Factors Contributing to the Development of Mathematical Talent [R] 1

Petri Nokelainen1, Kirsi Tirri2, and Hanna-Leena Merenti-Välimäki3 University of Tampere, 2University of Helsinki, 3Espoo-Vantaa Institute of Technology, Finland In this paper we examine the influence of self-attributions and parental attitude to the development of mathematical talent with self-report questionnaires presented to three groups of mathematically gifted Finnish students (n=203) and their parents (n=188). The first group, “Olympians”, represents highly able adults who have participated in international Olympics in mathematics. The second group, “Prefinalists”, consists of secondary school students, who have taken part in national competitions in mathematics. The third group, “Polytechnics”, consists of adolescent students in Polytechnic institute with mathematics as their field of specialization. The student version of the instrument included 18 items measuring four factors of ability and effort attributions (Weiner, 1974). The parent version included 39 items measuring five factors of parental influence (Campbell, 1996). The research questions were as follows: (1) Do the self-attributions of the three groups of mathematically gifted differ by the group membership, gender, and the level of giftedness? (2) What are the most important forms of the parental influence? (3) How parental influence differ in the three groups? The results showed that the Olympians and Prefinalists did not connect hard work to mathematical ability. However, in all groups effort was shown to be more important factor of success than ability. The Polytechnics had more parental pressure and less psychological support than Olympians and Prefinalists. Olympians’ parents reported smaller frequencies of parental help for homework and studying than Polytechnics and Prefinalists. Olympians and Prefinalists parents emphasized more the value of books and reading than Polytechnics parents did. Polytechnics and Prefinalists parents were more eager to know how well their child did in school. In addition, they were monitoring more their children’s behavior regarding homework, studying and T.V.

Factors Contributing to the Development of Mathematical Talent Introduction The purpose of this study is to explore self-attributions of three different groups of mathematically gifted Finnish students (n = 203) and their parents (n = 188) influence in order to find what factors contribute to or impede the development of mathematical talent. The first group represents highly able adults who have participated in international Olympics in mathematics. The second group is constructed from students of Polytechnic institute who study mathematics as part of their studies. The third group consists of secondary school students, who have taken part in national competitions in mathematics. All the student participants completed Self-confidence attitude attribute Scales (SaaS) questionnaire (Campbell, 1996a). The instrument used a six-point Likert scale ranging from strongly disagree to strongly agree. The instrument included 18 items measuring the students' ability and effort attributions, based on Weiner’s attribution theory (1974), on four dimensions: (1) ”Success due to Ability”, (2) ”Failure due to a lack of Ability”, (3) ”Success due to Effort”, and (4) ”Failure due to a lack of Effort”. The parents completed Inventory of Parental Influence (IPI) questionnaire (Campbell, 1996a). The instrument used a five-point Likert scale ranging from strongly disagree to strongly agree. The instrument included 39 items measuring the following five dimensions: (1) Pressure, (2) Psychological Support, (3) Help, (4) Press for Intellectual Development, (5) Monitoring/Time Management. Our research questions are as follows: (1) Do the self-attributions of the three groups of mathematically gifted differ by the group membership, gender, and the level of giftedness? (2) What are the most important forms of the parental influence? (3) How parental influence differ in the three groups? Theoretical Framework There is much literature and research on attribution theory, as the role of motivation in academic achievement has proven to be an interesting topic. The interest is apparent as we examine the structure of the measurement instruments: Bigg's (1985) 42 item Study Process Questionnaire (SPQ) consists of two scales (motive and strategy) with three approaches: (1) surface, (2) deep, and (3) achieving. The questionnaire contains six subscales (surface motive, deep motive, achieving motive, surface strategy, deep strategy, and achieving strategy). Entwistle's and his colleagues (Ramsden & Entwistle, 1981) Approaches to Studying Inventory (ASI), as one of the most widely used questionnaire on student learning in higher education, contains subscales including, for example, fear of failure, extrinsic motivation, and achieving orientation. Marsh (e.g., Marsh & O’Neill, 1984) has developed a set of scales (Self-description Questionnaire I-III) for different age groups measuring self-concept with multifaceted (e.g., mathematics, verbal, academic, physical) view. According to Strein (1995), research results over the past fifteen years have strongly supported the multifaceted view emphasizing domain-specific self-concepts. Respondents in the first group (“Olympians”) are the most gifted Finnish population in mathematics. The group consists of individuals of different ages who participated in Olympiad Studies in mathematics during the years 19651999. Separate programs exist for the Mathematics, Physics and Chemistry Olympiads. In recent years, programs have been created for Biology and Computer Science Olympiads as well. Distinct studies have been undertaken in each of

these academic areas. In the Mathematics, Physics and Chemistry Olympiad programs, series of increasingly difficult tests are administered. This testing concludes with the identification of the top national finalists (6-20 Olympians). These individuals are trained to compete in the International Olympiad programs. The second group (“Polytechnics”) students of Espoo - Vantaa Institute of Technology, need gradually more and more advanced mathematical skills as they advance in their studies. However, compared to higher level mathematics studies in universities, technological mathematics studies in polytechnics are more practically oriented. The third group (“Prefinalists”) involved in this study consists of secondary school students who have taken part in the national competitions in mathematics during the years 2000 and 2001. Each year schools all over the Finland send their most talented students into this annual competition. In this study we concentrate both on students self-evaluations on the basis of mathematics achievement and academic ability, and their parents’ self-evaluations of parental influence. One of the most widely investigated constructs is Weiner’s achievement attribution (1974; 1980; 1994). According to Weiner (1980), in explaining prior success or failure, an individual would assess (1) the level of ability, (2) the amount of effort that was expended, (3) the difficulty of the task, and (4) the magnitude and direction of experienced luck. The principal of attribution theory is that a student’s search for understanding, trying to discover why an event has occurred (Weiner, 1974). According to Campbell (1996a), parental influence has two sections. First consists of family member’s perceptions of the family processes, namely (1) parental pressure and (2) psychological support. Second consists of family practices, namely parental (3) help and (4) press for intellectual development, and (5) monitoring/time management. Parental pressure is defined as children perceiving parental influence with fear. Psychological support is defined as children perceiving support from the parents. Parental help is defined as children reporting frequency of parental help for homework and studying. Press for intellectual development is defined as children reporting frequency that parents emphasize the value of books, reading and educational T.V. Monitoring and time management is defined as children reporting frequency that parents monitor their behavior regarding homework, studying and T.V. (Campbell, 1996a, 489490.) Previous Research Campbell has conducted several cross-national studies on Mathematics Olympians (for example, 1994; 1996b; Nokelainen, Tirri & Campbell, 2002). He made two interesting findings: first, the international data with mathematics self-concept verified the finding that the academic self-concepts fluctuate from grade school to high school, and second, the Olympians attributed effort to be more important in their success than ability (1996b). The latter research finding has been verified by Chan (1996) who reported that adolescent gifted students were more likely to attribute failure to lack of effort than to attribute it to low ability. The American, Finnish and Taiwanese Olympians have also attributed success and failure more to effort than to ability (Feng, Campbell & Verna, 2001; Nokelainen, Tirri & Campbell, 2002; Wu & Chen, 2001). Heller and Lengfelder (2000) investigated 100 German Olympians finalists and 135 Prefinalists in mathematics, physics, and chemistry. In contrast to Campbell’s findings, their results showed that participants in both groups valued ability significantly higher than effort. Effort was estimated to be equally important in the case of failure as in the case of success (Heller & Lengfelder, 2000). Marsh (1983) found as he studied relationships among dimensions of self-attribution, self-concept and academic achievements, that those who attribute academic success to ability and who do not attribute failure to a lack of ability were found to have better academic self-concepts and better academic achievement. In an American study by Verna and Campbell (1999), a small significant difference between the males and females was found with regard to ability. The female American Chemistry Olympians considered ability to be a more important factor for success than did the males. However, no difference was found for the effort factor. Kerr (1994) and Reis (1998) have identified external barriers to gifted women as including the attitudes of parents and school, environmental options and possible discrimination or harassment at school or at work. The possible internal barriers among gifted females included self-doubt, self-criticism, and too low expectations. According to Siegle and Reis (1998), gifted girls tend to underestimate their abilities, especially in mathematics, social studies and science. Research results have also shown a positive correlation between perceived ability and achievement (Multon, Brown & Lent, 1991). Method Sample and Procedure All the student participants completed self-confidence attitude attribute scales (SaaS) questionnaire (Campbell, 1996a) based on Weiner’s self-attribution theory (1974). The Mathematics Olympians’ data (n = 77) consists of 68 male and nine female respondents. The sample is quite representative as the total number of Finnish mathematicians is 84 (14 females and 70 males). The polytechnic student data (n = 74) is a fully representative sample of an advanced mathematics course held at Espoo - Vantaa Institute of Technology in autumn 2001. The total number of the population is around 3000. The third group (n = 52) is a sample from about 200 secondary school national competitors in mathematics. Olympiad data was collected between 1997 and 2002, the Polytechnic data in 2001, and the Prefinalists

data in 2002. Information was gathered from parents with Inventory of Parental Influence (Campbell, 1996a) to have more versatile look into the background factors contributing to the development of mathematical talent. Table 1 shows, except for the Polytechnics, that the gender is biased towards males. The student’s age is a good predictor for group membership. Measurement Instruments The SaaS instrument, developed originally for cross-cultural Academic Olympiad studies, was mailed to respondents in a traditional paper and pen form. The instrument used a six-point Likert scale ranging from strongly disagree to strongly agree. The self-confidence attribute attitude scale included eighteen items measuring the students’ attributions based on self-attribution theory (Weiner, 1974). Although Weiner’s original conceptualization contained four attributions (ability, effort, difficulty, luck), the statistical analysis based on numerous empirical samples produced only two distinct scales, effort and ability (Campbell, 1996a; 1996b; Feng et al., 2001; Heller & Lengfelder, 2000; Tirri, 2001). In each of these studies a consistent factor structure was found for the ability and effort factors. Statements linking success and effort produced high scores on the effort factor. Statements on the ability factor expressed the view that ability is more important than hard work. In addition to SaaS scale, we asked the following background information from the respondents: gender, age, number of programming languages known, and average of mathematics, physics and chemistry secondary school grades. We constructed an additional variable, level of giftedness, by combining the knowledge of programming languages and the secondary school grades. Also the (IPI) instrument (Campbell, 1996a) was mailed to the students’ parents in a traditional paper and pen form (see Table 3). The instrument used a five-point Likert scale ranging from strongly disagree to strongly agree. The instrument included 39 items measuring the following five dimensions: (1) Pressure, (2) Psychological Support, (3) Help, (4) Press for Intellectual Development, (5) Monitoring/Time Management. Campbell has reported for all the aforementioned scales alpha values ranging between 0.71 and 0.85 (1996a). Statistical Analysis The statistical procedures were conducted in four stages: (1) variable selection (student and parent data), (2) analysis of variance (student and parent data), (3) explorative factor analysis (student data), and (4) Bayesian classification modeling (student data). First, we analyzed all the items to see if they were technically applicable for linear statistic computations, such as exploratory factor analysis, based on multivariate normality assumption. Bayesian modeling techniques are free from such presuppositions (Nokelainen & Tirri, 2004; Nokelainen, Ruohotie & Tirri, 1999, 113). Second, we conducted oneway ANOVA with Bonferroni post hoc test to see if there exist any item level differences between the groups. The third stage was to conduct explorative factor analysis to see if the four dimensions of the SaaS instrument (success due to ability, failure due to lack of ability, success due to effort, failure due to lack of effort) are identified in this domain. The fifth stage of the analysis was to find best predictors for the group memberships among the self-attribute scale and background variables with Bayesian classification modeling. Results: Self-confidence Attitude Attribute Scales Variable Selection The aim of the first stage was to examine the self-attribution variables and choose the acceptable ones for further analysis. Frequency analysis was carried out for all the variables. Results show that the respondents used whole scale from 1 to 6 for all the items. Distribution of the mode is biased towards positive values: (1) n = 0; (2) n = 5; (3) n = 0, (4) n = 11; (5) n = 0; (6) n = 0. Numerous publications declare that certain attributes belong to data that is appropriate for multivariate analysis (e.g., Tabachnick & Fidell, 1996, 13-17; Thompson, 1999; Bradley & Schaefer, 1998, 79-83). The most commonly used criteria for accepting variables for multivariate analysis are: (1) standard deviation maximum half the mean; (2) skewness less than +/- .3; (3) correlation between +/- .3 - .7. When we examined the eighteen items by the first two criteria, we obtained the following results: (1) all items pass the first criteria and (2) four items pass the second criteria. As it seemed impossible to take the second criteria literally due to high rejection rate at .03 level, we examined the skewness of items in three additional levels (.05, .07, .08). The .07 level proved to be suitable for this data set suggesting rejection of three items (4, 6, 7). A non-parametric inter-item correlation matrix was produced in order to examine the third criteria. Thirteen items reached the desired level as the values ranged from –0.48 to 0.71 (M = .05, SD = .16). The rejected items were: 4, 7, 10, 14, and 18. Finally, when we combine the results of the variable selection phase, it is seems obvious that at least items “4. I worked harder if I liked the teacher,” and “7. You have to have the ability in order to succeed in most things” should be omitted from further analysis.

Item Level Analysis of Variance One-way analysis of variance revealed statistically significant mean level differences in eight items (Table 2). We examined those items with Bonferroni and Tukey’s B post hoc tests to see how the groups were located in the subsets. We found three different group combinations: (1) Olympians and Prefinalists vs. Polytechnics (items 4, 12), (2) Olympians vs. Prefinalists and Polytechnics (items 2, 3, 8, 16), and (3) Prefinalists vs. Olympians and Polytechnics (item 10). It was interesting to see that Olympians and Prefinalists efficiency was more dependent on teacher’s capability to conduct learning situations than Polytechnics students. Olympians and Prefinalists believe in success due to ability. The items that Prefinalists and Polytechnic students agree with are related to failure due to a lack of effort. The only proposition that connects Olympians and Polytechnics is “10. The smart kids tried the hardest.” Explorative Factor Analysis Our next task was to explore if the three samples contained the following four dimensions: (1) ”Success due to Ability”, (2) ”Failure due to a lack of Ability”, (3) ”Success due to Effort”, and (4) ”Failure due to a lack of Effort”. We continued the analysis with sixteen items, as the variable rejection based on communalities of two-dimensional PCA structure did not appear to provide a feasible solution. Factor analysis with Maximum Likelihood extraction method and Varimax (orthogonal) rotation was conducted for each data set. A four-factor solution grouped the variables in all three data sets as we expected. We present here only the strongest loading variables for each factor. Factor 1 “Success due to Ability” included variables “10. The smart kids tried the hardest,” and “5. Being smart is more important than working hard”. Factor 2 “Failure due to a lack of Ability” included items like “13. When I did poorly in school it was because I did not have the needed ability,” and “14. Why work in an area where your ability is low?” Factor 3 “Success due to Effort” included items like “9. Self-discipline is the key to school success,” and “17. Hard work is the key to get good grades.” Factor 4 “Failure due to a lack of Effort” included items like “6. When I scored low on a test, it was because I didn’t study hard enough,” and “8. My achievement would have been better if I tried harder.” Total variance of the four-factor solution varied within the samples as follows: Olympist data 53.5%, Polytechnics data 53.2%, and Prefinalists data 57.2%. The Cronbach’s alpha values for the four factors within the three groups varied as follows: Olympist data (factor 1 = 0.38, factor 2 = 0.16, factor 3 = 0.55, factor 4 = 0.54), Polytechnics data (factor 1 = 0.24, factor 2 = 0.33, factor 3 = 0.26, factor 4 =0 .66), and Prefinalists data (factor 1 = 0.01, factor 2 = 0.42, factor 3 = 0.68, factor 4 = 0.68). Correlations between factors and background variables are presented in Table 3. Spearman’s rho values range from –0.376 to 0.311 (M = -0.013). It is interesting to see that Level of Giftedness (as operationalized from number of known computer languages and mathematics grade average) correlates positively with success due to ability and failure due to lack of ability, but negatively with success due to effort and failure due to lack of effort. In order to study the differences between the independent and dependent variables, we performed both the t-test and ANOVA. The results of the t-test indicated that the Olympist group’s female and male respondent’s means differed significantly in terms of Level of Giftedness (t = 4.173, df = 14.12, p = .001). As this is a self-report composite variable, one reason for this result may lie in Siegle’s and Reis’s (1998) finding that gifted girls tend to underestimate their abilities. Also a small significant difference between the males and females in the same group was found with regard to Success due to Ability (t = -1.885, df = 74, p = .063). This research finding is in parallel with the findings of the earlier study of Verna & Campbell (1999). (Table 4.) Campbell’s (1996b) observation that effort is more important to success than ability was accurate with all the samples present in this study. The difference is most distinguishable among the Polytechnics students. ANOVA indicated that there were significant differences between the groups in terms of Level of Giftedness (F = 173.770, df = 2, p = .000), Ability (F = 12.163, df = 2, p = .000), Effort (F = 6.080, df = 2, p = .003), Success due to Ability (F = 9.319, df = 2, p = .000), Failure due to a lack of Ability (F = 8.063, df = 2, p = .000), and Success due to Effort (F = 14.351, df = 2, p = .000). We made pairwise comparisons with Tukey’s-b test between the groups in order to examine subset memberships. The results show three different group combinations: (1) Olympians and Prefinalists vs. Polytechnics (Level of giftedness, Ability), (2) Prefinalists vs. Olympians and Polytechnics (Success due to Ability), and (3) Olympians vs. Polytechnics vs. Prefinalists (Effort, Failure due to a lack of Ability, Success due to Effort). The superscripts in Table 4 represent the group memberships from post hoc tests. Bayesian Classification Modeling We conducted the Bayesian classification modeling with the B-Course analysis tool (Myllymäki, Silander, Tirri & Uronen, 2002) in order to find out which variables measuring self-attributions are the best predictors for the group membership, gender, and the Level of Giftedness. In the classification process, the automatic search tried to find the best set of variables to predict the class variable for each data item. This procedure is akin to the stepwise selection procedure in the traditional linear discriminant analysis (Huberty, 1994, 118-126). First, we derived the model for classifying data items according to the class variable “Group” (“Mathematics Olympians”, “Polytechnics”, and “Prefinalists”) with the 18 variables of self-concept attribute attitude scale (see Table 2) as predictors. The estimated classification accuracy for the model was 65.35%. Second, we derived the model for classifying data items according to the class variable “Gender”. The estimated classification accuracy for the model was

79.70%. The last classification task was to find the best predictors for the class variable “Level of giftedness” describing the self-rated knowledge of programming languages and the secondary school grades in a continuous scale from 0 to 5 (“Low level” 0 - 1.66, “Middle level” 1.67 - 3.33, ”High level” 3.34 - 5). The estimated classification accuracy for the model was 74.75%. Table 5 lists the variables ordered by their estimated classification performance in the model. The strongest variables, i.e. those that discriminate the independent variables best, are listed first. The percentual value attached for each variable indicates the predicted decrease in the classification performance if the variable is dropped from the model. The table shows that variables in first two models, Group and Gender, have a clear order of importance. The most important variable for both models is ”12. I had to work hard to get good grades.” If we remove that variable from the first model, it would weaken the performance from 65.35% to 58.42%. Removal of the variable from the second model would weaken the performance from 79.70% to 72.77%. We conducted a classification analysis with the secondary school average mathematics grade as a class variable and eighteen self-attribute variables (SaaS) as predictors. The mathematics achievement variable was categorized into three classes: top, middle, and low on the basis of the average grade points. Only two variables, “12. I had to work hard to get good grades,” and “5. Being smart is more important than working hard” were related to mathematics achievement. The results suggesting that high mathematics achievement was related to “success is due to ability” thinking, is in parallel with Marsh’s (1983) earlier findings. The estimated classification accuracy of the model was 65.31%. “Failure due to lack of ability” was the only self-attribute scale that was able to predict respondent’s age. The youngest students (15-28 years) believed more in their abilities than the older ones (29-41 and 42-55 years). The estimated classification accuracy of the model was 69.54%. Results: Parental Influence Scales Variable Selection Frequency analyses were carried out for all the 39 variables of the IPI instrument. Results show that the respondents used whole scale from 1 to 5 for all but five items. Distribution of the mode is strongly biased towards low-end values: (1) n = 17; (2) n = 6; (3) n = 3, (4) n = 10; (5) n = 2. When we examined the 39 items by the first acceptance criteria, standard deviation maximum half the mean, we learned that all but following seven items passed: 1, 3, 5, 11, 25, 43, 46. As only 8 items passed the second criteria (skewness less than +/- .3), we gradually lowered the cut point to 1.5, still indicating rejection of the following 11 items: 1, 4, 5, 8, 22, 25, 26, 32, 42, 44, and 46. A non-parametric inter-item correlation matrix was produced in order to examine the third criteria, correlation between +/- .3 - .7. 36 items reached the desired level as the values ranged from – 0.28 to 0.68 (M =.11, SD =.16). The rejected items were: 19, 21, and 26. The items are presented in Table 6. Finally, when we combine the results of the variable selection phase, it is seems obvious that at least variables “5. I felt that it's important not to miss a day of school”, “25. My child was basically lazy, and if it were not for me he/she would not have done as well in school”, “26. I am proud of my child”, “32. I kept track of the amount of time my child gave to homework”, “42. When my child needed help I hired a tutor” and “46. I insisted my child set aside a certain time for reading” should be omitted from further analysis. Item Level Analysis of Variance One-way analysis of variance revealed statistically significant mean level differences in 28 items (Table 6). Next we report the factors for each IPI scale that were the most important in all the tree groups. On the Parental Pressure scale the most important items were “3. I think my child could have done better in school” and “6. I did not feel that my child did his/her best in school”. The group means differed most in items “3. I think my child could have done better in school” and “16. School would have been more pleasant for my child if I were not as strict”. Parent’s responses showed that the following four items had the highest values on the Psychological Support scale: “5. I felt that it's important not to miss a day of school”, “9. I was satisfied if I knew my child did his/her best”, “21. I get along very well with my children”, “26. I am proud of my child.” The group means differed most in items “17. I wanted my child to go to a ”good” college”, “23. I felt children need parental guidance when it came to schoolwork” and “24. I expect my children to go to college”. The most important items on the Help scale were support with difficult homework (item 33) and selecting books to read (item 34). The group means differed most in items ”30. I helped with my child's mathematics homework”, ” 37. I helped my child study before a test” and ” 45. Before leaving for school I would ask if my child had everything needed (homework, books, reports)”. Press for Intellectual Development was actualized with encouragement to go to local library (item 31) and spend more time in bookstores (item48). Parents also reported that they preferred to buy books for presents (item 49). The group means differed most in items ”41. I wanted my child to bring home test papers to see how well he/she did” and ” 50. When my child was absent, I would tell him/her to telephone a friend to get the homework”. Parents reported the item “40. When my child watched too much TV I restricted his/her TV time” to be the strongest way of Monitoring and Time Management. The group means differed most in items ”40. When my child watched too much TV I restricted his/her TV time”, ”42. When my child needed help I hired a tutor” and ”46. I insisted my child set aside a certain time for reading”. (Table 6.)

Next we examined the IPI scale items with Bonferroni and Tukey’s B post hoc tests to see how the groups were located in the subsets. The following three group combinations were found: (1) Olympians and Prefinalists vs. Polytechnics (items 1, 16, 42), (2) Olympians vs. Prefinalists and Polytechnics (items 17, 23, 28 30, 37, 41, 46, 50), and (3) Prefinalists vs. Olympians and Polytechnics (item 40, 45). The results show, that on the Parental Pressure scale both Olympians and Prefinalists parents felt their children had succeeded as well as they could in school. They were not as strict in their education as Polytechnic students parents. On the Psychological Support scale the group comparison results showed that Polytechnics students parents did not expect their child to go to “good” college as much as the Olympians and Prefinalists parents did. Polytechnics and Prefinalists parents felt more than Olympians parents that their child needed parental guidance when it came to schoolwork. On the Help scale both Polytechnics and Prefinalists parents helped their child more with mathematics homework and before a test than Olympians parents did. On the Press for Intellectual Development scale both Polytechnics and Prefinalists parents were more eager than Olympians parents to see their children’s test papers. Olympians parents bought more books for presents than Polytechnics and Prefinalists parents. On the Monitoring and Time Management scale the comparison by the groups showed that Polytechnics parents were more willing to hire a tutor when their child needed help than Prefinalists and Olympians parents. Polytechnics and Prefinalists parents were more insisting on their children to set aside certain time for reading than Olympians parents. Conclusions In this paper we have examined the influence of self-attributions and parental attitude to the development of mathematical talent in three groups of mathematically gifted Finnish students (n = 203) and their parents (n = 188). All the student participants completed Self-confidence attitude attribute Scales (SaaS) questionnaire, and their parents completed Inventory of Parental Influence (IPI) questionnaire (Campbell, 1996a). The student version of the instrument included 18 items measuring the students' ability and effort attributions, based on Weiner’s attribution theory (1974), on four dimensions: (1) ”Success due to Ability”, (2) ”Failure due to a lack of Ability”, (3) ”Success due to Effort”, and (4) ”Failure due to a lack of Effort”. The parent’s version of the instrument included 39 items measuring the following five dimensions: (1) Pressure, (2) Psychological Support, (3) Help, (4) Press for Intellectual Development, (5) Monitoring/Time Management. Analysis of variance in the student data revealed several statistically significant mean level differences among the group subsets: the Olympians and Prefinalists did not believe in hard work as much as the Polytechnics in order to get good grades. The results of the group means comparison indicated that the Olympist females and males abilities differed significantly in terms of secondary school mathematics grade average. Also, a small significant difference between the males and females in the same group was found with regard to Success due to Ability. Furthermore, Effort was shown to be more important factor of success than ability in all three samples. The difference was most distinguishable among the Polytechnics students. Additionally, analysis of variance pointed out several significant differences between the groups. We found three combinations of the Group variable in terms of Level of giftedness, Ability, Effort, Success due to Ability, Failure due to a lack of Ability, and Success due to Effort. The results of Bayesian classification modeling showed that the polytechnic students as a group and female respondents in all the three groups felt that they “had to work hard to get good grades”. The classification analysis was conducted with the secondary school average mathematics grade as a class variable and eighteen self-attribute variables (SaaS) as predictors. We found that only two variables, “12. I had to work hard to get good grades,” and “5. Being smart is more important than working hard” were related to mathematics ability. The results suggesting that high mathematics achievement was related to “success is due to ability” thinking, is in parallel with the previous research findings. “Failure due to lack of ability” was the only self-attribute scale that was able to predict respondent’s age. The youngest students (15-28 years) believed more in their abilities than the older ones (29-41 and 42-55 years). The research questions in this study were as follows: (1) Do the self-attributions of the three groups of mathematically gifted differ by the group membership, gender, and the level of giftedness? (2) What are the most important forms of the parental influence? (3) How parental influence differ in the three groups? The results of parental data showed that Polytechnics had more parental pressure and less psychological support than Olympians and Prefinalists. Olympians’ parents reported smaller frequencies of parental help for homework and studying than Polytechnics and Prefinalists. Olympians and Prefinalists parents emphasized more the value of books and reading than Polytechnics parents did. Polytechnics and Prefinalists parents were more eager to know how well their child did in school. In addition, they were monitoring more their children’s behavior regarding homework, studying and T.V. About the Authors EdLic. Petri Nokelainen is a Senior Research Scientist at the Research Centre for Vocational Education, University of Tampere, Finland. His research interest lies on the study of applied statistical modeling, modern network-based learning, and gifted education. Dr. Kirsi Tirri is a Professor of Education at the Department of Education, University of Helsinki, Finland. Her research interests include gifted education, teacher education, moral education and cross-cultural studies.

Dr. Hanna-Leena Merenti-Välimäki is a Principal Lecturer of Mathematics at the Espoo-Vantaa Institute of Technology. Her research interests include mathematical education, mathematical modeling and statistical and technical analysis. Contact Details EdLic. Petri Nokelainen Senior Research Scientist Research Centre for Vocational Education University of Tampere P.O.Box 229 13101 Hameenlinna Finland Email: [email protected] Phone: +358 3 687 0011 References Bradley, W.J. and Schaefer, K.C. (1998). The Uses and Misuses of Data and Models. Thousand Oaks: Sage. Campbell, J. (1994). Developing cross-cultural/cross-national methods and procedures. International Journal of Educational Research, 21(7), 675-684. Campbell, J. (1996a). Developing cross-national instruments: Using cross-national methods and procedures. International Journal of Educational Research, 25(6), 485-496. Campbell, J. (1996b). Early identification of mathematics talent has long-term positive consequences for career contributions. International Journal of Educational Research, 25(6), 497-522. Chan, L. (1996). Motivational orientations and metacognitive abilities of intellectually gifted students. Gifted Child Quarterly, 40, 184-193. Feng, A., Campbell, J. and Verna, M. (2001). The Talent Development of American Physics Olympians. Gifted and Talented International, 16(2), 108-114. Heller, K. and Lengfelder, A. (2000, April). German Olympiad study on mathematics, physics and chemistry. A paper presented at the Annual Meeting of American Educational Research Association, New Orleans, USA. Huberty, C. (1994). Applied Discriminant Analysis. New York: John Wiley & Sons. Marsh, H. (1983). Relationships among Dimensions of Self-Attribution, Dimensions of Self-Concept and Academic Achievements. ERIC Clearinghouse on Information & Technology ED243914. Kerr, B. (1994). Smart girls: A new psychology of girls, women and giftedness. (Rev. ed.). Scottsdale, AZ: Gifted Psychology Press. Marsh, H. and O’Neill, R. (1984). Self Description Questionnaire III: The construct validity of multidimensional selfconcept ratings by late adolescents. Journal of Educational Measurement, 21, 153-174. Multon, K. D, Brown, S. D. and Lent, R. W. (1991). Relation of self-efficacy beliefs to academic outcomes: A metaanalytic investigation. Journal of Counseling Psychology, 38, 30-38. Myllymäki, P., Silander, T., Tirri, H. and Uronen, P. (2002). B-Course: A Web-Based Tool for Bayesian and Causal Data Analysis. International Journal on Artificial Intelligence Tools, 11(3), 369-387. Nokelainen, P., Ruohotie, P. and Tirri, H. (1999). Professional Growth Determinants - Comparing Bayesian and Linear Approaches to Classification. In P. Ruohotie, H. Tirri, P. Nokelainen and T. Silander (Eds.), Modern Modeling of Professional Growth vol. 1, (pp.85-120). Hämeenlinna, Finland: Research Centre for Vocational Education, University of Tampere. Nokelainen, P. and Tirri, H. (2004). Bayesian Methods that Optimize Cross-cultural Data Analysis. In J. R. Campbell, K. Tirri, P. Ruohotie and H. Walberg (Eds.), Cross-cultural Research: Basic Issues, Dilemmas, and Strategies, (pp. 141-158). Hämeenlinna, Finland: Research Centre for Vocational Education, University of Tampere. Nokelainen, P., Tirri, K. and Campbell, J. (2002, April). Cross-cultural findings of computer literacy among the Academic Olympians. A paper presented at the Annual Meeting of American Educational Research Association, New Orleans, USA. Reis, S. (1998). Work left undone. Mansfield Center, CT: Creative Learning Press. Siegle, D. and Reis, S. (1998). Gender differences in teacher and student perceptions of gifted students’ ability and effort. Gifted Child Quarterly, 42(1), 39–47. Silander, T. and Tirri, H. (1999). Bayesian classification. In P. Ruohotie, H. Tirri, P. Nokelainen and T. Silander (Eds.), Modern Modeling of Professional Growth vol. 1, (pp.61-84). ). Hämeenlinna, Finland: Research Centre for Vocational Education, University of Tampere. Strein, W. (1995). Assessment of Self-concept. ERIC Clearinghouse on Counseling and Student Services Greensboro, NC ED389962. Tabachnick, B. and Fidell, L. (1996). Using Multivariate Statistics. New York : Harper Collins.

Thompson, B. (1999, April). Common Methodology Mistakes in Educational Research. A paper presented at the Annual Meeting of American Educational Research Association, Montreal, Canada. Tirri, K. (2001). Finland Olympiad Studies: What Factors Contribute To The Development Of Academic Talent In Finland? Educating Able Children, 5(2), 56-66. Verna, M. and Campbell, J. (2000, April). Career orientations for American Chemistry Olympians. A paper presented at the Annual Meeting of American Educational Research Association, New Orleans, USA. Weiner, B. (1974). Achievement motivation and attribution theory. Morristown, NJ: General Learning Press. Weiner, B. (1980). The role of affect in rational (attributional) approaches to human motivation. Educational Researcher, 9, 4-11. Weiner, B. (1994). Integrating social and personal theories of achievement striving. Review of Educational Research, 64, 557-573. Wu, W. and Chen, J. (2001). A follow-up study of Taiwan physics and chemistry Olympians: The role of environmental influences in talent development. Gifted and Talented International, 16(1), 16-26.

This paper has been formally refereed according to DEST requirements.

Table 1. Description of Mathematics Olympians, Polytechnics, and Prefinalists Data Olympians (n=77) n

%

Olympians Parents (n=66) n %

Polytechnics (n=74) n

%

Polytechnics Parents (n=44) n %

Gender Male 68 88 40 54 28 42 12 Female 9 12 34 46 38 58 32 Age Median 37 years 24 years Range 20 – 55 years 20 – 34 years Note. Total n of the student’s data is 203; total n of the parent’s data is 188.

27 73

Prefinalists (n=52) n 43 9

Prefinalists Parents (n=78) n %

% 83 17

35 43

45 55

17 years 15 – 20 years

Table 2. Self-concept Attribute Attitude Scale Comparison by Groups

Effort (12 items) 1. I did poorly only when I did not work hard enough. 2. You can be successful in anything if you work hard enough at it. 6. When I scored low on a test, it was because I didn't study hard enough. 8. My achievement would have been better if I tried harder. 9. Self-discipline is the key to school success. 10. The smart kids tried the hardest. 11. Poor study habits are the main cause of low grades. 12. I had to work hard to get good grades. 15. When I didn't understand something, it meant I didn't put in enough time. 16. I could have done better in mathematics if I had worked harder. 17. Hard work is the key to get good grades. 18. I let people down when I don't work hard enough. Ability (6 items) 3. There are some things you can't do no matter how hard you try. 4. I worked harder if I liked the teacher. 5. Being smart is more important than working hard. 7. You have to have the ability in order to succeed in most things. 13. When I did poorly in school it was because I did not have the needed ability. 14. Why work in an area where your ability is low?

Olympians (n=77) M SD

Polytechnics (n=74) M SD

Prefinalists (n=52) M SD

F

p

3.79

.970

3.46

1.149

3.56

1.146

1.810

.166

3.27

1.234 3.99

.852

3.78

1.026

9.149

.000

3.92

.790

3.53

.954

3.63

.971

3.683

.027

3.29

1.252 4.09

.686

3.83

.964

12.506

.000

3.27 2.43 3.32

.905 .929 .912

3.41 2.22 3.54

1.059 .926 1.036

3.47 2.81 3.44

.924 .951 .978

.750 6.153 .999

.474 .003 .370

2.11 3.69

.946 .870

2.74 3.51

1.034 .940

2.08 3.58

.947 1.073

10.319 .681

.000 .507

3.11

1.165 4.01

.852

3.81

1.049

15.459

.000

2.83 2.64

1.045 3.00 1.054 2.45

.891 1.087

2.77 2.62

1.131 1.140

.929 .649

.397 .524

3.68

1.187 2.97

1.193

3.29

1.171

6.641

.002

3.16

1.223 3.77

.987

3.57

1.237

5.531

.005

2.99

1.034 2.64

1.028

3.23

.921

5.635

.004

3.92

.736

3.86

.746

3.90

.693

.107

.899

2.46

1.040 2.09

.797

2.37

.979

3.020

.051

2.81

1.026 2.58

1.159

2.75

1.230

.800

.451

Table 3. Correlations Between the Factors Level of Success due to Failure due to Success due to Failure due to lack Giftedness Ability lack of Ability Effort of Effort Level of Giftedness 1.000 Success due to Ability .248** 1.000 Failure due to lack of Ability .285** .182** 1.000 Success due to Effort -.299** -.137 -.267** 1.000 Failure due to lack of Effort -.106 .121 -.219** .311** 1.000 ** = Correlation is significant at the .01 level (2-tailed). * = Correlation is significant at the .05 level (2-tailed).

Table 4. Group and Gender Comparison by the Level of Giftedness and Self-Attributions Level of giftedness

Ability

Effort

Success due to ability

Failure due to lack of ability M 3.01*c 2.98 3.02

SD .73 .63 .75

M 2.92* 3.18 2.89

SD .53 .56 .52

Failure due to lack of effort M SD 3.39 .59 3.43 .45 3.39 .60

2.55*c 2.58 2.52

.64 .66 .64

3.38* 3.39 3.38

.47 .48 .46

3.51 3.45 3.57

.55 .50 .60

3.06*a .52 3.34c .52 3.31*b .51 2.81c .75 3.13* .60 3.49 Prefinalists 4.31*a .44 Female (n=9) 4.17 .33 2.98 .45 3.17 .60 3.15 .50 2.83 .75 3.02 .74 3.28 Male (n=43) 4.34 .45 3.08 .53 3.38 .50 3.35 .51 2.80 .76 3.15 .57 3.53 * = The mean difference is significant at the .05 level. Note. a = Olympians and Prefinalists vs. Polytechnics, b = Prefinalists vs. Olympians and Polytechnics, c = Olympians vs. Polytechnics vs. Prefinalists.

.61 .57 .61

Olympians Female (n=9) Male (n=67)

M 4.54*a 4.16* 4.59*

SD .43 .27 .43

M 3.06*a 3.20 3.05

SD .47 .43 .48

M 3.20*c 3.32 3.18

SD .45 .34 .46

M 3.10b 3.41 3.06

SD .53 .49 .53

Polytechnics Female (n=34) Male (n=40)

2.64*a 2.59 2.68

.95 1.00 .91

2.73*a 2.70 2.75

.42 .47 .38

3.46*c 3.42 3.49

.44 .38 .48

2.91*b .53 2.81 .54 2.98 .51

Success due to effort

Table 5. Importance Ranking of the Variables in the Bayesian Classification Model Class variable

Predictor variables

Decrease in predictive classification if variable is dropped (%)

10. The smart kids tried the hardest. 16. I could have done better in mathematics if I had worked harder. 12. I had to work hard to get good grades. 5. Being smart is more important than working hard. 3. There are some things you can't do no matter how hard you try. 4. I worked harder if I liked the teacher. 8. My achievement would have been better if I tried harder.

14.36 7.92 6.93 4.95 3.96 2.48 1.98

12. I had to work hard to get good grades. 8. My achievement would have been better if I tried harder. 2. You can be successful in anything if you work hard enough at it. 1. I did poorly only when I did not work hard enough. 14. Why work in an area where your ability is low? 5. Being smart is more important than working hard.

6.93 6.44 3.96 3.47 2.97 1.98

3. There are some things you can't do no matter how hard you try. 10. The smart kids tried the hardest. 12. I had to work hard to get good grades.

1.98 1.98 1.49

Group

Gender

Level of giftedness

Table 6. Inventory of Parental Influence Scale Comparison by the Groups Olym. Par. (n=77) M SD Pressure (8 items) 1. I was never satisfied with my child's grades in school. 3. I think my child could have done better in school. 6. I did not feel that my child did his/her best in school. 8. My child was afraid to come home with a poor grade. 11. I used to have doubts when my child said that she had no homework. 16. School would have been more pleasant for my child if I were not as strict. 22. I was only pleased when my child got a 100% on a test. 25. My child was basically lazy, and if it were not for me she would not have done as well in school.a Psychological Support (10 items) 4. My child did well in school mostly because of my help. 5. I felt that it's important not to miss a day of school.a 9. I was satisfied if I knew my child did her best. 12. I had much patience with my child when it came to her education. 17. I wanted my child to go to a ”good” college. 19. I took a big interest in my child's schoolwork. 21. I get along very well with my children. 23. I felt children need parental guidance when it came to schoolwork. 24. I expect my children to go to college. 26. I am proud of my child.a Help (8 items) 27. I went over my child's mistakes when she brought home a test. 30. I helped with my child's mathematics homework. 33. I helped my child with schoolwork he/she didn't understand. 34. I helped my child select books to read. 35. I checked my child's homework. 37. I helped my child study before a test. 43. I helped with my child's school reports. 45. Before leaving for school I would ask if my child had everything needed (homework, books, reports). Press for Intellectual Development (7 items) 28. I encouraged my child to read right before going to sleep. 31. I encouraged my child to go to the local library. 41. I wanted my child to bring home test papers to see how well she did. 48. I encouraged my child to spend more time in bookstores. 49. I bought books for presents. 50. When my child was absent, I would tell her to telephone a friend to get the homework. 52. I insisted that my child watch ”educational” television programs.

Polyt. Par. (n=74) M SD

Pref. Par. (n=52) M SD

F

p

1.42 1.98 2.14 1.42 1.55

0.95 1.17 1.26 0.79 0.81

1.37 2.89 2.52 1.32 2.05

0.62 1.22 1.30 0.47 0.94

1.09 1.61 1.79 1.46 1.64

0.51 0.95 1.05 0.75 0.93

4.23 19.06 5.37 0.58 4.49

0.016 0.000 0.005 0.559 0.012

1.45

0.71

1.95

0.95

1.42

0.57

8.74

0.000

1.40 1.33

0.58 0.85

1.47 1.41

0.67 0.76

1.35 1.19

0.64 0.54

0.51 1.48

0.604 0.231

1.55 4.36 4.23 3.37 4.17 2.79 4.42 1.95 4.61 4.52

0.79 0.99 0.82 1.24 0.82 0.95 0.58 0.98 0.55 0.66

1.77 3.93 4.23 3.27 3.35 3.05 4.09 2.89 3.31 4.77

0.91 1.17 0.80 0.95 1.15 1.03 0.83 1.04 1.14 0.42

1.58 4.36 4.40 3.46 3.99 3.08 4.45 2.58 4.16 4.78

0.89 0.94 0.63 0.93 0.95 1.07 0.60 1.17 0.72 0.45

1.00 3.02 1.20 0.45 10.01 1.59 4.76 11.14 35.16 5.35

0.370 0.051 0.304 0.637 0.000 0.206 0.010 0.000 0.000 0.006

2.23 1.38

1.06 0.65

2.27 2.14

0.79 0.93

2.76 1.91

1.19 0.84

5.26 13.62

0.006 0.000

2.62

1.28

3.30

0.95

3.27

1.29

6.16

0.003

2.23

0.89

2.33

1.04

2.76

1.02

5.80

0.004

1.71

0.78

2.14

0.86

2.14

0.99

4.93

0.008

1.88

0.90

2.59

0.90

2.78

1.03

16.89

0.000

1.69

0.85

2.16

0.94

2.21

1.00

6.11

0.003

1.41

0.63

1.57

0.87

1.96

0.99

8.01

0.000

2.05

1.10

2.72

1.10

2.63

1.21

6.20

0.002

3.38

1.13

3.36

0.99

3.85

1.06

4.47

0.013

2.35

1.37

3.20

1.32

3.47

1.37

12.41

0.000

3.56

1.07

3.58

1.01

3.96

0.96

3.44

0.034

3.83

0.83

3.25

1.04

3.68

0.99

5.15

0.007

2.94

1.19

3.43

1.25

3.81

1.13

9.53

0.000

1.46

0.76

1.70

0.86

1.74

0.95

1.96

0.145

1.06

0.39

1.07

0.26

1.05

0.27

0.05

0.951

2.22

1.12

2.07

0.85

2.88

1.15

10.61

0.000

Monitoring/Time Management (6 items) 32. I kept track of the amount of time my child gave to homework.a 40. When my child watched too much TV I restricted her TV time. 42. When my child needed help I hired a tutor.a 44. I expected my child to do her homework at the same time each night.

1.08

0.33

1.57

0.95

1.06

0.25

14.68

0.000

1.38

0.89

1.57

0.95

1.87

1.02

4.77

0.010

46. I insisted my child set aside a certain time for reading.a

1.22

0.54

1.84

0.94

1.65

0.89

9.19

0.000

1.75

0.91

1.84

0.91

2.27

1.10

5.43

0.005

51. I determined how much television my child could watch. Note. a = Item was not accepted for the t-test and ANOVA.