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November 1999, Volume 30, Issue 5


Students' Probabilistic Thinking in Instruction
Graham A. Jones, Cynthia W. Langrall, Carol A. Thornton, A. Timothy Mogill
In this study we evaluated the thinking of 3rd-grade students in relation to an instructional program in probability. The instructional program was informed by a   research-based framework that included a description of students' probabilistic thinking. Both an early- and a delayed-instruction group participated in the program. Qualitative evidence from 4 target students revealed that overcoming a misconception in sample space, applying both part-part and part-whole reasoning, and using invented language to describe probabilities were key patterns in producing growth in probabilistic thinking. Moreover, 51% of the students exhibited the latter 2 learning patterns by the end of instruction, and both groups displayed significant growth in probabilistic thinking following the intervention.

A Meta-Analysis of the Relationship Between Anxiety Toward Mathematics and Achievement in Mathematics
Xin Ma
In this meta-analysis I examined 26 studies on the relationship between anxiety toward mathematics and achievement in mathematics among elementary and   secondary students. The common population correlation for the relationship is significant (–.27). A series of general linear models indicated that the relationship is consistent across gender groups, grade-level groups, ethnic groups, instruments measuring anxiety, and years of publication. The relationship, however, differs significantly among instruments measuring achievement as well as among types of publication. Researchers using standardized achievement tests tend to report a relationship of significantly smaller magnitude than researchers using mathematics teachers' grades and researcher-made achievement tests. Published studies tend to indicate a significantly smaller magnitude of the relationship than unpublished studies. There are no significant interaction effects among key variables such as gender, grade, and ethnicity.

Cross-National Comparison of Representative Competence
Mary E. Brenner, Sally Herman, Hsiu - Zu Ho, Jules M. Zimmer
Flexible use of multiple representations has been described as a key component of competent mathematical thinking and problem solving. In this study, 6th-grade American students are compared to 3 samples of Asian (Chinese, Japanese, and Taiwanese) 6th graders to determine if the well-documented mathematical achievement of students from these Asian nations may be due in part to a greater understanding of mathematical representations. The results show that, among all groups, Chinese students generally scored highest on the representation tasks and, except on items about the visual representations of   fractions, all Asian samples scored significantly higher than the American sample. The results are discussed in terms of possible instructional antecedents and textbook differences.

The Meaning of Randomness for Secondary School Students
Carmen Batanero, Luis Serrano
In the experimental study reported here we intended to examine possible differences in secondary students' conceptions about randomness before and after instruction in probability, which occurs for the Spanish students between the ages of 14 and 17. To achieve this aim, we gave 277 secondary students a written questionnaire with some items taken from Green (1989, 1991). With our results we extend Green's previous research to 17-year-old students and complement his results with the analysis of students' arguments to support randomness in bidimensional distributions. Our results also indicate that students' subjective understanding of randomness is close to some interpretations of randomness throughout history.  

Revitalizing and Refocusing Our Efforts
Glenda Lappan
We are currently standing at one of the most important crossroads we have faced as a Council and as a profession in the past 20 years. We have more than a decade of direction setting and progress under our belt. And we have learned a lot. We have every right to celebrate our successes even as we look to the future and the continuing need for improvement.