Math Achievement Essay
Math Achievement
Abstract
This paper outlines the author’s purpose for reviewing literature on gender differences in mathematics education. An overview of research findings on gender and mathematics from industrial societies (USA, Australia, and UK) and from some developing countries in Southern Africa (South Africa, Mozambique, and Botswana) is then presented. Some causal factors for the existence of gender differences in mathematics achievement are critiqued and the link between mathematics and social entities (democracy and power) are challenged. The implications of the above for research on girls learning mathematics in Botswana (and Africa) are finally suggested.
Introduction
Literature review should not be considered as merely part of the requirements in scholarly enterprises, but as a critical undertaking in which the investigator exercises a constant scepticism on an issue of interest. In this paper, literature review is used as a process to critique the conscious and unconscious assumptions of scholarly research on gender differentials in mathematics education. It serves as a qualitative analysis to determine how these assumptions force the definition of problems and findings of such scholarly research efforts.
The paper examines literature on research studies which have dealt with gender differentials in mathematics classroom dynamics. The disenfranchisement of girls in mathematics learning discourses and girls’ motivational orientations in mathematics are important issues for the human development efforts in Botswana. The paper draws upon literature from Western countries, specifically the USA, the UK and Australia where research on gender differences in mathematics has been considerable and influential.
The sociopolitical, cultural and socioeconomic contexts in these countries, however, differ from those of Southern Africa in many aspects of development (education, technology, economic, etc.), but there are possibilities to draw parallels, albeit in a limited way. Through considering parallels and differences between Western industrial cultures and Africa, the paper examines issues pertinent to African girls affecting their education.
The literature analysis is against the backdrop of problems such as HIV/AIDS and unplanned pregnancies faced by girls within African communities. Botswana (like most of Africa) is grappling with the HIV/AIDS pandemic; high levels of unemployment and poverty (BIDPA, 2000). The African Economic Commission (1999:5) states that:
Data from Botswana, Burundi, Central African Republic, Uganda, Zambia and Zimbabwe indicate that girls 15 to 19 years old have an (HIV/AIDS) infection rate four to ten times that of boys in the same group.
This is the age group within which research on gender and mathematics has tended to focus. According to Okojie (2001), the Botswana study, commissioned by the African Academy of Sciences Research Programme, indicated the rate of teenage pregnancy being higher than that of most other African countries. HIV/AIDS, unplanned pregnancies and lack of interest in mathematics are amongst real problems that girls in the developing world face which must be taken on board when embarking on a sociological research analysis involving gender differences.
Notwithstanding these developments, the question of how to motivate students in the classroom is a leading concern for teachers of all disciplines. Student motivation becomes especially relevant to mathematics education in the light of recurring questions about how to get more students interested and involved in the subject. As we proceed in the new millennium, Botswana is plagued with significant highschool dropout rates and declining interest in mathematics among secondary school students. Educators and policy makers need to understand the educational techniques that may ‘suffocate students’ interest in learning’ (Boggiano and Pittman, 1992), then work to rekindle that interest.
This paper is concerned with the use of mathematics as a ‘filter’ for further education and career choices. This affects girls more as they tend to shy away from the study of higher level mathematics, science and engineering as reflected in the University of Botswana yearly intake (Fact Books 2002; 2003; 2004/5; 2005/6). The literature analysis proceeds from an articulation of girls’ reported achievement tendencies within mathematics learning discourses in the developed world and explores the situation in Africa, particularly Southern Africa, with a special focus on Botswana.
Gender differences in mathematics education
The developed world’s perspective on gender and mathematics Contemporary research studies reflect scholars’ maturing view of the complexity of causation of differences between males and females in mathematics education. As Fennema (2000) rightly points out, from around 1970, ‘sex differences’ index was used to imply that any differences found were biologically, and thus, genetically determined, immutable and not changeable. During the 70’s and 80’s ‘sexrelated differences’ criterion was often used to indicate that while the behaviour of concern was clearly related to the sex of the subjects, it was not necessarily genetically determined. Latey, ‘gender differences’ refers to social or environmental causation of differences that are observed between the sexes.
This paper critically reviews work by leading researchers in the era of this new understanding of gender differences. According to Leder (1996) there were probably more research studies published on gender and mathematics than any other area between 1970 and 1990. Fennema (1993, 2000) concluded that while many studies had been poorly analysed and/or included sexist interpretations, there was evidence to support the existence of differences between girls’ and boys’ learning of mathematics, particularly in activities that required complex reasoning; that the differences increased at about the onset of adolescence and were recognised by many leading mathematics educators. Salmon (1998) concurred with the notion that gender differences increase at secondary school level, particularly in situations that require complex reasoning. In the absence of an African position disputing such views, it suffices to assume that similar differences might occur in the Southern African contexts.
Studies by Fennema and Sherman (1977, 1978) documented sexrelated differences in achievement and participation, and found gender differences in the election of advanced level mathematics courses. They hypothesised that if females participated in advanced mathematics classes at the same rate that males did, gender differences would disappear. Stanley and Benbow (1980) used interpretations of some of their studies as a refutation of this ‘differential coursetaking hypothesis’. They argued that gender differences in mathematics were genetic, a claim which was widely attacked and disproved, but whose publication had unfortunate repercussions (Jacobs and Eccles, 1985).
Fennema and Sherman (1977, 1978) identified as critical, beliefs about the usefulness of, and confidence in learning mathematics, with males providing evidence that they were more confident about learning mathematics and believed that mathematics was, and would be, more useful to them than did females. There was evidence that while young men did not strongly stereotype mathematics as a male domain, they did believe much more strongly than did young women that mathematics was more appropriate for males than for females. The importance of these variables (confidence, usefulness and male stereotyping), their longterm influence, and their differential impact on females and males was reconfirmed by many other studies (Hyde et al., 1990; Tartre and Fennema, 1991; Leder, 1992).
Earlier, Maccoby and Jacklin (1974) had reported differences between females and males in spatial skills, particularly spatial visualization or the ability to visualize movements of geometric figures in one’s mind. The FennemaSherman studies and the Fennema and Tartre (1985) longitudinal study investigated spatial skills or spatial visualisation. They found that while spatial visualisation was positively correlated with mathematics achievement (that does not indicate causation), not all girls were handicapped by inadequate spatial skills, except those who scored very low on spatial tasks.
Fennema (1993) suggested that an appropriate curriculum redesign could compensate for these weak skills. Other studies (Kerns and Berenbaum, 1991; Voyer, Voyer and Bryden, 1995) reported boys outperforming girls on tests of visual/spatial abilities: the ability, that is, to draw inferences about or to otherwise mentally manipulate pictorial information. The male advantage in spatial abilities was reportedly not large, but detectable by middle childhood and persisted across the life span. Casey, Nuttall and Pezaris (1997) concluded that sex differences in visual/spatial abilities and the problemsolving strategies they support contribute to sex differences in arithmetic reasoning.
Although they were not particularly innovative nor offered insights that others were not suggesting, the FennemaSherman studies had a major impact since they were published when the concern with gender and mathematics was growing internationally. They were identified by Walberg & Haertel (1992) and others as among the most often quoted social science and educational research studies during the 80’s and 90’s. The problems of gender and mathematics were defined and documented in terms of the study of advanced mathematics courses, the learning of mathematics, and selected related variables that appeared relevant both to students’ selection of courses and learning of mathematics. The FennemaSherman Mathematics Attitude Scales have been widely used as guidelines for planning interventions and research studies.
Campbell (1986) found that girls’ lack of confidence in themselves as mathematics learners, their perception of mathematics as difficult, and their view that mathematics is a male activity, all had impact on girls’ attitudes, achievement, and participation in advanced courses. In a longitudinal study of sixth, eighth, tenth, and twelfth grades, Tartre and Fennema (1991) found that, for girls, viewing mathematics as a male domain was correlated to mathematics achievement. Girls in singlesex schools or in outofschool mathematics projects – who did not see mathematics as an exclusively male domain tended to have higher mathematics success. When this dynamic was changed to make mathematics accessible to both girls and boys, girls’ interest and involvement were found to rise.
Reyes and Stanic (1988) and Secada (1992) have argued that socioeconomic status and ethnicity interact with gender to influence mathematics learning. Forgasz and Leder (1998) share the view that gender differentials in participation rates are associated with the interaction of positive attitudes and beliefs about mathematics and socioeconomic status. The transferability of these findings, based on Western cultural concepts, poses a problem for African contexts. Socioeconomic status indicators in Botswana for instance, somewhat differ from the UK model and need be appropriately contextualised. The question of ethnicity also becomes problematic in the Botswana context since about 85% of the population is of Tswana ethnic origin. Moreover, ethnic differences have never been of significance and might not necessarily affect gender differences in mathematics in the same way as in Western contexts.
Trends of gender differences in mathematics from the United Kingdom The gender gap in performance throughout the subjects in the United Kingdom has been shifting in favour of girls since the early 1990s. In national curriculum tests and at higher level GCSE grades, girls outperform boys. For example, in 1997, 49% of girls achieved five or more higher grade GCSEs compared with 40% boys (DfEE, 1997). However, at the lower levels of GCSE attainment, the gender gap is smaller in percentage point terms. In 1997, 8.8% of boys and 6.5% of girls failed to gain GCSE qualifications (DfEE, 1997).
These figures show some of the paradoxes in gender and attainment. Males gain most of the higher education top awards but the trend is for girls in general to do better in public examinations than boys – differences which are apparent in the earlier years of schooling. Consequently, current concerns about schooling are now more related to boys’ underachievement (as demonstrated in public examinations) than to that of girls. The question is whether such outcomes at school and higher education reflect approaches to assessment, methods of teaching, and/or expectations of society.
The OfSTED (2003) report found that boys progress more than girls in mathematics throughout schools. Research indicated that in mathematics the gap between boys and girls attaining level 4 and above at the end of Key Stage 2 was only one percentage point, with boys at 73% and girls at 72%; however, 32% of boys achieved level 5 and above whilst only 26% girls did (OfSTED, 2003:13). According to OfSTED (2003:14) although the differences are smaller than those in English, it is a continuous trend and it is therefore still vital to understand why girls perform better in certain subjects such as literacy and underachieve in comparison to boys in mathematics.
One key reason may be the perception girls have of this subject area. The 1998 OfSTED Report on ‘Recent Research on Gender and Education Performance’ stated that “science, mathematics, technology, ICT and PE are rated as ‘masculine’ by pupils and preferred by boys” (Arnot et al., 1998:31). Girls rated English, humanities, music, PSE and RE as feminine and preferred by girls. However, Archer and Macrae (1991) are cited in the same OfSTED report suggesting that mathematics has become more gender neutral perhaps reflected in the smaller gap between genders than that of literacy. The reason the gap has become smaller may be because girls are more prepared to tackle ‘masculine’ subjects.
Public concern about the underperformance of boys has risen since the early 1990s as girls outstripped their male classmates academically. Although the proportion getting five C’s or better increased from 38% in 1996 to 46% in 2003, the gender gap remained steady at 10 percentage points in favour of girls. Both boys and girls in deprived areas got much lower grades than their more advantaged peers. But while girls in poor areas were improving faster than those in affluent areas, the gap between rich and poor boys remained constant. Dr. Deborah Wilson, Bristol University expert on the gender gap in schools, argued that the differences are likely to be a result of factors outside school: “The effect of poverty on exam results is greater than the effect of gender. If we focus more on the reasons for poverty affecting performance we might get better results for both boys and girls” (TES, 13 August 2004).
According to Mendick (2002), in England, the evolving gendered patterns of attainment in mathematics need to be juxtaposed with the unchanging gendered patterns of participation in the subject. There are very few remaining differences between the attainment of male and female students in either GCSE, AS, or Alevel mathematics examinations (taken at ages 16+, 17+ and 18 respectively) (Gorard et al., 2001; Guardian, 2002a, 2002b). Although boys are still more likely to secure the top A* and A grades at GCSE and Alevel respectively, the differences are small and getting smaller. In contrast to these shifting patterns of attainment, the decision to continue with advanced mathematics remains highly gendered in favour of boys.
This polarization persists despite decades of feminist intervention; as Shaw (1995:107) argues: “the most striking feature of subject choice is that the freer it is, the more gendered it is.” In fact, from 1994 to 2002, the proportion of the total number of 17 and 18 yearolds entered for Alevel mathematics in England who are male showed little change, dropping only slightly from 65% to 63% (Government Statistical Service, 1995 to 2002; Guardian, 2002b). This greater participation of males in mathematics courses becomes more pronounced as you go up the levels from Alevel, to undergraduate, and then to postgraduate, and is reflected in the larger number of men than women working in mathematicallyoriented fields.
Mendick (2002:1) argued:
The gender gap in maths performance in this country, while still marginally in favour of boys, is continuing to narrow (Smithers, 2000; Gorard et al., 2001). However, the gender gap in participation in maths remains in spite of more than two decades of feminist initiatives for change. Moreover, maths becomes increasingly male dominated as we progress from sixthform (ages 16 to 19) to undergraduate levels, and from undergraduate to postgraduate levels (Boaler, 2000)… girls continue to disproportionately opt out of maths, a powerful area of the curriculum that provides a ‘critical filter’ (Sells, 1980) to high status areas of academia and employment.
The above suggests that although girls are doing better than boys overall across the subject areas in the UK, they still fall behind when choosing mathematics at higher levels of the education system. Mendick also portrays mathematics as a powerful subject, a signifier of intelligence that acts as a ‘critical filter’ controlling entry to higher status areas of academia and employment. Thus, for those concerned with social justice, it is pertinent to ask how it is that people come to choose mathematics and in what ways this process is gendered, which is the point of concern for this paper.
According to Bevan (2005), the findings from the review of existing research included evidence that girls outperform boys in mathematics up to the beginning of Alevel, but that the differences are small, and are not consistent across all components of the subject; attitudes to mathematics vary according to gender; there are significant differences in the expectations of boys and girls regarding their own performance in mathematics; boys and girls differ in their typical learning styles; and that ability grouping impacts differently on boys and girls.
Bevan’s (2005) interviews revealed that teachers with very limited exposure to formal research were able to articulate judgments about gender differences in learning mathematics based solely on classroom experience; and that their intuitive judgments were often broadly correct, but tended to exaggerate the extent of any real differences. Presently there is no comparative research concerning Botswana teachers’ judgments on gender differences in the learning of mathematics.
Sparkes (1999) pointed out that the gender gap in the UK was related to a variety of social issues including: parents’ educational attainment, growing up dependent on an income support recipient/eligible for free school meals, housing tenure and conditions, family structure (such as lone parent family), parental interest, involvement, practice, etc. These trends are different from the situation in Botswana and any comparisons need a contextual analysis of the situation.
Perspectives from Africa with specific reference to Southern Africa
Gender differences in mathematics education in developing countries are one critical area of research that needs further exploration. There is limited information about the status of contextual research on women and girls in those settings in relationship to their mathematical education. As Kitetu (2004:67) acknowledges from an African view:
Unfortunately, while a lot of gender programmes have been carried out, not much research has been done within the classroom in the continent. Our understanding of gender in classroom practices is most often based on what has been studied in Western Europe and North America. I would like to argue that there is always a cultural angle in studies of social practices.
Fortunately, there are emerging research efforts in the area of mathematics as the African continent begins to face up to the realities of gender differences in classroom practices. The persistent patriarchal attitudes in Africa tended to prevent researchers from problematising the gender issue.
Investigating gender differences and Black South African learners’ attitudes towards mathematics, Mahlomaholo and Sematle (2004:45) reported that:
The differences between boys and girls were very clear at all levels of analysis… For example they (girls) said it was because of parental pressure/choice or because their friends were studying the discipline, or because their teachers instructed them to study mathematics. Others even went to the extent of citing chance or fate as responsible for them taking mathematics as an area of study… They were apologetic and not taking responsibility on themselves… They even expressed their embarrassment at not being good at mathematics, they also expressed the fear for their teachers whom they compared to lions… they tended to agree that mathematics is for all and not for a particular gender.
For the girls in Mahlomaholo and Sematle (2004:67), mathematics was “too difficult” and …they were fed up with the subject and… cannot be expected to continue with a subject that they were failing so dismally… did not even have an interest in the subject as it demanded too much work and time to study while the boys saw much value in the discipline…There is no reason at all why some human beings do not have appropriate views regarding the study of mathematics, it is only because the views of a culture and a milieu that undermines women speak through them and have manifested themselves firmly in their minds.
In their study of three successful women in mathematics related careers, Mahlomaholo and Mathamela (2004:3) reported the prevalence of a conventional patriarchal approach in the South African society. They argued that:
It tends to privilege male interests and their privileged positions at the expense of women through the belief that the status quo where male dominate is natural and given… Schools tend to operate in line with this approach.
To underscore how the three women persevered in mathematics within the hostile cultural attitudes, Mahlomaholo and Mathamela (2004:7) argued that:
…socialisation and upbringing, including home and family background, as well as parental support, were identified as factors that enabled the three women to go beyond the limitations of their situations.
Mahlomaholo and Mathamela were convinced that beyond contextual and social factors the women had strong conceptions of themselves. They had selfbelief in their abilities and a love for mathematics, which could not be dampened either by teachers’ negative remarks or the social structure’s negative stereotypes. The study identified social contextual factors and intrapsychic motivational factors as responsible for enabling female learners of mathematics to either excel or fail at the subject.
Cassy (2004:56) reported from Mozambique that: “Although the main aim of the education policy of the country is to promote, among others, gender equity in access to all education levels, there are more females than males, who do not benefit from this. This gender discrepancy increases over the education levels, being more at the tertiary level and particularly in mathematics and its related fields.” Cassy found significant differences between the patterns of attitudes towards mathematics expressed by boys and girls in which boys rated their attitudes more positively than girls did. Boys were more confident in working in mathematics than girls, and girls were more convinced that mathematics was a male domain than boys.
Furthermore, girls were reported to believe much more than boys that mathematics is more appropriate for males than for females. Both girls and boys were found to agree that mathematics was useful. These findings are not different from what has been reported in Western research studies. Perhaps this was to be expected since the study used the FennemaSherman Mathematics Attitude Scale with its robust Western cultural questioning style. Cassy (2004:6) acknowledges that: “the majority of girls did not like the connotation of the items.” This calls for a more contextualised itemisation of the scales adopted from Western research contexts.
Chacko (2004) presented another study from a Southern African perspective on the problems of students in learning mathematics and the approaches used in teaching mathematics in South Africa. Chacko reported no differences between girls and boys in terms of liking the subject. Chacko (2004:4) wrote:
… they do like mathematics and would like to do well in it but for them it is a very difficult subject. This interest in doing mathematics came out more prominently in township schools where they considered it important for future jobs. The South African students’ belief that mathematics is difficult was found among secondary school students in Zimbabwe (Chacko, 2000).
Chacko (2004:45) further argues that students were encouraged to do well in mathematics because “their goals in life are something that is urging them to like mathematics which according to Hannula (2002) is ‘the value of mathematics – related goals in the student’s global goal structure.’” It seems, from Chacko’s arguments that the liking of mathematics was not intrinsic to the students, but driven by the urge to do well in the subject because of the need and importance it presented for their future trajectories.
According to Chacko (2004:8), girls in township schools seemed to spend more of out of school time on household chores, which could affect their studies. The same could be said about Botswana girls as Chacko (2004:56) further argued:
… chores took most of their time while school work was at the end when they were already tired to concentrate. This is more a developing country problem where chores in the house are kept for girls, which could affect the time they spent on learning and their vision for the future. … Some of the girls in the township schools said that when they do not find time to complete homework, due to the reprimand from teachers, they would rather miss school. Once they miss school, it becomes difficult to catch up, which eventually lead to failure and drop out.
Some of these problems are unique to the African contexts, and cannot be ignored when embarking on research on gender and mathematics.
Chacko (2004:8) reported that the majority of students wanted mathematics to be made fun and to be related to life where they can see its use. “Girls in particular would like to see the content related to situations in life where these could be applied.” Some reported being shy and afraid to tell teachers that they did not understand, to avoid being ridiculed in public (by fellow classmates or teachers). Some of these issues are distinctive features of gender differences in African contexts which distinguish them from those of Western industrial societies. From the researcher’s experiences of teaching in secondary schools in Botswana and Nottingham (UK), there seems to be common ground with Chacko’s arguments.
Over the years there have been efforts to address the gender disparities in education in Africa, with a particular concern on the enrolment of girls, which for years has been very low. As Kitetu (2004) put it:
The imbalance in boys’ and girls’ participation in schooling was linked to the agelong belief in male superiority and female subordination. This situation was further explained as aggravated by patriarchal practices, which gave girls no traditional rights to succession… encouraged preference to be given to the education of a boy rather than of a girl.
These smallscale investigations are recent efforts towards a better understanding of gender differentials in mathematics from an African perspective.
A+

Subject: Gender,

University/College: University of Arkansas System

Type of paper: Thesis/Dissertation Chapter

Date: 13 October 2016

Words:

Pages:
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