equity issues affecting mathematics learning using ict

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EQUITY ISSUES AFFECTINGMATHEMATICS LEARNINGUSING ICTSara Hennessy a & Penelope Dunham ba University of Cambridge , UKb Muhlenberg College , PA, USAPublished online: 14 Apr 2008.

To cite this article: Sara Hennessy & Penelope Dunham (2002) EQUITY ISSUESAFFECTING MATHEMATICS LEARNING USING ICT, Research in Mathematics Education,4:1, 145-165, DOI: 10.1080/14794800008520107

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9 EQUITY ISSUES AFFECTING MATHEMATICS LEARNING

USING ICT

Sara Hennessy, University of Cambridge, UK

Penelope Dunham, Muhlenberg College, PA, USA

Our concern is the inequities that arise from dzferential access and use of educational technology in mathematics for groups characterised by gender, ethnicity, income level and ability. As access to information and communications technology (KT) increases both in homes and schools, our paper asks whether previous inequities are being ironed out or exacerbated. Equity is consideredj-om the three perspectives proposed by Fennema (1990), namely in terms o$ (a) opportunities to learn (physical access); (b) educational treatment (how technology is used, by whom), and the social and psychological factors influencing its use; (c) educational outcomes (impacts on achievement, attitudes and motivation). Suggested policies and pedagogies for removing the boundaries between technology 'haves' and 'have-nots ' are presented.

INTRODUCTION

For several decades, mathematics educators and researchers have described the impact and explored the potential of using technology-based activities to facilitate and transform mathematical learning at all levels. With electronic technologies, students can explore concepts, engage in experimentation, model problem settings, experience greater success in problem solving, compute more efficiently, focus on decision making and reasoning instead of computation and manipulation, collect and analyse real-world data, and examine many examples from graphical, numerical and algebraic perspectives (e.g. Dunham & Dick, 1994). It can be argued that since technology has such a powerful potential impact on teaching and learning - and on employment and everyday life - then all students deserve equal access to its benefits. In this paper we present an overview of research on technology in mathematics education fiom the perspective of equity in terms of 'fairness' and justice. Our concern is with inequities - and consequent barriers to learning - that arise from differential access and use by various groups, particularly those identified by gender, ethnicity, social class/income level, geographical location and ability.

Definitions of Equity

What does 'access to the benefits of technology' imply? Researchers in mathematics education use several definitions of the 'equity' construct, most of which focus on equity as a social justice issue concerned with students'opportunities to achieve their full potential (e.g., Secada, 1994). Some researchers note that equity does not necessarily mean equality. In fact, if equal outcomes are a goal, equity and equality

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Research in Mathematics Education Volume 4

may conflict, so that achieving equity may require inequality (Sutton, 1991). Thus, equity is not merely 'sameness' or lack of difference in some measurable index (such as the ratio of students per computer among schools) but may entail differential treatment1 in order to achieve 'fairness' (Lee, 1999).

For this review, we employ Fennema's (1990) three perspectives on equity to examine research in terms of equal opportunity to learn, equal educational treatment, and equal educational outcomes. Fennema - like Sutton (1991) and Secada (1994) - argues that the outcomes perspective is the one that most promotes fairness and justice in mathematics education, even if it conflicts with the results of the first two.

TECHNOLOGY IN SCHOOLS: EQUITY ISSUES IN ACCESS AND USE

Access to computer and Internet technology in schools

Equity as 'equal opportunity to learn' focuses attention on research about availability of technology. Students' access to ICT at school and at home has increased astronomically over the last few years, particularly in the US, Australia, and Great Britain and, to a lesser degree, in other economically-advantaged nations (particularly Finland, New Zealand and Sweden: OECD, 2000, ch.4). A host of government initiatives, including most recently the ambitious National Grid for earning,^ scheme in the UK, has helped to increase availability of ICT since the mid-1980s (DfES, 2001; Smerdon et al., 2000). A majority of schools in the UK (BESA, 2000), Australia (ABS, 2001), and the US (NCES, 2001) now have Internet access - although some offer it only to older or technologically competent pupils (Valentine et al., in press). Some policies, particularly in the US, have been successfully targeted at low-income, minority, and rural schools, reducing some previous inequities in access. However, several manifestations of the 'digital divide'' are still apparent. To summarise, inequities in access and use of computing technology and the Internet include:

a "global digital divide" between poor and rich nations

' For example, differential benefits for female students using portable technologies rather than desktop machines are reported in the 'Outcomes' section.

The NGfL scheme aims to connect all UK educational institutions to on-line resources by 2002. Other developed countries are also creating infrastructures for digital learning, such as Sweden's "Schoolnet." In Japan, the "Virtual Agency" aims to connect all schools, then to train all teachers and provide computers and high-speed Internet access in every classroom by 2005 (OECD, 2000, ch.9).

The term 'digital divide' is no longer a unitary concept but encompasses a spectrum of levels of access to and use of technology, relating to a range of technologies, themselves varying in age and capability (Damarin, 2000).

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UK Government figures for 2001 showed that the ratios of instructional computers to pupils were 1 : 12 in primary schools, 1 :7 in secondary schools and 1:3 in special schools (DfES, 2001). By contrast, Brandenburg & Dudt (1998) reported that only 8% of Belize schools had computers available for student use and no school was connected to the Internet. In the mid-1990s nearly half of all people with Internet access were in the US, and in 1999 one in four Australians had Internet access compared to one in 4000 Afi-icans (Selwyn, 2000). By 2000, 47% of Australian adults reported Internet use with one-third of the households having home access to the Internet (ABS, 200 1).

inequitable distribution between schools and regions

International differences are compounded by inequities in computer access within nations, districts, and schools. Students from predominately white, high-SES (socioeconomic status) schools or schools with low minority enrolment have more computers per school and lower studentkomputer ratios (Becker, 2000; Levin et al., 2000; Tate, 1997; Williams, 2000). Urban and rural schools often have fewer computers and greater studentlcomputer ratios than suburban schools (Brush, 1999; Neuman, 1993; Williams, 2000). Ethnic minority children, often over-represented among low income families and in urban schools, may experience a compounding of racial and SES effects on equity (Ladson-Billings, 1997; Page, 1998; Waxrnan & Padron, 1994).

disadvantaged schools have more unreliable technology

Even when rates of access seem similar, computers in poorer schools and those with high minority enrolments are often outdated models with limited capability (Becker, 2000; Smerdon et al., 2000). In the UK, many primary schools cannot afford the high-speed connections they need for efficient Internet access (BESA, 2000).

gender gap in use of computers

While classroom use of ICT is theoretically equitable between the sexes, complex social factors serve to limit girls' participation both in school and at home, as expanded below. The gap is slowly narrowing, however (Butler, 2000; Durndell & Thompson, 1997).

(Dunham & Hennessy, in press, offer a more detailed exploration of these inequities, with further examples and statistical information, than space allows here.)

Access to portable technology

The majority of school students at all levels in the UK and US have access to some form of handheld computing technology (Dion et al., 2000) as do students in a host of other countries. Calculator availability in the mathematics classroom has increased steadily, although primary classrooms have limited access. Calculator access seems fairly equitable (re. gender, ethnicity, income), although as technology becomes more sophisticated and costly, inequities may increase. Disparities in access to graphic calculators between Western and other nations are evident, and differential national

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policies on access in secondary school classes and examinations result in differences among Western countries.'

CLASSROOM AND HOME USES OF ICT

For equity as 'equal educational treatment,' we look beyond physical access to examine how, where, and by whom technology is used. A note of caution is necessary in examining the results of statistical surveys concerning technology access; much of the data available is self-reported by institutions so that access figures are somewhat unreliable (for example, teachers report more classroom use of technology than their students do: Braswell et al., 2001). Independent validation and smaller scale, more focused studies are called for to address this. Nonetheless, survey data can offer a sense of trends over time or between different groups within an institution. As a consequence of their potentially misleading nature, survey results are not presented in detail here but they do allow us to paint a general background picture that consistently indicates inequities in access to computing technology for disadvantaged groups. This is merely a starting point, since knowing what technology is available in a school does not of course tell us how often, in what manner, and by whom it is used.

Research shows that available technology is often underused and poorly integrated into mathematics curricula. Since 1998 the British government has spent over 900

'million pounds on ICT initiatives, yet despite the potentially significant technological and pedagogic change and extended learning opportunities expected within subject teaching by 2002 (DEE, 1998), the National Curriculum hardly mentions using ICT, and classroom 'take-up' is low and variable between schools. Similarly, in the US, data from three national surveys showed that only half of the teachers who had access to computers used them in their lessons (Smerdon et al., 2000). Moreover, although 98% of the 220 middle schools studied by Huang and Waxman (1996) had computers and calculators available, students actually used calculators in mathematics classes only 25% of the time and computers less than 1% of the time. (As this study, unusually, used actual classroom observations, its findings are compelling.) In sum, it is unsurprising that good practice in teaching mathematics with technology remains uncommon. For example,

Mathematics departments are making good use of ICT in just over one-fifth of schools. Its use is ineffective in just over one-third of schools. (Ofsted, 200 1, p.5)

Ethnicity, SES and ability issues

Differential experiences with educational technology can create barriers and inequities so that some groups - ethnic minority, low income, inner-city, rural,

These vary from generally no encouragement of use in secondary schools through discretionary use, to established or compulsory use (Oldknow, 1997).

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disabled, and female students - do not achieve the full potential of computers and calculators in mathematics education (e.g., Croom, 1997). In particular, the common practice of 'tracking' or 'setting' students by ability limits opportunities and adversely affects ethnic minority and economically disadvantaged students. It has an impact on use of ICT, reinforcing or even increasing inequities (Page, 1998). American research shows that for students in low status classes (with low teacher expectations), computer activities most often involve tutorials and remedial work with drill-and-practice software (e.g., Wenglinsky, 1998). The predominant pedagogy is a teacher-centred, controlled instructional style that encourages passivity and little thinking or engagement on the part of the students (Waxman & Huang, 1997; Waxman & Padron, 1994). In higher ability classes, the emphasis is on tool application and conceptual development activities such as problem solving, reasoning and programming (Becker, 2000; Braswell et al., 200 1 ; Strutchens and Silver, 2000; Sutton, 1991). Despite increased access to technology, disadvantaged students remain disproportionately assigned to low ability groups, while white and more affluent students in higher groups are more likely to experience effective technology use at school. Thus, inequities in technoIogy use result from a wider problem that some have dubbed the "pedagogy of poverty" (Ladson-Billings, 1997; Page, 1998; Roy, 2000; Waxman & Padron, 1994).

Finally, while calculator access is generally high, equity issues arise from the variety of functionalities for different calculators, the effect of course selection on the kind of calculator used, and equal access to effective .instruction with calculators (Dunham & Dick, 1994). Nevertheless, caIculators and portable computers seem to provide more equitable use patterns and may offer more opportunities than desktop machines to tackle the ability differences that interact with equity issues. Portability effectively supports differentiated teaching (Hennessy, 1999; Stradling et al., 1994) and using portables can increase student control, self esteem, independence and confidence in using technology among students with learning disabilities (NCET, 1993).

Social factors and home access to technology

Technology is more than a physical resource; it is intertwined with social factors that differentially affect interactions. As elaborated below, these include family computer cultures and encouragement, "psychological access" (Wood, 1998), social identities and exclusion &om peer group culture, the setting (alone or with others) for technology use (O'Malley, 1995), and group composition for technology activities. These issues are particularly connected with gender identity and home access to technology.

The same pattern of rapidly widening access found in schools is apparent for home access; currently 70-80% of British and American homes have computers and about 30% have Internet access. However, surveys from both countries (Becker, 2000; British Household Panel Study, 1998; Furlong et al., 2000) show that the distribution of home PCs and of Internet access is becoming increasingly skewed towards

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middle-class and suburban homes. (For example, the report "Falling Through the Net7' (NTIA, 1999) found that in 1999, high-income households became more than 20 times as likely as rural, low-income households to have Internet access. Twice as many British households in the two highest SES groups own PCs compared to those in the two lowest groups: Becta, 2001) Many families are unable or unwilling to purchase and constantly update computing equipment. In the US, ethnicity creates additional inequities in home access; Hispanic and African American children are far less likely than other children to have computer and Internet access in the home (Becker, 2000). People in rural communities and certain geographical areas (e.g. the north of Britain) are also at risk from exclusion. In sum, gender, ethnic and economic differences in physical access to machines at school can be exacerbated by gaps in home access.

This is reflected in an interaction between home and school access, whereby privileged children gain greater confidence and familiarity with ICT and then experience greater educational advances and achievement. Children with home computers tend to dominate school technology and teachers choose them to use it more often (e.g. Valentine et al., in press). Thus the division between those with and without home access - especially the gap between middle- and working-class children, and possibly the gender gap too - is increased rather than challenged.

Differential values placed on computer expertise within family and peer cultures can influence children's ICT skills; parental guidance and encouragement for young learners are of paramount importance (Facer et al., 2001; Sutherland et al., 2000; Valentine et al., in press). However most parents have no experience of educational technology, and many lack an understanding of the role that digital technology may play in children's learning. The degree of integration into family life, prioritisation as a support for children's learning, age and range of hardware and software available, and adult role modelling of computer use vary enormously, posing a subtle source of potential inequity within the group of students with home access. Lower SES groups perceive less relevance for using new technology. The issue of parental support is also closely related to gender; parents' positive attitudes are crucial in motivating girls to use computers (Comber et al., 1997; Shashaani, 1994). Thus the notion of a digital divide in home access subsumes some more complex issues than is generally realised, and these are collectively serving to move us towards a new conception of social exclusion (Darnarin, 2000).

Gender differences in interactions with ICT

Male and female students interact differently with technology in terms of physical control, software choices, types of applications, and group settings (e.g. Turkle, 1995). Gendered use of the Internet is a new domain for research as connectivity rapidly increases. Girls voluntarily use computers and the Internet more frequently and confidently at home than at school (Wood, in preparation). Gender role socialisation - linked to technology use within home, school and peer cultures - operates here. Valentine and colleagues (in press) described how teenage girls in

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particular actively resist opportunities to interact with technology, perceived as threatening their identities, social relationships and inclusion within their peer group culture. Computer users remain stereotyped as predominantly male and that can limit girls' interest.

Thus, students' attitudes and confidence levels play a significant role (beyond levels of prior experience) in their voluntary use of ICT; this is the notion of "psychological access" (Wood, 1998). In addition, female exclusion strategies operate even where access appears equivalent. For example, boys tend to dominate school computer clubs and free access sessions (Siann & MacLeod, 1986; Wood, in preparation). Despite a diminishing gender division in terms of home ownership of computers, the location of computers and degree of actual accessibility within the home means that girls may continue to be disadvantaged in practice. (Boys tend to have computers situated in their own rooms and often restrict access to their sisters: Harris, 1999; Millard, 1997). According to Underwood (1994), "Boys, girls and computers are a dangerous combination ... because the boys see themselves as the rightful and superior users of the technology" (p. 9).

The private nature of handheld technology mutes the issue of male dominance. The advantages of access to portables (confidence and anxiety reduction, control, independent investigation) may explain the benefits of calculator use evident among female students and iron out gender differences (Dunham, 2000; Ruthven, 1990; Stradling et al., 1994). Collaboration between students - whether sharing machines or not - suits girls and appears to allay their perception that computing is an unsociable activity (Pryor, 1995).

Teachers' access and attitudes to technology

Although the majority of Australian, British, and American teachers now have access to computers and the Internet at school and at home, teachers report that constraints upon classroom use include: inadequate software and hardware, not enough time to become familiar with the technology or plan its use, lack of support and training (e.g., Becker, 2000). These factors result in lack of confidence and, in part, explain why teachers tend to use technology only for drill-and-practice (Manoucherhri, 1999).

Teachers' attitudes toward technology, plus their experience with it and associated pedagogies, significantly affect the integration and use of computers and calculators in mathematics curricula. Teacher attitudes have particular equity implications for minority, low income and low ability students. Many teachers believe that drill-and- practice activities are more effective for lower-achieving students than for higher- achieving ones because of beliefs about the role of basic skills in mathematics education. Despite evidence to the contrary (Hembree & Dessart, 1992; Heid, 1997), they believe that children must master basic computation before moving to higher order thinking and that poor and minority children lack the basics (Sutton, 1991; Waxman & Padron, 1994).

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The impact upon teachers struggling to cope with the home digital divide must not be underestimated. Teachers already deal with an ability range within their subjects; a diverse range of prior experience with technology compounds the issue of differentiation. Adapting to all pupils' needs simultaneously can be nearly impossible and potentially demotivating for using technology. Variation in ICT access between children means that setting homework tasks involving technology further advantages those with home computers. By contrast, some teachers assert the importance of integrating ICT within the curriculum in order to overcome the disadvantages of those without machines at home.

EQUITY AND OUTCOMES OF TECHNOLOGY USE

Equity defined as 'equal educational outcomes' focuses attention on inequities in learning that result from practices described in previous sections. Differential opportunities to use technology in school and at home can lead to unequal outcomes in mathematics achievement for skills and concepts, student behaviour in the classroom, and computer competency. Moreover, the social and psychological factors underlying inequities in access and experiences with educational technology can result in differential attitudes towards mathematics and toward technology.

Student attitudes

Research consistently demonstrates a relationship between limited computer experience (and competence) and levels of anxiety, perceived difficulty and negative student attitudes towards computers (e.g. Lagrange, 1999). There is also a circular feedback effect of computer attitudes (especially enjoyment) upon performance. Thus, the differences reported in availability and frequency of technology use among groups have important equity implications concerning attitudes. Home access and support are critical factors in building children's competence and confidence with technology (Selwyn, 1998; Shashaani, 1994). Indeed, home use may have a stronger effect on affective and cognitive attitudes towards computers than school use (Kirkman, 1993; Wenglinsky, 1998), gender (Comber et al., 1997; Levin & Gordon, 1989) or SES (Shashaani, 1994). Facer & Furlong (2000) assert that social pressure on the 'digital generation' to use technology confidently can make those with obstacles or resistance to using computers feel inadequate.

The gender effect is very pronounced for attitudes to desktop computing, although not for attitudes to portable computers and calculators, which seem to suit girls very well. Despite the advent of more user-friendly technology, the computer culture is perceived as alien by girls, who lack confidence and show more dislike, anxiety and disinclination to participate in computer activities, than boys (Durndell & Thornson, 1997; Valentine et al., in press; Wood, in preparation). Male students across the globe enjoy computing more than girls do (Reinen and Plomp, 1997). The gender difference in attitudes is most apparent in adolescents; girls begin to lose interest in computers around the age of 12, a critical time for intervention (Butler, 2000; Comber et al., 1997; Facer et al., 2001; Harrell, 1998), before they drop out of

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computing courses altogether (e.g. Grundy, 1996). The gender gap is unsurprising since girls continue to lack the motivation, encouragement and opportunities to use ICT which boys enjoy (Butler, 2000). Providing encouragement and experience with technology over time can counter negative attitudes and increase motivation among all disadvantaged groups (e.g. Robertson et al., 1995; Waxman & Huang, 1997), however, and break the self-perpetuating cycle in which confident, enthusiastic users tend to compete more successfully for computer time and to achieve more.

Mathematics achievement

Meta-analyses of research over two decades tend to support the conclusion that technology-based instruction, particularly concerning calculator use, is linked with significantly higher achievement scores across most ages and ability levels on paper- and-pencil tests of basic skills, problem solving and conceptual understanding (e.g. Hembree and Dessart, 1986; 1992; Smith, 1997; Dunham and Dick, 1994). Nonetheless, the link between mathematical achievement and use of ICT - particularly frequent calculator use for young children - has been a topic of debate for the public as well as researchers. First, research indicates that continual, long- term exposure to computers and calculators is necessary for a positive effect on achievement. There are also some serious methodological issues. Correlations at some age levels (Braswell et al., 200 1) and for some countries like Japan (Tan et al., 2000) are actually found to be negative. Correlations between student characteristics and achievement do not imply causality, of course, and the data (even within a single study) can be contradictory. Many of the research studies reporting learning gains as a consequence of using technology rely on a highly impoverished pedagogical model that does not integrate computer-based tasks with other learning (e.g., Woodward and Rieth, 1997); others fail to measure the degree of technology-based activity undertaken by their subjects; most ignore the potentially confounding factor of learners' use of technology at home, and many inaccurately assume a direct relationship between levels of technology integration into learning activities and performance in attainment measures (McFarlane et al., in press).

Moreover, studies contrasting performance of 'control' and experimental groups using technology are fraught with difficulties because complex factors arising (particularly teacher behaviours and pedagogy) are rarely accounted for; fair comparison using test scores alone is almost impossible (Dunham & Dick, 1994). Research by Hennessy, Fung & Scanlon (2001) and others has highlighted the integral role which ICT can play in actually 'shaping mathematical activity; the resulting quandary about using technology in the tests themselves (e.g., Hammond, 1994) further muddies the water.

The equity picture for technology-enhanced achievement is similarly not entirely consistent, and research studies vary considerably in the degree of insight provided into how the technology being tested benefits members of certain groups. The literature certainly raises concerns for those students who have limited experience with technology because of economic issues or teacher practices and beliefs.

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Nevertheless, frequent use of computers and calculators in a technology-integrated program and access to technology for testing seems to 'level the playing field', alleviating inequities for some traditionally low-performing groups through reduction of computational deficiencies, changes in student behaviour and confidence, and 'fiendly' pedagogies that promote more equitable instruction and learning. This is especially true of the gender gap. Despite sex differences in attitudes about technology and mathematics, and persistent differences favouring boys for computer knowledge and programming achievement, gender-related differences in mathematics achievement do diminish when students use technology. With calculators particularly, female students often perform as well or better than male students (e.g. Ruthven, 1990). However, when students collaborate, group composition interacts with gender in inconsistent ways. Some researchers find that mixed-sex grouping undermines girls' confidence and competence on computer- based problem solving (Culley, 1988; Littleton et al., 1992; Underwood, 1994), while others find that girls in mixed-sex groups outperform girls-only groups (e.g. Kutnick, 1 997).

More benefits than deficits are associated with computer and calculator use among groups characterised by ethnicity, SES, and language difficulties. For example, Bridgeman et al. (1995) reported no differences in performance scores among four racial or ethnic groups (white, African American, Asian, Hispanic) for those who used calculators on the SAT-M (college entry test). The levelling effect for low- ability and low-confidence students is a strong argument for using ICT to achieve equity for disadvantaged groups. One obstacle here is a positive correlation between achievement in mathematics and home access to technology. Those without adequate home access (usually low-SES students) are denied the innovations that promote increased mathematical understanding and increase their achievement. Access to technology at home - or at school - thereby tends to widen the gap further between the 'haves' and 'have-nots' (Roy, 2000).

The nature of technology use at school by disadvantaged groups is critical too, since the computation and drill programs which they traditionally experience are associated with lower attainment (Braswell et al., 2001). By contrast, students who use calculators regularly in creative ways over an extended period have a greater advantage (e.g. Dunham & Dick, 1994). Schacter and Fagnano's (1999) review of research found that using software based on socio-cultural learning theories benefited ethnically diverse students in co'llaborative setfings, 'in kerns 05 s?uhwit learning, reflection and project quality. Moreover, motivation is influential. An investigation of levels of adopting portable computing innovations with a class of learning disabled students (Anderson-lnrnan, Knox-Quinn and Homey, 1996) indicates that individuals' persistence with new technology and their development of strategies for working successfidly with it are important influences upon effective use, which was linked to higher ability. This and related findings could reflect not greater previous experience but instead the students' realisation that certain digital

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educational tools can offer an interesting challenge at their own level of ability and can help them achieve more (Robertson et al., 1995).

Using ICT can 'level the playing field' in another sense: carefully designed environments can provide scaffolding which structures mathematical activities such as problem solving (Heid and Blume, in press) or graphing (Hennessy, 1999) so that conceptual leaps could become easier for low ability students. By offloading some of the process tasks, the 'computational onus7 or drudgery is removed (Horton et al., 1992), complex activities such as algebraic manipulation are simplified, and the freedom to focus on concept development is enhanced. Thus, access to appropriate technology can increase access to advanced mathematics, even for students on remedial courses (e.g. NCTM, 2000; Roy, 2000).

The role of ICT in assessment is still emerging, but studies show that access to technology during assessments has an impact on the difficulty of the tasks presented, raising equity concerns about the type of calculator available on assessments, especially for high stakes national tests. In particular, tests may become unfair when they seriously disadvantage (low income) students without access to more advanced calculators, increasing the technology divide accordingly.

Some further caution is appropriate in summarising the 'impact' of using ICT on mathematical achievement. Apart from the methodological issues and inconsistencies outlined already, achievement-focused studies rarely - if ever - offer a detailed cognitive model of likely cause and effect regarding performance improvements. Correlation between technology use and attainment gains using national tests as standard measures is particularly weak; these large-scale, often content-knowledge oriented, measures cannot capture what and how children are learning with technology (Watson et al., 1993). By contrast, other outcome measures, which are directly or indirectly related to improved learning, have been regularly demonstrated, e.g., enhancements in specific skills such as information handling, higher level conceptualisation and critical thinking, better problem solving, more complex small- group talk, improved motivation and confidence (McFarlane et al., in press). There is some evidence that use of technology can improve problem-solving and the other skills listed at the expense of a negative impact on content knowledge. Moreover, the literature indicates that we cannot assume that positive effects on student motivation and attitude will improve - or even relate to - actual performance consistently and significantly (Hennessy, 1999; Watson et al., 1993).

Finally, available forms of ICT (e.g. spreadsheets, graphing tools, Internet), their contexts of use within mathematics classrooms, and the conditions governing them, are remarkably diverse (McFarlane et al., in press). We can only conclude that using some kinds of ICT can enhance some forms of learning for some disadvantaged students under some conditions. The classroom learning environment and the teacher's pedagogic approach and strategies play an important role here - particularly in terms of increasing equity - as elaborated below.

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SUPPORTIVE TEACHING AND LEARNING ENVIRONMENTS FOR EQUITY

Merely providing technology does not guarantee that it will be used effectively. To integrate ICT successfully and equitably, teachers must deal with content that is structured in new ways, delivered in new formats, and demands new pedagogies. Adapting classroom practice to better accommodate technology use by all students involves: active and autonomous behaviour; more feedback; higher-order thinking; increased problem solving; diversity in instructional approaches; changing teacher role from knowledge deliverer to facilitator (Waxrnan & Padron, 1994). Farrell (1996) reported such changes in teacher roles while technology was in use: teachers engaged in more inquiry and consulting, with less lecturing and explaining, as they monitored student investigations and motivated discussion. These behaviours create more welcoming environments for female and minority students and facilitate greater interest in mathematics. Students need pedagogies that build on their cultural experiences and prior knowledge, nonthreatening and supportive environments, classrooms that encourage exploration, conjecturing, reasoning and decision making, and activities that make mathematics exciting and usehl (Croom, 1997, p.5). These 'culturally relevant' and 'friendly' pedagogies often emerge in technology-rich classrooms and can lead to supportive environments that promote equity.

Chisholm (1995) described how one effective teacher in a multicultural classroom managed computer use to accommodate cultural and gender differences and provide equitable access. Success factors included: respecting all children as contributors; high expectations of students; software that fostered creativity, higher level thinking, and transfer of skills; monitoring equal access to hardware and software, and supporting cultural values (such as collaboration for African and Mexican Americans or self-reliance in white culture) through flexible grouping of students. Encouraging students to share their knowledge and expertise with less experienced peers additionally benefits more students when they do have computer access.

Female-friendly technology-based activities and pedagogies include: open-ended tasks; teacher as participant, not dictator; cooperative learning in small groups; peer evaluation; emphasis on process rather than outcome; minimal tension between computer and other schooi work; time for induction; familiarisation and working at the students' own pace. Meaningful and socially relevant applications, contexts and data are particularly attractive to minority and female students (e.g. Millard, 1997). children's real life concerns about social exclusion from peer group cultures also need to be addressed explicitly (e.g. by encouraging children to use e-mail and the Internet - activities connected to their off-line lives) so that digital technology becomes more inclusive and less threatening (Valentine et al., in press).

Some researchers recommend selecting software and activities carefully for content and style as well as screening for sexist, racial or religious stereotypic images (Culley, 1988; Harrell, 1998; Littleton et al., 1992). Minority and female role models - teachers who are competent, confident and enthusiastic technology users -

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are also important. Parents have a role to play too, in providing children with equipment and support for learning. Software and technology activities also need to build on the diverse experiences of different groups. In sum, if all students are to view technology as a useful resource that plays an increasing role in their lives, then we must avoid further alienating and disadvantaging certain groups.

The differential needs of certain groups of learners have some uncomfortable implications since equality of opportunity to learn may result in unequal outcomes that promote inequity (Lee, 1999). Reaching diverse populations who traditionally have not performed well in mathematics in the past could necessitate inequality in terms of treatment in order to achieve fairness in outcomes (Sutton, 199 1).

CONCLUSIONS AND POLICY RECOMMENDATIONS

Any approach to narrowing the digital divide must be multi-pronged. Equitable distribution of school resources must be a priority. Programmes to provide equipment and resources to targeted groups have had some impact on outcomes but have not eliminated inequities for all. Funding for equipment alone does not provide the requisite curricular support and on-going professional development that is crucial. Training for this new age must incorporate pedagogical issues and the potential of using technology to develop conceptual understanding of mathematics. It should also raise teachers7 awareness of equity issues and ensure that computing is taught in a way that enthuses and engages all pupils, particularly adolescents. This involves some appreciation of the psychological issues that affect engagement. with technology. Successful interventions for equity may include: compulsory computer classes for all students; monitoring computer use to minimise domination by confident users and ensure equal access for all; establishing policies for software selection and use; and training more women and members of minority groups as computer teachers (Butler, 2000).

While children may have equal access to ICT they will not all necessarily take up the opportunities on offer. There is a need to explicitly address how technology is introduced within the school context and children's real life concerns about exclusion from peer group cultures. Those outside schools - parents and the public - also need increased awareness of equity in ICT use. There is an ongoing need for direct action to counter perceptions in all quarters that computers are for affluent, high-achieving, white, male students (Warren-Sams, 1997). Increasing out-of-school access, particularly for families with limited means, is one approach currently being implemented5; however, because those without home computers are least motivated

The e-Learning Foundation raises public and private funding to ensure that all UK pupils will soon have access to their own personal computer for use at school and home, irrespective of background or means (www.elearnin~foundation.com). Moreover, the UK government's 'Computers Within Reach' programme leases refurbished computers to poor families and 'UK Online' works towards

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and confident about using them, schemes to bring technology into disadvantaged communities may have a limited impact in the same way that a lack of access to books in homes was never completely solved by public libraries. Even where home access exists, technology may not be exploited for educational purposes. Action to plug the gap needs to purposefully avoid actually increasing inequity in the classroom between those students with and without home experience with technology. Specifically, teachers need to develop strategies aimed at developing the skills and understanding of students in both groups, using a wide range of resources (Downes, 1998); this is a significant challenge for teachers already having to differentiate work by subject ability. Further suggestions include home-school collaboration, such as schools providing advice in selecting hardware and software, offering technology workshops for parents, and allowing electronic access of school resources from home (Cole, 2001).

We can conclude that opportunities for access are only a starting point; they may mask physical or psychological restrictions on use and may not translate into equitable use of technology in practice. Haddad (quoted in OECD, 2000, p.56), asserts that we need to "empower people with appropriate educational, cognitive and behavioural skills and tools to access the information avenues efficiently, effectively and wisely" so that knowledge is internalised, applied and continuously upgraded. Developing information skills and a culture of knowledge creation requires a radical departure from conventional and less equitable methods of schooling (based on knowledge transmission) and this is particularly pertinent for traditionally disadvantaged groups. In sum, it is naive to expect development of technology skills or increased use to automatically break down traditional barriers of difference (Harrell, 1998).

Finally, researchers can help the education community better understand the causes of inequities and can devise and test appropriate instructional strategies and policies for addressing the gaps. More research on the contributory role that using technology plays in developing mathematical cognition, the effect of the home technology environment, computer practice among different social and ethnic groups, and effective intervention strategies, are all needed. Above all, we need models which acknowledge the complex nature of interactions between learner, family, peer group, teacher, mathematical activity and new technology.

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