The impact of mathematics interest and attitudes as determinants in order to identify girls' mathematical talent

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The impact of mathematics interest and attitudes as determinants in order to identify girls’ mathematical

talent

Ralf Benölken

To cite this version:

Ralf Benölken. The impact of mathematics interest and attitudes as determinants in order to identify

girls’ mathematical talent. CERME 9 - Ninth Congress of the European Society for Research in Math-

ematics Education, Charles University in Prague, Faculty of Education; ERME, Feb 2015, Prague,

Czech Republic. pp.970-976. �hal-01287295�

attitudes as determinants in order to identify girls’ mathematical talent

Ralf Benölken

University of Münster, Münster, Germany, rben@wwu.de

In proportion, girls often are decidedly underrepresent- ed in support programs that aim at mathematically tal- ented primary school children. Thus, it is of interest to ascertain aspects that might make possible a more dif- ferentiated identification and support. In the following article, a questionnaire study will be presented which can clarify the significance of mathematics interest and attitudes as determinants for the identification of mathematical talent: Boys and girls who were identified to be mathematically talented, and boys who were not showed a stronger mathematics interest (in and beyond the classroom) and more advantageous mathematics attitudes compared to girls who were not identified to be mathematically talented.

Keywords: Mathematical talent, mathematical giftedness, interest, attitudes, gender.

INTRODUCTION AND RATIONALE

In Germany just like in other western European countries, girls are in proportion decidedly under- represented in programs that foster mathematical talent (Benölken, 2011). This phenomenon contradicts the consensus on the fact that both sexes have equal potentials across all academic domains (Endepohls- Ulpe, 2012). When it comes to primary school children, aspects such as gender stereotyping of mathematical occupational fields cannot really act as possible expla- nations, especially because there cannot be found any gender-specific differences in mathematical compe- tencies at this age (Lindberg, Hyde, Petersen, & Linn, 2010). In addition, studies have indicated a decline of such differences at subsequent ages for many years (Hyde, Lindberg, Linn, Ellis, & Williams, 2008). This is why it is of interest to look for aspects that improve the identification of girls’ mathematical talent (see

[1]). With a holistic approach, diagnostics should be organized as a process considering both cognitive and co-cognitive, e.g. motivational, parameters as deter- minants in order to identify talents. For instance, girls and boys who were identified to be mathematically talented (“imt”) as well as boys who were not (“n-imt”), often show more advantageous self-concepts and at- tributions in mathematics than n-imt girls (Benölken, 2014). Findings like these raise the question how other motivational factors can be characterized in view of these groups. In this article, the significance of both mathematics interest and attitudes as determinants for the identification of mathematical talent at pri- mary school age will be examined by a questionnaire study. Its aim is to investigate boys’ and girls’ frequent characteristics as to these factors by a comparison of the four groups mentioned above. Based on literature reviews, hypotheses on the characteristics in question will be deduced that correspond to the questions of the study. Afterwards, the design and the results of the study will be reported.

BACKGROUND

Theoretical frameworks

Mathematics interest: The conception of interest applied in the study refers to Prenzel, Krapp and Schiefele (1986): Interest is seen as a result of an in- teraction between a person and an object that – along with adjuvant conditions – might cause to focus on a long-term preoccupation with this specific object.

This relation is characterized by (1) value-related, (2)

affective and (3) cognitive aspects. Additionally, in

accordance with current approaches on a multidimen-

sional structure of interests, a distinction between

subject-, context- and topic-related interest was con-

sidered (Krapp, 2010). The first two dimensions were

summarized in the term of “mathematics interest in

The impact of mathematics interest and attitudes as determinants in order to identify girls’ mathematical talent (Ralf Benölken)

971 the classroom” because it cannot be expected that

primary school children differ between activities and contexts applied in classrooms (Hellmich, 2006).

The third one is referred to by the term “mathematics interest beyond the classroom”.

Mathematics attitudes: The construct of “attitudes”

focuses on an evaluation of objects which an individ- ual imagines or perceives in his or her environment.

Attitudes can be explicitly and consciously accessed, or they can emerge implicitly and spontaneously – in both cases influencing an individual’s behavior (Bohner, 2003). The conception of attitudes applied in the study refers to the classical operationalization consisting of (1) cognitive, (2) affective and value-re- lated as well as (3) behavior-related components (Aronson, Wilson, & Akert, 2004).

Brief literature reviews

Preliminary notes: Research on both mathematics in- terest and attitudes mostly focuses either on children at middle school age or on gender-specific differences without regarding specific aspects of giftedness or talent. Studies which investigated mathematics inter- est or attitudes in the context of exceeding abilities mostly refer to “giftedness” as a “g-factor-concept” im- plying standardized diagnostics. Thus, their results cannot be transferred automatically to “mathemat- ical talents” regarding domain-specific criteria and implying long-term process diagnostics (see [1]). The findings collectively show, however, the significance of both factors as determinants for the identification of girls’ mathematical potentials. Therefore, they are suited to provide a basis for the intended deduction of hypotheses.

Mathematics interest: Primary school children of- ten have a lot of interests like sports, TV, computer games or reading (Pruisken, 2005). Furthermore, gender-specific differences can already be found at this early age (Hoberg & Rost, 2000): horseback riding, animals or reading seem to be “typical” interests of girls; football, technics or computer “typical” inter- ests of boys (Fölling-Albers, 1995). Boys more often show stronger mathematics interest – even at prima- ry school age and both in and beyond the classroom;

girls interest in language or literature (Hellmich, 2006; Pruisken, 2005). Though gifted children show the same differences, they do not have any extraor- dinary interests compared to non-gifted children.

However, gifted children generally seem to be more

interested in both mathematics and languages or liter- ature (Pruisken, 2005). In contrast to non-gifted girls, gifted girls have more interests which are supposed to be “typical” interests of boys, and they have a larger spectrum of interests than gifted boys (Kerr, 2000).

Regarding specific mathematical talents (in the sense of [1]), girls (irrespective of the identification of talent) more often show a larger spectrum of interests than boys (Benölken, 2014). The majority of primary school children does not differ between mathematics interest in the classroom and beyond the classroom (Hellmich, 2006). However, current studies do not focus on gen- der- or giftedness- respectively talent-specific aspects in this context. Furthermore, there are only very few studies with a focus on ability-related mathematics interest. Their findings indicate, that the mathematics interest of students with lower achievements exceeds that one of higher achievers (Frenzel, Goetz, Pekrun,

& Watt, 2010), but these studies do not focus on gifted or talented students. Finally, an often reported phe- nomenon is a decline in mathematics interest in the years of adolescence (Fredricks & Eccles, 2002), which is of little importance when conducting studies with primary school children.

Mathematics attitudes: Boys show advantageous mathematics attitudes more often than girls (Hyde, Fennema, Ryan, Frost, & Hopp, 1990). As to the cog- nitive aspect, studies primarily focus on individuals’

assessments of usefulness and difficulty of mathe- matics. There seem to be no gender- or talent-specific differences between imt and n-imt children regard- ing usefulness (Benölken, 2011), but some studies indicate that mathematically gifted boys and girls as well as non-gifted boys ascribe mathematics a low- er level of difficulty compared to non-gifted girls (Wieczerkowski & Jansen, 1990). Finally, there are findings on gender stereotypes: The older girls are the more they ascribe mathematics to males (Newton

& Newton, 1998), which seems to be less important at

primary school age, since such differences mostly

appear from an age of ten onwards. Concerning the

affective aspect, results on gender- or giftedness-spe-

cific differences of individuals’ intrinsic values (such

as enjoying mathematical task solving) seem to play

the most important role: Similar to characteristics of

the assessment of mathematics’ difficulty, some stud-

ies show that mathematically gifted boys and girls as

well as non-gifted boys show a higher intrinsic val-

ue doing mathematics compared to non-gifted girls

(Wieczerkowski & Jansen, 1990). On the other hand,

studies indicate that boys in general ascribe a higher intrinsic value to mathematics than girls (Bos, Wendt, Köller, & Selter, 2012). As to the behavior-related as- pect, boys seem to engage in mathematics beyond mathematical school lessons more often than girls (Schiepe-Tiska & Schmidtner, 2013).

THE STUDY Questions

The study was designed to answer the question how mathematics interest and attitudes can be character- ized with the regarded groups. The following hypoth- eses were deduced from the theoretical findings: (1a) Imt girls and boys as well as n-imt boys show a stron- ger mathematics interest in the classroom than n-imt girls. (1b) Imt girls and boys as well as n-imt boys show a stronger mathematics interest beyond the classroom than n-imt girls. (2) Imt girls and boys as well as n-imt boys show more advantageous mathematics attitudes than n-imt girls.

Design

The study adds to previous research on the signif- icance of motivational factors as determinants for the identification of mathematical talent using ques- tionnaires that are appropriate to primary school children, and that can be completed within a short time (e.g., Benölken, 2011; 2014). Operationalizations of mathematics interest in and beyond the classroom as well as of attitudes were tested within pilot studies.

Sample and procedure

The sample contains N=162 children of the third and fourth grade (71 girls, 91 boys). The subsample of imt children is n=83 (32 girls, 51 boys). Children who are assessed as “imt” take part in a project that fosters mathematical talent at the University of Münster called “math for small pundits”. They were chosen by long-term process-diagnostics that are a synthesis of standardized and non-standardized tools (see [1];

Benölken, 2014). The sample contains n=79 n-imt pri- mary school children (39 girls, 40 boys) from common classes. The probands were questioned during the school year of 2014/2015. All procedures of question- ing were consistent: The children were told how to fill in the questionnaire. In this context, possible differ- ences between mathematics interest in and beyond the classroom were emphasized (see [2]). The children completed the questionnaire on their own without

any time limit (no one took more than ten minutes and no one refused to fill in the questionnaire).

Method

Apart from declaring sex, the questionnaire was an- onymized. The phrasing of all items (following styles of common operationalizations in each case) was for- mulated in German. In order to measure mathematics interest in the classroom by a value-related, an affec- tive and a cognitive aspect, the following instruction was given: “This is about mathematics in the class- room. Mark with a cross a statement that you think fits best to you: (1) Mathematics in the classroom is really important to me. (2) I always look forward to mathematics in the classroom. (3) I am interested in mathematics in the classroom.” An analog instruction was composed to collect data about mathematics inter- est beyond the classroom: “This is about mathematics beyond the classroom. Mark with a cross a statement that you think fits best to you: (1) Mathematics is really important to me. (2) I always look forward to doing mathematics. (3) I am interested in mathematics.” In order to measure attitudes by cognitive, affective and behavior-related aspects, the following instruction was given: “Mark with a cross a statement that you think fits best to you: (1) Mathematical tasks are some- times too difficult. (2) I enjoy doing mathematics. (3) I engage in mathematics beyond mathematical school lessons.” To evaluate the items, in each case a four-step Likert-scale was offered (“that’s not correct”, “that’s almost not correct”, “that’s almost correct”, “that’s correct”; instead, the children could choose “I don’t know”).

Evaluation

Statements about all items except the one relating

to cognitive attitudes were translated into numbers

from 1 (“that’s not correct”) to 4 (“that’s correct”). As

to the cognitive attitude-item, the assignment was

turned around: “that’s not correct”, e.g., was translated

into 4 and “that’s correct” into 1, because statements

that focus on a low level of difficulty reflect advan-

tageous characteristics of attitudes. Regarding the

mathematics-interest-in-the-classroom-scale, the co-

efficient of correlation as defined by Pearson between

the included items moves in a range from .366 to .475

(with p<.01 in each case) and the internal consistency

is only just acceptable (Cronbachs α =.680). As to the

mathematics-interest-beyond-the-classroom-scale the

coefficient of correlation as defined by Pearson be-

tween the included items is in a range from .378 to .576

The impact of mathematics interest and attitudes as determinants in order to identify girls’ mathematical talent (Ralf Benölken)

973 (with p<.01 in each case) and the internal consistency

is between acceptable and good (Cronbachs α ^=.731).

Finally, the coefficient of correlation as defined by Pearson between the included attitudes items moves in a range from .334 to .617 (with p<.01 in each case) and the internal consistency is between acceptable and good, too (Cronbachs α =.710). In all cases, the items have been combined to one scale with mean values.

Data have been evaluated by an analysis of variance with two factors (“talent” and “sex”) to find significant differences between the four groups. In addition to that, η

-values have been calculated to see the possible importance of both the factors and their interaction by their effect size. The requirements of the statisti- cal procedure need the independence of subsamples and a normal distribution of the regarded trait within the groups amongst homogeneity of variance: The subsamples are obviously independent because of the distinction between sex and talent-identification.

As a consequence of a graphical analysis of the dis- tributions-histograms and the corresponding quan- tile-quantile-plots, the data are leptokurtic, but suffi- ciently similar to normal distributions (Hatzinger &

Nagel, 2009). The requirement of homogeneity of vari- ance is statistically firm as a result of Levene-testings.

RESULTS

Mathematics interest

Regarding mathematics interest in the classroom, the averages of imt boys and girls are relatively similar, while the value of n-imt boys is slightly larger and the value of n-imt girls is slightly lower (Table 1). There is no significant main effect on talent (F(1,158)<.001, p=.990, η

<.001), but there can be found a significant main effect on sex (F(1,158)=12.795, p<.001, η

=.075) as well as a significant effect of interaction (F(1,158)=4.139, p=.044, η

=.026). As indicated by η

-values, sex (medi- um effect of 7,5%) plays a bigger part to explain vari- ance than the interaction (medium effect of 2.6%).

Thus, the boys’ groups, especially the n-imt boys, show a stronger mathematics interest in the class- room compared to the girls’ groups, but as indicated by the significant effect of interaction, imt girls are more similar to the boys’ groups than to the n-imt girls, who show a lower mathematics interest in the classroom on average compared to all other groups.

Therefore, the statistical evaluation confirms hypoth- esis 1a in principle.

As to mathematics interest beyond the classroom, the averages of imt children and n-imt boys are very simi- lar and exceed the value of n-imt girls (Table 1). There are significant main effects on talent (F(1,157)=10.579, p=.001, η

=.063) and sex (F(1,157)=8.435, p=.004, η

=.051) just as there is a significant effect of inter- action (F(1,157)=7.579, p=.007, η

=.046). As indicated by η

-values, talent (medium effect of 6,3%) and sex (medium effect of 5.1%) play a similar role to explain variance. Thus, imt children and n-imt boys show sim- ilar characteristics of mathematics interest beyond the classroom which is stronger compared to n-imt girls, i.e. hypothesis 1b is confirmed. In addition, a descriptive data analysis of all groups’ mean values regarding both mathematics interest in and beyond the classroom indicates that only imt children seem to differ between these dimensions, since the values of n-imt boys and girls are quite similar in each case, while imt children’s mathematics interest beyond the classroom is stronger than in the classroom.

Mathematics attitudes

As to mathematics attitudes, the mean values of imt boys, imt girls and n-imt boys are relatively similar, even though the value of imt boys is slightly larger than the values of imt girls and n-imt boys. The value of n-imt girls is clearly lower in comparison to all oth- er groups (Table 2). There are significant main effects on both talent (F(1,158)=29.023, p<.001, η

=.155) and sex (F(1,158)=21.550, p<.001, η

=.120). Finally, there is a

mathematics interest in the classroom mathematics interest beyond the classroom

boys girls boys girls

imt children 3.07 (.83) 2.89 (.51) 3.39 (.70) 3.37 (.48)

n=51 n=32 n=51 n=32

n-imt children 3.30 (.76) 2.65 (.72) 3.33 (.79) 2.74 (.55)

n=40 n=39 n=40 n=38

Table 1: Averages (standard deviations) of mathematics interest-statements

significant effect of interaction (F(1,158)=7.597, p=.007, η

=.046). As indicated by η

-values, talent (strong ef- fect of 15,5%) and sex (medium effect of 12.0%) play a similar role to explain variance, even though the tal- ent effect is stronger. Thus, attitudes of imt children are more advantageous compared to n-imt children, but n-imt boys merely differ a little from the imt chil- dren. The statistical evaluation confirms hypothesis 2.

DISCUSSION

Synopsis: In this article, the significance of both math- ematics interest – by a distinction between in and be- yond the classroom – and attitudes as determinants for the identification of mathematical talent at pri- mary school age was investigated by a comparison of frequent characteristics with boys and girls who were identified to be mathematically talented (imt) as well as with boys and girls who were not (n-imt). Based on a review of existing empirical evidence, hypotheses on the mentioned characteristics were deduced: It has to be expected that imt children and n-imt boys show a stronger mathematics interest and more ad- vantageous attitudes than n-imt girls. The hypotheses were investigated by a questionnaire study. The sta- tistical results confirm the assumptions in principle:

First, the boys’ groups, especially n-imt boys, show a stronger mathematics interest in the classroom compared to the girls’ groups, while imt girls are more similar to the boys’ groups than to n-imt girls, who show a lower mathematics interest regarding this aspect than all other groups (similar to Pruisken, 2005). Second, imt children and n-imt boys show a stronger mathematics interest beyond the classroom than n-imt girls. In addition, only imt children seem to differ between mathematics interest in and beyond the classroom showing stronger interest beyond the classroom, while n-imt children on average took sim- ilar stances in both cases (which could explain the results of Hellmich, 2006). Finally, attitudes of imt children are more advantageous compared to n-imt

children, but n-imt boys merely differ a little (similar to Wieczerkowski & Jansen, 1990).

A deeper interpretation of the results indicates that all groups show a relatively strong mathematics interest and advantageous attitudes, even though the values of n-imt girls are lower compared to the other groups in each case. Regarding the significance of mathematics interest and attitudes for the identification of talent, the results insinuate that both a particularly strong mathematics interest (in and beyond the classroom) and advantageous attitudes can be found – indepen- dent of the identification of talent – more often with boys, while girls who have been identified to be mathe- matically talented are very similar to these groups. An observable stronger mathematics interest, especially in the classroom, and more advantageous attitudes might cause more efficient diagnostics of boys’ talents, because they might tend to a strong preoccupation with mathematics, or teachers might perceive their potentials primarily. By contrast, both lower mathe- matics interest, especially in the classroom, and dis- advantageous attitudes might lead to the fact that chil- dren do not develop a stronger preoccupation with mathematics and, e.g., turn to different interests. This might also apply to children who have a high potential that might be more difficult to identify. Though the findings are not suitable to predict how mathematics interest and attitudes can be characterized with math- ematically talented but not identified girls, they imply the following thesis: Disadvantageous characteristics of mathematics interest and attitudes are important aspects effecting a more infrequent identification of high potentials with girls. In addition, interest and attitudes have to be seen in a strong interdependence with other motivational factors as well as with influ- ences of socialization or gender-specific preferences in solving tasks (Benölken, 2011, 2014).

As to limitations of the study and directions for future research, within the imt group the underrepresenta- tion of girls has to be discussed: Because of the rare

boys girls

imt children 3.32 (.58) 3.11 (.60)

n=51 n=32

n-imt children 3.03 (.78) 2.23 (.76)

n=40 n=39

Table 2: Averages (standard deviations) of mathematics attitudes-statements

The impact of mathematics interest and attitudes as determinants in order to identify girls’ mathematical talent (Ralf Benölken)

975 identification of mathematical talent with girls, it

takes a long time to compose suitable subsamples (in particular, by process diagnostics). Nevertheless, despite the relative imbalance within the imt group, the size of all subsamples is sufficient in principle, even though follow-up studies should enlarge all subsamples and ensure a balance. The diagnostics procedures of talent identification that are used to compose the imt subsample have been established for many years. Thus, “imt” children most probably are rightly assessed in that way. In addition, there might be motivational effects caused by their participation in “math for small pundits” that cannot be found with children who have high potentials, but who are not taking part in such a program. Finally, the subsample of n-imt children is nothing more than an insufficient image of population. Thus, the sample’s representa- tiveness has to be seen as limited. The questionnaire was adequate to the aims of the study in principle. It is suited for a pragmatic use in classrooms because its design is appropriate to children, and it can be completed in a short time. However, mathematics interest and attitudes are strongly reduced in their conceptions, and the evaluation depends on very simple measurements. The external validity of the findings cannot be judged because tools that eviden- tially regard criteria of quality were not applied (in favor of the appropriateness to young children) and because the imt sample is very specifically composed.

In sum, the study has obvious limitations, and it rather has an explorative character. Despite the significant results, subsequent studies might focus on a deeper clarification using established tools.

As to a survey of exemplary practical consequences, first, any gender stereotyping of mathematics should be avoided. Second, the development of mathematics interest and advantageous attitudes seems to play an important role for girls in order to support their po- tentials to emerge. In this context, e.g., task-fields that are composed to foster girls especially – without ste- reotyping – might be useful (Benölken, 2013). The dis- tinction between mathematics interest in and beyond the classroom that was observed with imt children indicates the significance of a challenging education, e.g., by using enrichment tasks in common classes (Fuchs & Käpnick, 2009).

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ENDNOTES

1. According to Fuchs and Käpnick (2009), “mathe- matical talent” is seen as an above-average potential regarding the criteria of Käpnick (1998), i.e., remem- bering mathematical facts, sensitivity and fantasy, structuring and transferring structures or revers- ing thoughts. This potential is characterized by in- dividual determinants and a dynamic development depending on inter- and intrapersonal influences in interdependence with personality traits supporting the talent.

2. As to the distinction between the interest dimen- sions, the questionnaire instructions contained the

following elucidation (translated from German): “I would like to know how you like mathematics in and beyond the classroom. ‘Mathematics in the classroom’

focuses on everything you do in mathematical school

lessons. ‘Mathematics beyond the classroom’ focuses

on, e.g., mathematical activities or themes in your life

beyond mathematical school lessons or even outside

the school.”