Mathematics and Gender
3.10. Math gender differences in believability in own abilities or self-concept
subjects that are mathematics-dependent.
3.10. Math gender differences in believability in own abilities or self-concept
Stipek & Gralinski (1991) have found, that there are gender differences regarding believability in own math abilities among children as young as in grade 3 (ibid, 1996): girls rated their own abilities more negatively than boys. Lent et al (1996) have found latent gender differences in mathematics self-efficacy among high school students.
Lucock (1987) has found, that high-ability boys tended to keep a fairly constant level of believability in their abilities in spite of failure, while low-ability girls tended to keep a fairly low level of believability in their own abilities in spite of success. However, the question of whether this tendency is valid also for average ability boys and girls, for low ability boys and for high ability girls needs further research. Without getting into the reasons why a certain sub-population holds a lower or higher level of believability in on math ability, we shall refer here only to differences in the magnitude of this believability.
Scott (2000) has studied the question, how come that in spite of the fact that females receive higher grades in schoolwork they have inferior achievements in problem solving and reasoning tests. The researcher has hypothesized, that believability in own math abilities, which has a substantial influence on achievements, accounts for males’ and females’ opposite outcomes through their differential effect on performance and preparation effort. While according to Scott (ibid), mathematically confident students would invest more effort in problem solving and reasoning tests, and thus receive higher grades, they would invest less effort in preparations and homework, assuming their high ability might compensate for the lack of effort. With students who perceive themselves as less able the situation would be reversed: they would study harder in order to compensate for their low ability.
However, Scott (ibid) has assumed that only less able female students will adopt this behavior, while less able males would drop mathematics if possible and if not – give up on the hope of achieving highly. In studying a sample of 318 high school students it was found that believability of own math ability proved to be the strongest predictor of problem solving; it had more influence than any other educational or psychological
component examined. However, gender differences were found, as expected, namely, confidence in math abilities influenced girls’ scores more than boys. In a study of remedial college mathematics course (Stage, & Kloosterman, 1995) a similar result was found: beliefs about mathematics ability were significantly related to final course grade only for females.
In a study of 186 8th grade students Seegers, & Boekaerts (1996) found gender differences in mathematical self-concept, that were correlated to mathematics test achievements. Believability in own math abilities has also proved to be positively correlated to math performance among male and female students selecting mathematics-based college majors (Cooper & Robinson, 1991). Let us see how confidence in math abilities influences achievements on large samples examined in international studies.
3.10.1. Believability in own math abilities and the TIMSS results
The 1999 TIMSS study has shown, that there are gender differences both in Israel and in many other countries examined in mathematics self confidence (Mullis et al., December, 2000). However, there is no correlation between the actual gender achievements differences in each country – or even between the existence of such differences – and the gender differences in mathematics self confidence.
In the 1999 TIMSS study, no significant differences in math self confidence were found in Israel among 14-year-olds with high, average, or low achievements (ibid, table 4.9). Among high achieving students gender differences favoring boys were found in 10 countries; among average achievers gender differences favoring girls were found in 9 countries, and only in Morocco these differences favored boys;
among low achievers – in 4 countries gender differences favored girls, and in Thailand – boys. Do these differences reflect anything but accurate self-perception? It seems that no, when we check the actual female achievements in all these groups.
Israel, for example, scores no. 9 among the 43 examined countries in math self-perception, but only 28 in actual achievements (ibid, table 4.8). The children that scored 1-8 in math self-perception had all higher achievements than Israel.
Furthermore, Singapore, who scored the first in the world in achievements, scored 28 in math self-perception. Hong Kong, no. 4 in the world regarding achievements, was no. 29 regarding math self-perception. China, no. 3 regarding achievements, was no.
30 regarding math self-perception, and Japan, no. 5 regarding achievements, was no.
39 regarding math self-perception, with only Morocco, Indonesia, the Philippines, and Thailand behind it! Thus we can see, that in Israel math self-perception of both boys and girls was substantially exaggerated. Movshovitz-Hadar (1997) has already suggested after the TIMSS 1995 results were published that the unrealistically high math self-esteem of Israeli students might be one of the reasons that they do not study enough mathematics, and thus helps the deterioration of the math level among boys as among girls.
Brew, Pfarn, Leder & Bishop (1996) have found, that even girls who were successful in mathematics had a low confidence in their abilities. Malpass (1996) has studied a sample of mathematically gifted high school students in southern California and found that boys had higher self-efficacy than girls. These findings should be examined in the light of the low level of participation rate in high-level mathematics on the one side, and the high achievements of the girls who did choose mathematics on the other. Interviews with world famous mathematicians (David, 2000f, 2000g;
Zorman & David, 2000) reveal that many talented women had once been girls who did not believe in having supreme math abilities, but their realistic self-concept led them to invest maximal effort and thus achieve at the highest possible level.
3.10.2. The double-edgedness of believability in own math abilities
In the TIMSS 1999 science study the percentage of boys with high self-concept was significantly higher than that of girls in Finland, Hungary, and Latvia (David, 2001a).
In no country was the self-concept of girls higher than that of boys’. However, as already stated, in Israel more girls than boys studied chemistry at thigh school, more girls took the matriculation exams, the success percentage of girls was higher than that of boys and girls got higher grades than boys. Taking these results into consideration, a clear distinction should be made between realistic believability in own math abilities and too optimistic such perception. In a German-Japanese study of 1,487 11th grade students from Leipzig and Sendai (Randel, Stevenson, & Witruk, 2000), large differences were found between students from these two countries in students’ performance. One of the main reasons for the German students lesser achievement was their being less critical of themselves and their academic abilities.
We can thus conclude that believability in own math abilities is a double-edged characteristic: when estimated correctly it can be used for enhancing learning in
general and mathematics in particular, but it can also be misused, as has been the case in the Israeli TIMSS 1999 results for 8th graders (David, 2001a), or with German 11th graders as has been shown by Randel et al (2000).
Girls have been found, on the one hand, to be more vulnerable than boys to decrease in their believability in on math abilities, but on the other hand, there are remedies to this vulnerability. For example: Kelly (2001) has found, that among high school American students, girls scored lower than boys in confidence in the ability to learn mathematics when the dominating learning style was recitation. In classrooms dominated by more student-centered discussions both boys and girls had stronger confidence in their ability to learn mathematics.