There are several ways to solve this problem. Boys tend to solve problems like this using invented strategies; girls tend to use concrete strategies. What does this mean?

This question comes from a study of the mathematics problem solving strategies of students in grades 1-3.¹ Students in this study were in classrooms where they were given an opportunity to invent ways to solve problems through a variety of strategies. The study revealed gender differences in strategy use: girls tended to use modeling or counting strategies (i.e. concrete solution strategies), while boys tended to use more abstract strategies such as invented algorithms or derived facts. This occurred despite the fact that boys and girls were equally successful at using invented strategies. Individuals who did choose to use invented algorithms were more successful on extension problems (complex multi-step mental calculations) than those who utilized more traditional methods. The researchers concluded that the use of invented algorithms in the early grades provided a foundation for solving extension problems in the third grade.

A study of first-grade mathematics strategy use by Martha Carr and Donna Jessup found similar results: "Girls were more likely to count on fingers or use counters (overt strategies); boys were more likely to use retrieval (from memory) to solve addition and subtraction problems."² This effect increased over the course of the school year (the period of this study). During groupwork, all children were more likely to solve problems using retrieval, indicating a dominance of male strategy preferences. Despite their differences in strategy use, both girls and boys were equally successful at solving mathematics problems.

Why are these gender differences important?

In both research studies the use of invented algorithms and complex mental calculations produced better solutions to complicated problems. This facility with invented problem solving strategies can be a precusor to successfully solving the multi-step, complex problems that are the basis of high school and college mathematics and the job world. These skills may be utilized in fields such as engineering, computer programming, and physics, and can act as gate keepers to individuals interested in those fields.

Here are a few ways to address this disparity:

• Look in your own classroom to see if these differences exist. Do girls tend to stick with more basic strategies while boys tend to try new or more complex approaches?

• Stretch students' thinking by asking them to show multiple ways to solve a problem.

• Pair students who tend to use invented strategies with those who have a narrower repertoire of approaches. Have each student explain his or her method for solving the problem so that each student can build on the other's thinking.

• Encourage girls to be confident using multiple strategies. One theory behind the differences in problem solving strategies posits that girls are taught to "play it safe" and not take risks, whereas boys are encouraged to step outside of the rules. This reliance on what's safe could lock girls into using mostly counting or teacher-taught standard algorithms instead of challenging themselves with alternative strategies. Activities involving estimation, hypothesizing, and multiple ways to solve a problem all support risk taking. By showing girls (and all students) that it's OK to take chances, make mistakes, and succeed in math, teachers can promote students' confidence and risk taking.
  
  
  
  
  
  
  ¹Fennema, Elizabeth, Thomas Carpenter, Victoria Jacobs, Megan Franke, and Linda Levi. (1998). "A Longitudinal Study of Gender Differences in Young Children's Mathematical Thinking." Educational Researcher, Vol. 27 (No. 5), 6-11.

  ²Carr, Martha and Donna Jessup. (1997). "Gender Difference in First-Grade Mathematics Strategy Use: Social and Metacognitive Influences." Journal of Educational Psychology, Vol. 89 (No. 2), 318-328.

  
  
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