ASIAN/AUSTRALIAN PERCEPTIONS OFASIAN SUCCESS INMATHEMATICS Paul LAyres University of W. Sydney,Nepean 1994 AARE CONFERENCE, NEWCASTLE, NSW. Faculty ofEducation UWS (Nepean) PO BOX10 Kingswood NSW 2747 Tel 047 360 784 Fax 047 360 400 Email p.ayres@nepean.uws.edu.au AbstractÙÈ In Experiment 1, Australian and Asian students from a Sydney girls school were asked torank particular attributes which might explain why Asiansdo well in mathematics. Significant differences between thetwo groups were found on attributes of age, luck, parentalpressure and quality of teaching.In Experiment 2, a groupof Australian university students in Education were giventhe same task. Differences within this group were found which suggested that mathematical experiences and gender were factors in formulating perceptions of Asian success in mathematics.All groups in the study ranked _ _rd work_as the most likely reason for Asian success. A vast quantity of cross_cultural research which has compared educational issues between Western countries and East Asians countries has now been conducted. A wide spectrum of issues has been investigated, encompassing such areas as educational expectations (Wong, 1980), problem behaviour (Langfeldt, 1992)and creativity (Rudowicz, Kitto & Lok, 1994). However, much of the research has been concerned with mathematics education. In particular, studies have focused on mathematical comparisons between the United States and East¬ian countries.yY*\&YYUyY+\YY[ber the last fifteen years extensive studies have investigated a multitude of mathematical disciplines such as number (Miura & Okamoto, 1989), pattern recognition (Yoshida, Fernandez & Stigler, 1993) and problem solving (Mayer, Tajika & Stanley,1991),for a varity of schooløe groups.In most cases, the conclusions are always the same: US students perform badly on mathematical tasks compared with their Asian counterparts (see Stevenson, Lee & Stigler, 1986; Chen, Lee & Stevenson,1993).Although comparative studies of this nature have attracted some criticism (see Chen et al.,1993), there has been wide _aleconcern in the US over these findings. This concern has initiated many studies to find out the reasons why Asian students perform so comparatively well in mathematics.Mayer et al. (1991) proposed two major explanations for these differences: an exposure hypothesis and an ability hypothesis.The former is based around cultural values for education and mathematics in particular, whereas the latter assumes innate differences in the ability to learn mathematics. Most researchers favour the former.Studies which have investigated cultural differences have often focused on the _ _me_factors.Two such studies by Crystal and Stevenson (1991), and Hess, ChiõMei & McDevitt (1987) have looked at the role of mothers in their children_l mathematics education. Crystal and Stevenson(1991) found that American mothers tended to hold lower standards than Asian mothers; whereas Hess et al. (1987) found significant differences in cultural beliefs about success and failure. In the Hess et al. study, Chinese and American mothers were asked to rank five attributes in the order they considered important for success or failure in mathematics. Significantly different profiles emerged. Chinese mothers believed success in mathematics was highly dependent on school training, whereas failure was attributed to lack of effort. American mothers Ny„nded to be less specific by ranking the attributes more evenly. Surprisingly there has been little crosscultural research conducted into mathematics education between Australia and Asia(see Bell, 1993). This is surprising because modern Australia is a multicultural society which includes many Asian communties.Furthermore, in recent years many Asian students have come to Australia to study for the HSC (in NSW) and attend university.Throughout Australia, Asian and Australian students are observing each other in an educational setting every day.It is an environment rich in potential to study similarites and differences. An ideal situation for a comparative study exists in schools in NSW which have Asian students who specifically join the school in Year 11 to sit the HSC. These students have been previously taught mathematics in their own countries and can directly compare new and old experiences. Equally, the Australian students will form perceptions about Asian learning methods and expertise directly from their own experiences. In this study, Australian and Asian perceptions were compared on Asian success in mathematics. In Experiment 1, a school in NSW which receives a group of Asian students in Year 11 was selected. Experiment 1 Subjects One group of subjects consisted of fifty seven students,studying Year 12 mathematics, from an Independent Girls Schools on Sydney_l North Shore. The school was non selective and non denominational. All subjects were Caucasian. Most were born in Australia, those who were born elsewhere had lived in Australia for at least nine years.yY8_YY[ÈYY£YYUThe second group consisted of eighteen Asian students from Years11 and 12 of the same school, who were mostly in Australia tocomplete the HSC. All students had been in Australia for lessthan three years. Most would have been in the country for one ortwo years.Consequently all subjects would have been primarilyeducated in their countries of birth. All subjects in this groupwere from one of four countries: Hong Kong, Taiwan, Korea andChina. Materials and Procedure Australiansubjects were asked whether they believed that_Asians performed better than Australians in Mathematics Exams__Fifty seven students (77%) thought that they did. These subjects(11 studying Mathematics in Society, 19 2¸it and 14 3¸itMathematics) were then asked to complete a survey (seeAppendix). The survey asked subjects to rank, on a scale of 1Ethe possible reasons (attributes) why they thought Asiansperform well in mathematics.The eighteen Asian subjects also completed this survey. The survey (see Appendix) was composed of nine attributes whichmay be perceived as contributing towards mathematical success.Five of these attributes were adopted, with slight variations,Yy‰k9_om the Hess et al.(1987) study which focused on i_0¹mnTimesº__atural ability,YyY<[b‰YsXorking hard, good training in mathematics at school, good training inYy‰k9_thematics at home, and luckÙ_ƒD™opCourierÚ‚n addition, the following fourYy$YU[c‰kù«tributes were included: i_0¹mnTimesº_cge, previous experience of the work, rewardsYy1Yb[c‰kù_r doing well, pushed more by parentsÙ_ƒD™opCourierÚYAn age attribute was includedYyYo[cyYsEecause many of the Asian students were older than theAustralian students. For example, one Australian in the 3¸itclass, who had been radically accelerated, was only 14, comparedwith a 20 yearRd student from Hong Kong. The perception thatthe Asians may have done the work before might easily occurbecause they are both older and come from a differenteducational system. The final two attributes, which anecdotalevidence had suggested could be a factor, were included to explore the _ _me_factor further. Results and conclusions The Australian subjects were grouped according to the level of mathematics studied (MIS, 2¸it & 3¸it). Although the school allowed somefreedom of choice, the particular level of study was a reliable indicator of mathematical ability. This groupingallowed differences in perception across mathematical ability tobe examined for this population. Mean scores for each attributeper group were calculated (see Table 1).One2y ANOVAs were alsoconducted for each attribute (see Table 2).Significantdifferences were found on two attributes: luck and rewards for Insert Tables 1 and 2 here Šing well. Post hoc procedures indicated that the Mathematics in Society (MIS) group had different perceptions to the other groups on these two measures. To analyse these differences further, each attribute was ranked according to its order ofimportance. The attribute with the highest mean score was rankedfirst, and the lowest mean score was ranked last (see Table 3).It can be seen that the luck attribute for each group was rankedninth (last) indicating that, overall, each group did notconsider luck to be a factor in Asian success, even though theMIS group scored it higher.yYKbYY[ÈY_YYUYR__i‰SSSSSSNi¦c.YYUYR_sert Table 3 hereyYNc:YYUYRSSSSSSNi¨cFYYUYYÈYRKYYU_º__In contrast, the _ _wards for doing well_attribute was rankedthird (mean score of 3.1) by the MIS group, but seventh (meanscore of 1.8) by the 3¸it group. Clearly this attribute israted differently and may indicate a real variation inperception according to mathematical ability. In spite of thisdifference, overall results suggest a fairly homogeneous groupi/YY_™_]YYYZ© Yù/Xf Australian students. Therefore, all three groups wereNyOmbined together to form one group, and their responsescompared with the results of the Asian students.yYQc^YYUyYRcYY[2an attribute scores for the Australian group (combined) andAsian group are shown in Table 1.Comparisons between groups wereconducted for each attribute, ANOVA results are given in Table4. Insert Table 4 here Significantdifferences were found on four attributes: better teaching, age, luck and parental pressure. Again, to investigatethese differences with respect to the value of the attribute,each attribute was ranked from first to last in order ofperceived importance. Ranks for both groups are shown inTable5. Insert Table 5 here Apart from the luck attribute which both groups rank lowly,ranks for the otherthree attributes suggest real effects. The greatest difference in ranks was found with age. Although the Australian students did not consider this very important (mean score of 2.5, rank 4) it was given more credence than by the Asians (mean score of 1.2, rank 9). As the Asians ranked luck higher than age it might suggest a sensitivity on their part about their age, which in most cases was comparativly older. On the other hand it may just be the perception that age is not a factor in mathematical ability. For the parental pressure attribute, the Australian subjects perceive this to be a real factor. It is ranked second with a mean score of 3.6 suggesting that there is a strong belief about the infuence of the parents.The final attribute, quality of teaching, which produced a significant difference is the most interesting. Consistent with the Hess et al.(1987) study, this group of Asians perceived teaching as a highly important factor in success in mathematics.In contrast, the Australians, all of whom acknowledged that Asians do well in mathematics, did not rank teaching as such an important attribute. It should be noted that two factors approached significance:natural ability (p=0.06), and work ethic (p=0.08). In the former case, Asian responses suggested that ability could be a factor.However, for the latter attribute, both groups considered that the work effort is the premiere factor for Asian success in mathematics. This comes as no real surprise, as the _ Asian work ethic is perhaps the most universal stereotype applied to the Asian countries. Certainly the Australian students in this study perceive that Asians work very hard. Their personal experiences may make this more of a judgment than a perception. Similarly,the Asian students have made the same decision.Finally, both groups ranked (third) prior knowledge as a medium factor in Asian success. EXPERIMENT 2 _ Experiment 1, the subjects were taken from a very narrowsection of Australian society: all girls from a high socio economic area of Sydney. In this experiment the perceptions of a different section of Australian society were canvassed.Although the survey of Experiment 1 (see Appendix) was designed specifically for those subjects, it was thought robust enough to be used elsewhere. Subjects Forty four education students from a University in Sydney participated. This sample included twenty nine students (18Female and 11 Male) in the 3rd year of a B. Teaching (Primary) degree, and fifteen students (6 Females and 9 Males) enrolled in either a Dip. Ed or B. Ed (3rd year) Secondary Mathematics course.Subjects were grouped (four) according to gender and the degree studied. Materials and Procedure The students were asked to fill in the survey, as shown in the Appendix. No other questions were asked. Subjects indicatedwhether they were male or female. Results and Conclusions Group mean scores for each attribute are shown in Table 6.Separate 2£ctor (degree_nder) ANOVAs were conducted for each attribute (seeTable 7). Insert Tables 6 and 7 here Twosignificant differences were found within each main effect.To put these these results into perspective each attribute was ranked (in the same fashion as Experiment 1) in order of importance within the groups (see Table 8).For the gender Insert Table 8 here ‰ƒffects, females scored both natural ability and parental pressure higher than the males. Each of the four groups ranked parentalpressure as one of the top two attributes, however,gender differences are clearly present in the natural ability rankings.An explanation for this second result may be found in the difference of confidence levels in mathematics between males and females. Much of the modern debate into the mathematicaleducation of girls has focused on their lack of confidence inmathematics. In particular, Southwell and Khamis (1994) found from a study of 2000 secondary students that females are more likely to rate themselves as having average mathematical ability than boys. This lack of confidence may influence their general perceptions of mathematical ability. The two degree ‹fects were found on the attributes of age and work ethic. All four groups ranked the work ethic as the most significant factor in Asian success in mathematics. However,rankings for the age attribute varied. One explanation for these differences may be found in the past experiences of the subjects. It is highly likely that students who have had at least three years studying a mathematics degree would have had more direct contact with Asian students, in both their university and school courses, than subjects pursuing the primary degree course, as very few Asian students are enrolled in the latter course at the University sampled. These personal experiences within the mathematics classes may have been influential in their responses. The subjects in this study varied considerably in their ages and personal experiences, as well as gender. They could not be considered a very homogeneous sample. However, they were all Caucasian and studied education degrees at the same University, therefore there were some common traits.Furthermore, each group ranked the two most important attributes as work ethic and parental pressure. In spite of some main effect differences it was considered of interest to combine these four groups together (see Table 8) as one group and make some _ „ntative comparisons with the group responses of Experiment 1. Mean scores for the three major groups in this study are displayed in Figure 1. Insert Figure 1here The graph illustratesquite clearly that the two most dominant Australian perceptions about Asian success in mathematics is the work ethic and the parental pressure factor. Although the Asian students agree with the perception of hard work, they rank the quality of school teaching as the second most important attribute. The graph also illustrates that there may exist some significant differences between Australian groups as well as between Asians andAustralians. General Discussion In Experiment2 it was discovered that perceptions about Asian mathematical success are influenced, to some extent, by gender and a student_l own mathematical experiences.As perceptions are influenced by our beliefs this was not a surprising result. However, the cross_ltural comparisons of Experiment 1 were more interesting. Experiment 1, significant differences were found in ranking the four attributes: age, luck, parental pressure and quality_of teaching. Whereas, there may exist genuine differences in perception between the groups on ranking the first three attributes, the finding concerning the quality of teaching could have more far_reaching implications. Obviously one can not generalisetoo much from a study in one school. The quality of mathematics teaching in that school may be poor, although HSC results suggest otherwise. However, perceptions of the Asian students would not be totally formed by their experiences at the school. They would have friends in other schools, brothers and sisters in Australian universities; all factors which would help formulate perceptions. Therefore, although the results should be treated cautiously, it is an areawhich should be researched further. Hess et al. (1987) found that Asian mothers attribute success in mathematics to the quality of teaching. The results of this experiment are consistent with those findings. A future study is being designed to discover possible crosscultural differences into what is considered good mathematics teaching. References Bell, G. (1993).Setting the theme: Researching Asian MathematicsEducation. In G. Bell (Ed.) Asian Perspectives on Mathematics Educationù Northern Rivers: Lismore. Crystal, D. S. and Stevenson, H. W. (1991). Mothers Perceptions of Children_l Problems with Mathematics: A cross>tional Comparison. Journal ofEducational Psychologyù9Vol 83,3, 372-376. Hess R.D., C. Chih2i, and T. M. McDevitt (1987). Cultural Variations in Family Beliefs about children_l performance in mathematics: Comparisons among People's Republic of China,Chinese American, and Caucasian American families. Journal of Educational Psychologyù9Vol 79,2, 179. Langfelt, Hb (1992). Teachers' perceptions of problem behaviour: A cross_cultural study between Germany and South Korea. British Journal ofEducational Psychologyù9 62, 217 MayerR.E., H Tajika and C. Stanley (1991).Mathematical Problem Solving in Japan and the United States: A controlled comparison. Journal of Educational Psychologyù9Vol 83, 1, 69r. Miura, I.T. &Okamoto, Y. (1989). Comparison of US and Japanese First graders' cognitive representation of number and understanding of place value. Journal of Educational Psychologyù9Vol 81, 1, 109 Rudowicz, E.,Kitto, J. & Lok, D. (1994). Creativity and Chinese Socialisation Practises: A study of Hong Kong Chinese Primary School Children. Australasian Jn. of Gifted Educationù9Vol 3,4 Southwell, B and Khamis, M (1994).Affective Constraints on Construction inMathematics Education. Proceedings of the 17th Annual Conference ofMERGAù9555V2. Rigler, J., Lee, S, and Stevenson, H. (1990). Mathematical Knowledge of Japanese, Chinese and American Elementary School Childrenù Eeston: NCTM. Wong, M.G.(1980). Model Students? Teachers'_Perceptions and Expectations of their Asian and White students. Sociology of Educationù953, 236 Yoshida, M., Fernandez, C. & Stigler, J.W. (1993). Japanese and American StudentsDifferential Recognition Memory for Teachers Statements during a Mathematics Lesson. Journal of Educational Psychologyù9Vol 85, 4,610a7.