Elizabeth Fennema

Gender differences in mathematics performance: a meta-analysis.

Reviewers have consistently concluded that males perform better on mathematics tests than females do. To make a refined assessment of the magnitude of gender differences in mathematics performance, we performed a meta-analysis of 100 studies. They yielded 254 independent effect sizes, representing the testing of 3,175,188 Ss. Averaged over all effect sizes based on samples of the general population, d was -0.05, indicating that females outperformed males by only a negligible amount. For computation, d was -0.14 (the negative value indicating superior performance by females). For understanding of mathematical concepts, d was -0.03; for complex problem solving, d was 0.08. An examination of age trends indicated that girls showed a slight superiority in computation in elementary school and middle school. There were no gender differences in problem solving in elementary or middle school; differences favoring men emerged in high school (d = 0.29) and in college (d = 0.32). Gender differences were smallest and actually favored females in samples of the general population, grew larger with increasingly selective samples, and were largest for highly selected samples and samples of highly precocious persons. The magnitude of the gender difference has declined over the years; for studies published in 1973 or earlier d was 0.31, whereas it was 0.14 for studies published in 1974 or later. We conclude that gender differences in mathematics performance are small. Nonetheless, the lower performance of women in problem solving that is evident in high school requires attention.

Sex-Related Differences in Mathematics Achievement, Spatial Visualization and Affective Factors

This study investigated (a) mathematics achievement (Test of Academic Progress) of 589 female and 644 male, predominantly white, 9th-12th grade students enrolled in mathematics courses from four schools, controlling for mathematics background and general ability (Quick Word Test); (b) relationships to mathematics achievement, and to sex-related differences in mathematics achievement, of spatial visualization (Differential Aptitude Test), eight attitudes measured by the Fennema-Sherman Mathematics Attitudes Scales, a measure of Mathematics Activities outside of school, and number of Mathematics Related Courses and Space Related Courses taken. Complex results were obtained. Few sex-related cognitive differences but many attitudinal differences were found. Analyses of variance, covariance, correlation, and principal components analysis techniques were used. The results showed important relationships between socio-cultural factors and sex-related cognitive differences.

Using Knowledge of Children’s Mathematics Thinking in Classroom Teaching: An Experimental Study

This study investigated teachers’ use of knowledge from research on children’s mathematical thinking and how their students’ achievement is influenced as a result. Twenty first grade teachers, assigned randomly to an experimental treatment, participated in a month-long workshop in which they studied a research-based analysis of children’s development of problem-solving skills in addition and subtraction. Other first grade teachers (n = 20) were assigned randomly to a control group. Although instructional practices were not prescribed, experimental teachers taught problem solving significantly more and number facts significantly less than did control teachers. Experimental teachers encouraged students to use a variety of problem-solving strategies, and they listened to processes their students used significantly more than did control teachers. Experimental teachers knew more about individual students’ problem-solving processes, and they believed that instruction should build on students’ existing knowledge more than did control teachers. Students in experimental classes exceeded students in control classes in number fact knowledge, problem solving, reported understanding, and reported confidence in their problem-solving abilities.

Problem Solving as a Basis for Reform in Curriculum and Instruction: The Case of Mathematics

We argue that reform in curriculum and instruction should be based on allowing students to problematize the subject. Rather than mastering skills and applying them, students should be engaged in resolving problems. In mathematics, this principle fits under the umbrella of problem solving, but our interpretation is different from many problem-solving approaches. We first note that the history of problem solving in the curriculum has been infused with a distinction between acquiring knowledge and applying it. We then propose our alternative principle by building on John Dewey’s idea of “reflective inquiry,” argue that such an approach would facilitate students’ understanding, and compare our proposal with other views on the role of problem solving in the curriculum. We close by considering several common dichotomies that take on a different meaning from this perspective

Sex-Related Differences in Mathematics Achievement and Related Factors: A Further Study.

In the past, many researchers have concluded that male superiority in mathematics achievement is almost always found (Glennon & Callahan, 1968); but many are currently suggesting that sex-related differences in mathematics achievement are not as prevalent as had been believed and that they are age related (Callahan & Glennon, 1975; Fennema, 1974, 1977; Hilton & Bergltind, 1974; Maccoby & Jacklin, 1974; Suydam & Weaver, 1975). Although the National Longitudinal Study of Mathematical Abilities (NLSMA) and the National Assessment of Educational Progress (NAEP) do report sex-related differences in favor of males (Wilson, 1972; Mullis, Note 1), inspection of their data indicates that these differences increase as learners progress from grade 6 to grade 12. Fennema and Sherman (1977) reported that when the number of years of studying mathematics was controlled, sex-related differences were found in only half the high schools studied.

Gender Comparisons of Mathematics Attitudes and Affect: A Meta-Analysis:

This article reports the complex results of meta-analyses of gender differences in attitudes and affect specific to mathematics. Overall, effect sizes were small and were similar in size to gender differences in mathematics performance. When differences exist, the pattern is for females to hold more negative attitudes. Gender differences in self-confidence and general mathematics attitudes are larger among high school and college students than among younger students. Effect sizes for mathematics anxiety differ depending upon the sample (highly selected or general). One exception to the general pattern is in stereotyping mathematics as a male domain, where males hold much more stereotyped attitudes (d = -.90). While affect and attitudes toward mathematics are not the only influences on the development of gender differences in mathematics performance, they are important, and both male and female affect and attitudes should be considered in conjunction with other social and political influences as explanations.

Capturing Teachers’ Generative Change: A Follow-Up Study of Professional Development in Mathematics

This study documents how teachers who participated in a professional development program on understanding the development of students’ mathematical thinking continued to implement the principles of the program 4 years after it ended. Twenty-two teachers participated in follow-up interviews and classroom observations. All 22 teachers maintained some use of children’s thinking and 10 teachers continued learning in noticeable ways. The 10 teachers engaged in generative growth (a) viewed children’s thinking as central, (b)possessed detailed knowledge about children’s thinking, (c) discussed frameworks for characterizing the development of children’s mathematical thinking, (d) perceived themselves as creating and elaborating their own knowledge about children’s thinking, and (e) sought colleagues who also possessed knowledge about children’s thinking for support. The follow-up revealed insights about generative growth, sustainability of changed practice and professional development.

Effective Teaching, Student Engagement in Classroom Activities, and Sex-Related Differences in Learning Mathematics

This research identified the classroom activities that were related to the low level and high level mathematics achievement of boys and girls. In December and in May, students in 36 fourth grade mathematics classes completed a mathematics test containing low level and high level items from the National Assessment of Educational Progress. During January through April, the engagement/nonengagement in mathematics activities was observed for six randomly selected students of each sex in each class. Results showed that girls and boys did not differ significantly in either mathematics achievement or in observed engagement/nonengagement in mathematics activities. However, engagement in the following four types of activities was consistently and differentially related to girls’ versus boys’ low level and high level mathematics achievement: competitive mathematics activities, cooperative mathematics activities, social activities, and off-task behavior.

A Longitudinal Study of Invention and Understanding in Children's Multidigit Addition and Subtraction.

This 3-year longitudinal study investigated the development of 82 childrens understanding of multidigit number concepts and operations in Grades 1-3. Students were individually interviewed 5 times on a variety of tasks involving base-ten number concepts and addition and subtraction problems. The study provides an existence proof that children can invent strategies for adding and subtracting and illustrates both what that invention affords and the role that different concepts may play in that invention. About 90% of the students used invented strategies. Students who used invented strategies before they learned standard algorithms demonstrated better knowledge of base-ten number concepts and were more successful in extending their knowledge to new situations than were students who initially learned standard algorithms. An understanding of most fundamental mathematics concepts and skills develops over an extended period of time. Although cross-sectional studies can provide snapshots of the development of these concepts at particular points in time, longitudinal studies provide a more complete perspective; however, relatively few studies have traced the development of fundamental mathematics concepts in children over more than a single year. In this paper we report the results of a 3-year longitudinal study of the growth of childrens understanding of addition and subtraction involving multidigit numbers. We focus particularly on childrens construction of invented strategies for adding and subtracting multidigit numbers. The overarching goal of the study was to investigate the role that invented strategies may play in developing an understanding of multidigit addition and subtraction concepts and procedures. We trace the development and use of invented addition and subtraction strategies and examine the relation of these strategies to the development of fundamental knowledge of base-ten number concepts and the use of standard addition and subtraction algorithms. Finally, we consider what the use of invented strategies affords by way of avoiding systematic errors and extending knowledge of basic multidigit operations to new problem situations.

Children's Conceptual Structures for Multidigit Numbers and Methods of Multidigit Addition and Subtraction.

Researchers from 4 projects with a problem-solving approach to teaching and learning multidigit number concepts and operations describe (a) a common framework of conceptual structures children construct for multidigit numbers and (b) categories of methods children devise for multidigit addition and subtraction. For each of the quantitative conceptual structures for 2-digit numbers, a somewhat different triad of relations is established between the number words, written 2digit marks, and quantities. The conceptions are unitary, decade and ones, sequence-tens and ones, separate-tens and ones, and integrated sequence-separate conceptions. Conceptual supports used within each of the 4 projects are described and linked to multidigit addition and subtraction methods used by project children. Typical errors that may arise with each method are identified. We identify as crucial across all projects sustained opportunities for children to (a) construct triad conceptual structures that relate ten-structured quantities to number words and written 2-digit numerals and (b) use these triads in solving multidigit addition and subtraction situations.