Recent research challenges the idea that gender differences in math first appear during adolescence. While previous research indicated that girls fell behind boys in math skills during adolescence, some recent studies suggest that gender differences in math may be declining and that girls’ achievement is now similar to boys,’ except at the most advanced levels. However, researchers Elizabeth Fennema and Thomas P. Carpenter, University of Wisconsin/Madison, found that on average, the girls in their study did not develop as good an understanding of mathematics as the boys.
Interviews of elementary boys and girls during this three-year study revealed that although there were few gender differences in performance in the early years of school, there were significant differences in problem-solving strategies. No gender differences in basic math problems were found, except that third-grade boys exhibited superior performance on more advanced multi-step word problems. At every grade level, however, there were unexpected differences in strategy. Girls tended to use concrete solution strategies such as counting or modeling, while boys tended to use more abstract strategies that indicated conceptual understanding.
Elementary children’s problem-solving
Fennema and Carpenter investigated gender differences and computational strategies in 44 boys and 38 girls as they progressed from the first through the third grade. Each child was individually interviewed five times during the three years. In each interview, children were asked to perform tasks involving basic number operations and their application to more complex problems.
All the students’ classroom teachers were participants in a three-year professional-development program designed to help them understand their students’ intuitive mathematical ideas and how these ideas could form the basis for the development of more formal ideas. The teachers instructional methods varied. No curriculum materials or specific guidelines were provided, but a variety of materials including counters and base-10 blocks were available in all classes. Students were given time to invent ways to solve problems and alternative strategies were discussed, but all students learned the standard algorithms (the rules or procedures for solving problems) by the end of third grade.
During interviews, children were asked for the answer to the number fact they were shown on a card and then asked to tell how they figured it out in their heads. The correctness of each answer was recorded and researchers categorized each strategy as either counting, derived fact or recall. Multi-digit addition and subtraction word problems and non-routine computation tasks involving multiple steps and requiring interpretation and analysis were also administered during each interview.
These tasks involved joining, separating or part-whole relationships. For most of these problems children had a choice of materials. However, in order to encourage them to use invented strategies if they could, some problems in each interview were administered without materials.
Solution strategies to these problems were described as modeling or counting, invented algorithm, or standard algorithm. There were two additional problems in the third-grade interviews that were described as extension problems — problems involving money and three-digit numbers. To encourage the use of invented algorithms no materials were available for use in solving these problems. Each of the five interviews lasted about an hour. Each problem was read as many times as the children wanted and they were given as much time as they needed to complete each task.
Difference in third grade
Researchers analyzed the data from these interviews to identify patterns of gender difference across time and problem categories. They compared the performance and strategy use of girls vs. boys for the four problem types (number facts, addition/subtraction, non-routine, and extension). During the three years, no significant differences appeared between girls and boys in the number of correct solutions to number-facts, addition/subtraction or non-routine problems. However, on the extension problems during the third grade, boys correctly solved significantly more problems than did girls.
Strategy use presented a different picture. Starting in the first grade and persisting through the third, boys and girls showed strong and consistent differences in the strategies they used. Girls tended to use more concrete strategies involving counting or modeling, while boys tended to use more abstract strategies such as derived facts or invented algorithms.
By the third grade, girls used more standard algorithms than boys. At each interview, boys used more invented algorithms. By the end of the study, 95 percent of the boys had used an invented algorithm compared to 79 percent of the girls. On subtraction tasks, 80 percent of the boys had used an invented algorithm while just 45 percent of the girls had.
The importance of strategy-use differences
To investigate the relationship between the use of invented algorithms and success on extension problems, these researchers divided the students into two groups — those who had used invented algorithms by the fall of second grade (53 students — 35 boys and 18 girls) and those who had moved directly from concrete modeling and counting strategies to standard algorithms (16 students — 2 boys and 14 girls).
These researchers believe that these two groups represent divergent patterns of learning multi-digit problems. The invented-algorithm group appeared to have first developed a conceptual understanding that was reflected in their invented algorithm.
The second group appeared to have started using the standard algorithm before they demonstrated conceptual understanding. In both the fall and the spring third-grade interviews, the invented-algorithm group outperformed the standard-algorithm group on extension problems.
However, there was no difference in the number of extension problems solved correctly by the boys and girls in the invented-algorithm group. This suggests that using invented algorithms in the early grades is related to the ability solve extension problems in the third grade, for both boys and girls.
“A Longitudinal Study of Gender Differences in Young Children’s Mathematical Thinking,” Educational Researcher, June-July 1998, pp. 6-11.
Published in ERN November 1998 Volume 11 Number 8