Researchers have pointed out some of the underlying causes for concern in this area. The anecdotal and research evidence states that boys continue to outperform girls in math and science. Girls' attitudes towards math and science have become more negative; and evidence shows that males excel in math while females tend to excel in verbal skills. (Jovanovic and Dreves, 1996) However, it has also been found that major differences in performance due to gender are not usually seen until adolescence. These differences are usually demonstrated in higher-order mathematical tasks, such as multi-step problem solving. (Fennema et al., 1998) To some researchers, this indicates differences in how different genders think about fundamental mathematical concepts.
It has also been found, explicitly, that not only are there significant differences in achievement between genders, but as early as the first grade there are noticeable differences in the way that males and females solve problems. (Carr and Jessup, 1997) Females tend to use overt methods, such as using counters or fingers, while males tend to use retrieval methods, such as relying on memorized answers. In addition, boys tend to use more abstract strategies reflecting conceptual understanding. (Fennema et al., 1998; Carr and Jessup, 1997) Over the course of the year, the boys and girls tended to continue using their method of choice, irrespective of the success of that method. However, because of the nature of the each, over problem-solving techniques tended to deliver the correct answer, while retrieval did not necessarily do so (This would be because a student was unable to retrieve the correct answer from his or her memory). The interesting thing is that the children who opted for retrieval methods continued to use those methods, even if they produced the wrong answer. (Carr and Jessup, 1997)
As has been mentioned, in the higher grades, boys tend to be more successful in solving higher-order thinking problems. Some researchers suggested that the use of invented algorithms made for more success in these extension problems for both males and females, but that males tended to invent more algorithms in grades one to three (reflecting, perhaps, a better conceptual understanding of mathematics), while females tended to use more standard algorithms. (Fennema et al., 1998)
This concept is given more force by two statements put forth by the researchers. First, that the abstract processes that are used by males are important not only for solving problems correctly, but that the use of these algorithms seems to be important for development of an understanding of fundamental concepts as well. Secondly, the fact is that males and females who invented algorithms early have equal success in higher-order problem solving. (Fennema et al., 1998) The hypothesis put forth by these researchers is that the group that invented algorithms understood the conceptual procedures before continuing on to develop these algorithms, while the standard algorithms group developed a routine without that conceptual understanding. This would certainly account for the difficulties that those students have in solving more complicated mathematical problems.
Many of the researchers who put forth the case for differences in mathematical ability have support for the gender-based differences in cognitive ability, and put forth several reasonable arguments for the existence of these differences based on environmental factors while the students are developing.
The first factor is the influence of the social environment on their development. For example, boys are given the chance to play with building blocks, simple machines, and other toys that involve spatial conceptualization very early on, while girls often lack these experiences. As a result, when the children enter the classroom, girls feel more insecure towards their abilities in mathematics and science, so they believe that they cannot achieve as much as boys. (Jovanovic and Dreves, 1996)
Another factor that is attacked by some researchers is an argument that is common in teacher training as well - the idea that teachers have a different way to treat males and females within the classroom. Teachers who believe in the stereotype that girls fare more poorly at mathematical tasks than boys are less likely to encourage girls to continue on in mathematics. (Jovanovic and Dreves, 1996) In addition, the fact that girls tend to spend more time working in the concrete stage of cognition indicates the need for teachers to spend a significant portion of their time dealing with concrete strategies of problem-solving - a concept which has not been foremost in mathematical teaching methods until recently.
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