher socio-economic levels exhibited superior performance on realistic items than students in the lower socio-economic categories. However, they also observed that boys achieved slightly repair rack up than girls on realistic items (i.e. items to which they could relate, or were part of their experiences) in comparison to esoteric items (i.e. items that were more abstract.)More recent studies give up additional support for the above findings. For example, Williams, Wo and Lewis (2007) in their investigation of 5-14 year o ld students progress in mathematics attainment in England indicated that in the early years of schooling, individual differences in mathematics attainment are difficult to establish. In extending the discussion, Neuville and Croizet (2007) in a study of 7-8 year olds conducted in France, found that when gender identity is salient, girls perform better than boys on easy problems. On the other hand, boys performance on mathematics was not affected by gender identity. They were not subjected to stereotype menace that made negative assumptions about their mathematical ability, and so, they performed better on the more difficult problems. The study concluded that young girls are more supersensitized to the salience of their stereotyped gender identity than boys.An mental test of the Fourth locate info from the International Association for the Evaluation of Educational Achievement (IEA)s champion-third International Mathematics and Science Study (TIMSS), to some extent, contrasts slightly with Leahey and Guos (2001) findings. The TIMSS data show that in the majority of the participating countries boys attained higher mean scores in mathematics, however in only iii countries Japan, Korea and the Netherlands- were these kernel statistically solid at alpha = .05. The averages of all country nitty-gritty were males = 535 and womanishs = 533 (Mullis, Martin, Fierros, Goldberg Stemler, 2000) indicating that differences attributed to gender were minimal and random.In an digest of the OECDs 2000 Programme for International scholarly person Assessment (PISA), Marks (2008), found that in most countries, girls on average, have lower scores in mathematics than boys and the average across-country gender gap was 11 score points in favour of boys (p.96). He further explains that while in 15 of the 31 countries the gender difference in mathematics was not significant, in three countries, the difference was a sizable 27 score points, and in another two, the gap wa s moderate. In only three countries did girls do better than boys but the difference was not statistically significant (p.96). Despite the consistency in the research, there remains a maturation concern over the academic performance of boys, a concern which is echoed loud in England (Gorard, Rees Salisbury, 1999 Office for metres in Education (OFSTED), 1996 Younger, Warrington Williams, 1999) as evidenced from the runway debate and commentaries in the BBC News (09/18/2003), and the mentoring programme for underachieving Afro-Caribbean boys implemented by the British Government (Odih, 2002).From the above review, while there are slight inconsistencies in the findings, we can conclude that overall at the primary or elementary level, there is no significant difference in the mathematics performance of boys and girls. The differences only become noticeable at the secondary level where boys perform better than girls in geometry and on the more difficult mathematics items.Mathematic s Achievement Patterns The Trinidad and Tobago ContextsThe concern over the gender differential in mathematics performance remains the subject of intense debate in the English-speaking Caribbean (Caribbean Education Task Force, 2000). Specific to Trinidad and Tobago, and in contrast to the literature coming out of the U.S. and Western Europe, Jules and Kutnick (1990), Kutnick and Jules (1988) found that girls perform better than boys on t severallyer-made tests at all ages between 8 and 16, across all broadcast areas and in all curriculum subjects. They achieve better results on the supplementary Education Assessment (SEA) taken in Standard.5 (Std. 5) (age 11-12) and also achieve better results on the Caribbean Secondary Education Certificate (CSEC), the Caribbean equivalent to the British GCSE, administered by the Caribbean Examinations Council (CXC), taken at age 16-17 in Form 5 (Kutnick, Jules Layne, 1997 Parry, 2000). brownish (2005) corroborates the above findings, at least f or students in the lower primary school classes. In examining the performance of 7-9 year olds on the mathematics factor of the 2000 Trinidad and Tobago National Test, he found that overall the mean achievement score of girls was higher than that of boys. Additionally, he found that the non-response to items was significantly great for boys than girls, and a significantly greater number of boys than girls were in the lower tail of the distribution. In an attempt to determine whether the tests were biased in favour of girls, Brown and Kanyongo (2007) conducted differential item surgical operation (DIF) analysis on test items on the mathematics component of the 2004 National Test Std. 1 (age 7-9). They found that though quintuplet of thirty items on the test significantly differentiated in favour of girls, in working terms, the differences in item function were negligible and therefore could not explain the gender differential in performance on the test.With regard to Kutnick et al. (1997) and Parrys (2000) note of student performance on the CSCE, a review of the 2000-2002 CSEC ordinary level results for Trinidad and Tobago allows for alternative interpretations. The results showed that of the students taking mathematics at the general proficiency level, a greater per centum of boys than girls earned Grades I-III (Brown, 2005). This finding seems to give support to the deed of conveyance that boys on average perform better in higher-level mathematics (Leahey Guo, 2001 Manning, 1998 Randhawa, 1991, 1994) however, it call for to be qualified by the fact that a greater percentage of girls take general proficiency level mathematics the more pie-eyed course whereas more boys take basic level mathematics (Brown, 2005).Caribbean scholars have tried to understand this phenomenon and have offered a number of possible explanations. moth miller (1994) frames his argument in the context of the historical marginalization of the black male in the Caribbean of w hich disinterest in didactics has been an inevitable outcome. Chevannes (2001) and Parry (2000) contend while Conrad (1999) implies that the problem may be due(p) to socialization practices and cultural expectations of gendered behaviour which for males conflict with the ethos of the school, but alternatively, encourage females to be academically successful. Figueroa (1997), on the other hand, posits that what the Caribbean has been witnessing is the result of the traditional independence of Caribbean women, and historic male privileging of which one consequence has been male educational underachievement. The explanations presented all seem plausible. However, with the possible excommunication of studies by Kutnick et al. (1997) and Parry (2000) which looked at schoolroom variables, they are yet to be swell up-tried.In 2004-2005, the Trinidad and Tobago Ministry of Education (MOE) began collecting data that went beyond analysis of student performance on the National Tests. Whi le the instrument did not cut across socio-cultural factors, it address affective factors that predict academic achievement. From the instrument, we extract items that examine student motivation, academic self- science, emphases on the value and purpose of education, and perception of the school. Each of these factors has been found to be predictors of academic achievement in previous research. (Dweck Leggett, 1988 Marsh, 1992).Student Motivation, faculty member Self-perception and BeliefsDwecks Motivation Process Model (Dweck Leggett, 1988) posits that performance is impacted by an individuals touch about his or her ability (or lack thereof). This argument she frames within the concept of learn goals and performance goals. Students with high learning goal orientation are focuse on the acquisition of new knowledge or competencies. They place an intrinsic value on knowledge, which is reflected in a desire to learn. unstated to the desire to learn, is the willingness to make th e effort to achieve their goal. As a result, they are more likely to persist with challenging existent, responding with increased effort to sea captain the material.Performance oriented students, although also motivated to achieve, place greater wildness on proving their competence (Grant Dweck, 2003). In the present competitive atmosphere of the school, this lots means achieving a desired grade not as a validation of their learning, but as validation of their ability. The conceptualization of ability as a reflection of ones performance (Burley, Turner Vitulli, 1999) creates the tendency to avoid material that could result in poor performance. They display what Dweck and Leggett (1988) refer to as deep in thought(p) response low persistence when challenged by difficult material. The emphasis is on demonstrating ones competence and avoiding the appearance of incompetence (Ryan Deci, 2000, Lapointe, Legault Batiste, 2005).Researchers have studied the motivational orientation s and student academic self-perception from a variety of theoretical perspectives (Dweck Leggett, 1988 Heyman Dweck, 1992 Ryan and Deci, 2000 Ryan Patrick, 2001 Schommer-Aikens, Brookhart, Hutter Mau, 2000). A summary of the findings suggests a positive relationship between student motivation, self-esteem, academic engagement and academic achievement (Nichols, 1996 Singh, Granville, Dika, 2002). Further, the literature shows that inherent motivation is the individuals beliefs self theories (Lepper Henderlong, 2000). It is this belief in ones ability and its relation to achievement that drives persistence. Therefore, with regard to this study, students who believe in their mathematics ability, and further believe that their ability is linked to their effort in learning mathematics are motivated to work harder and as a result achieve at a higher academic level.But there are other factors both intrinsic and extrinsic to students that are think to their performance in mathemati cs. While we recognize that the classroom milieu created by the teacher and other institutional variables are critical elements in student learning, we also recognize it is students perception of the school and classroom environments that make these environmental factors powerful motivators or demotivators to their academic performance (Ireson Hallam, 2005 Ryan Patrick, 2001). Additionally, student attitude toward mathematics is highly cor think with achievement in mathematics (Ma, 1997 Ma Kishor, 1997). Their belief that mathematics is important to achieving their future goals results in greater effort to deliver the goods in mathematics and as a result, higher achievement scores (Bouchey Harter, 2005). Therefore, students scores on items that address these factors are expected to be related to their scores on the mathematics component on the national test.As part of the growing interest in gender differential in academic performance that is evident at all levels and across d isciplines in Trinidad and Tobago, this study seeks to determine whether students attitude towards mathematics and students beliefs in their mathematical abilities are related to the differential in mathematics attainment between boys and girls. specifically the study asksDo mean achievement scores differ by gender on a Std. 3 (age 9-10) large-scale mathematics estimate in Trinidad and Tobago?Is there a difference between boys and girls on their perception of school, their persistence when faced with academic challenges, their general academic self-concept and mathematics self-concept, and their educational values?MethodTrinidad and Tobago Education System A Brief redirect examinationTrinidad and Tobago is a multi-ethnic, multi-religious society in which no area is exclusive to one ethnic or religious grouping. The education system is run by a central authority the Ministry of Education (MOE). The country is dual-lane into eight educational rules which, with the exception of Tob ago which is predominantly of African descent, are even upative of all socio-economic levels, ethnic and religious grouping in the country. Each educational district is headed by a School Supervisor III (SS III) assisted by SSIIs responsible for secondary schools and SSIs responsible for primary schools. Early Childhood fright and Education is a separate department in the MOE. whole educational policies and mandates emanate from the central office to the respective supervisory levels (Oplatka 2004).The public education system of Trinidad and Tobago comprises four levels early childhood care and education (3-4 year olds), primary education (5-11/12 years) the secondary education (12-16/17 years) and the third level. The public primary education system consists of 484 schools. Of this number, 30 percent are government-funded and managed non-religious schools. The remaining 70 percent are government-funded schools but managed by denominational boards representing Christian, Hindu an d Muslim religious persuasions (MOE, 2001). Parents have the right to send their children to any school within their school district. Each primary school is divided into an infant department where students stay for two years (1st and 2nd year infants), and the primary level where students stay for phoebe bird years Standards (Std.) 1-5.ParticipantsThe participants were 561 public elementary school students from an educational district in northern Trinidad. The choice of the educational district was appropriate because its student population is representative of the student populations in the other six educational districts in Trinidad ensuring that the sample represented the demographic make-up of the country (See the- realness-factbook). Sixteen students were removed before analysis due to failure to include the student identification code, leaving 545 students (girls = 253, boys = 292, age roam 8-10 with a mean of 9.53 years). Of these students, 226 identified themselves as Tri nidadian of African descent, 201 of due east Indian descent, 4 Chinese, 3 White and 100 Mixed. Eleven students did not indicate their racial/ethnic origin. However, it is important to point out that ethnicity is not a variable of interest in this study.InstrumentsThe national test. Two sources provide the data for this study student scores on the mathematics component of the Std. 3 National Test and their responses to items on the questionnaire to provide supplementary data.The examination consisted of 25 items which fell into each of the following categories Number 11 items, bar and Money 8 items, Geometry 3 items, and Statistics 3 items. The national exam tested the following competency (skill) areas knowledge reckoning (KC), algorithmic thinking (AT), and problem solving (PS). Some items had multiple parts, with each part testing a different skill, whereas some items tested all three skills simultaneously ( plank 1).Items on the examination were dichotomously scored as either 1 for a remediate response or 0 for an incorrect response, or polytomously scored as either 2 correct, 1 partially correct or 0 incorrect.The cut scores on the test separated students into the following four dominance levelsLevel 1 Below Proficient. Score range of mountains 0-17.Level 2 Partially Proficient. Score range 18-29.Level 3 Proficient. Score range 30-39.Level 4 Advanced Proficiency. Score range 40-55.Table 1Examination questions (items) by kinsperson and skill areaCategoryStandard 3 (n=45 parts)KCATPSNo. partTotal ScoreNumber (11 items)9842124Measurement and money (8 items)7541619Geometry (3 items)11135Statistics (3 items)13157Entire exam1817104555We consulted with a mathematics education expert to determine the cognitive demand of the items on the test. The majority of the items were at the procedural without connections, or memorization difficulty level as expound by Stein, Grover and Henningsen (1996), and therefore, elicited low-level thinking and reasoning. O nly four items were at the level of procedures with connections and had the potential to elicit high-level thinking (Stein et al., 1996). The following are examples of the types of items on the test.Ruth had 7/8 of a kilogram of give up.She used 3/8 of a kilogram to make pies.How much cheese was left?Answer _______________________Mrs. Jack is teaching a lesson Measuring Distances to her Standard 3 class.She teaches that 100 centimetres = 1 metrePetrina used a taping marked in centimetres to measure the length of her classroom.She got a measurement of 600 centimetres.1. lay aside what Petrina must do to change the length of the classroom into metres.2. The length of the classroom is________ metresFigure 1. Examples of types of test items.The questionnaire. Factor analysis was performed on the questionnaire to develop the five factors (Persistence, Academic self-concept, Values and Goals, School Environment, and Mathematics self-concept) that were used in this study as subject var iables. Because these five dependent variables were considered simultaneously, (with gender as the individual variable), we utilized the multivariate analysis of version (MANOVA) procedure.Although one of the assumptions for the use of factor analysis is that the data are measured on an interval scale, Kim and Mueller (1978) note that ordinal data may be used if the assignments of ordinal categories to the data do not seriously distort the underlying metric scaling. In a review of the literature on the use of data poised on Likert scales, Jaccard and Wan (1996) concluded that, for many statistical tests, rather austere departures from intervalness do not seem to affect suit I and Type II errors dramatically. Other researchers like Binder (1984) and Zumbo and Zimmerman (1993) also found the validity of parametric coefficients with respect to ordinal distortions.Additionally, we used the Principal Axis calculate procedure as our method of extraction because it seeks the least a mount of factors that banknote for the most amount of common variance for a given raft of variables. We also employed oblique rotation because it often reflects the real world more accurately than orthogonal rotation since most real-world constructs are correlated. (See Fabrigar, Wegener, MacCallum and Strahan, 1999 and sermonizer and MacCallum, 2003 for a detailed but non-technical discussion of the topic). The five constructs that we extracted in this study are correlated, another justification for using MANOVA with the five constructs as dependent variables.The questionnaire comprised 50 items. Items 1 to 10 sought demographic information. Of the remaining xl items, twenty eight were variables of interest. These measured academic self-esteem, perception of school/classroom environment, relationship with teacher, goals and value of education, mathematics self concept and persistence on a 5-point scale anchored by 1 disagree very much and 5 agree very much. To test whether t he items really measured the underlying dimensions of interest, we subjected the items to a Principal Axis Factoring with Oblique rotation, suppressing loadings on variables lower than .40. This yielded a six-factor solution. The sixth factor accounted for only an additional four percent of variance therefore, five factors were specified. This resulted in the four items pertaining to student-teacher relationship loading on student perception of school/classroom creating the school environment factor. All other factors remained the same. Additionally, two of the items measuring academic self-concept yielded loading values less than .40, and therefore, were deleted from the scale leaving 26 items to provide the data for the study. Two items addressed mathematics self-concept. These items consistently loaded together yielding loadings of .846 and .772 respectively (see Appendix).Table 2Eigenvalues and variance percentages and scale reliability valuesFactorsEigenvalues% of Variance addi tive %Cronbachs alphaPersistence7.39728.44928.449.85General self-concept2.95311.35939.808.80Math self-concept2.1128.12347.931.79Values and goals2.0017.69655.628.74School environment1.2974.98860.616.85Overall scale reliability Cronbachs alpha = .90On this sample, the five factors accounted for 60.62 % of the variance in the set of variables with the graduation exercise and second factors accounting for 28.45% and 11.36% of the variance. All factors yielded inter-item correlations .35 with some(prenominal) correlations .70. Inversely, matrices of partial correlations were very low supporting the presence of factors. The factors were perception of school/classroom (8 items) e.g., I am glad I go to this school, persistence (6 items) e.g. When work is difficult I try harder, general academic self-concept, (6 items), e.g., I can learn new ideas quickly in school, goals and values (4 items) e.g., Doing well in school is one of my goals, and mathematics self concept (2 items) e.g., I am good at mathematics. Internal consistency reliability for the sinless instrument was .90. Table 2 shows the five sub-scales (factors) in the utmost instrument and their reliability values as well as the percentage of the variance they account for.ProcedureUsing the student ID numbers, student scores on the mathematics discernment were paired with their responses on the supplementary data questionnaire. to begin with conducting the statistical analyses, all appropriate statistical assumptions were tested. The assumptions homogeneity of variance and covariance, and one-dimensionality were tenable. As expected, all factors displayed negative skewness. To reduce skewness and kurtosis, and by doing so, achieve a better approximation to a normal distribution, variables displaying moderate to material skewness and kurtosis were subjected to either a square root or logarithmic transformation. Despite these transformations, some variables still yielded skewness and kurtosis slightly g reater than 1, (Sk = 1.5 and K = 1.27). However, with N 500, and pairwise within group scatterplots revealing no discernible patterns, these small deviations from normality should not present any concerns. Tests for multivariate outliers identified five cases with values above the criterion, (df, 4) = 18.47, p =.001. To remove their undue influence, these cases were deleted from the sample. Further cover identified an additional case. This case was removed resulting in a final sample n = 539.Data AnalysisFirst, to investigate gender differences on the mathematics assessment, independent t-tests were performed. Second, to determine the extent to which the male and female examinees differed on the five constructs, a univariate analysis of variance (ANOVA) was conducted on the school environment factor because this was not correlated with the other factors. Third, a multivariate analysis of variance (MANOVA) was performed on the four correlated factors (persistence, mathematics self -concept, general self-concept, and goal values) as dependent variables. Descriptive discriminant analysis was conducted as follow-up to a significant multivariate F to determine which variable or variables contributed most to differences between the groups. We used effect size to measure the magnitude of the difference between the mean score for boys and girls on each mathematics category tested. Effect size was obtained by dividing the difference between boys and girls mean by the pooled within-gender standard deviation. According to (Cohen, 1992), effect sizes of less than .20 are considered small and represent small practical significance effect sizes between .20 and .50 are strong point and represent moderate practical significance. Effect sizes greater than .50 are considered large.ResultsThe first step in this study sought to determine whether boys and girls differed in performance on a Standard 3 large-scale mathematics assessment in Trinidad and Tobago. To make this determ ination, we performed an independent t-test between the means of the two samples for each category and skill area. Table 3 shows the means and the effect sizes of the differences between the two samples for each category, cognitive demand level and skill area. In the table, we also report standard error of the means (SEM) to provide an index number of the sampling variability of the means. The results indicate that while girls achieved higher mean scores in all categories, difficulty levels and all skill areas on the test, the differences between boys and girls were statistically significant at pTable 3 represent normal curve equivalent(nce) scores of the test categories, difficulty levels and skills for male and female examineesCategoryBoys(n=289)Girls (n=250)Sig.Effect SizeMeanSEMMeanSEMpDNumber52.201.1757.831.22.001.29Measurement and money52.731.1856.481.26.031.19Geometry52.891.2056.041.22.068.16Statistics50.531.1656.871.23.002.27Skill AreaKnowledge and computation51.011.1657.44 1.24.000.33Algorithmic thinking53.811.1157.921.24.013.21Problem-solving53.601.2258.411.25.006.24Cognitive Demand let loose memorization49.081.2651.041.31.754.09Low procedural46.551.2553.921.28