Current reforms in mathematics education place increasing emphasis on statistics and data analysis in the school curriculum. The statistics education community has pushed for school instruction in statistics to go beyond measures of center, and to emphasize variation in data. Little is known about the way that teachers "see variation". The study reported here was conducted with 22 prospective secondary math and science teachers enrolled in a preservice teacher education course at a large university in the U.S. which emphasized assessment, equity, inquiry, and analysis of testing data. Interviews conducted at the beginning and end of the course asked the teachers to make comparisons of data distributions in a context that many U.S. teachers are increasingly faced with: results from their students' performance on high-stakes state exams. The results of these interviews revealed that although the prospective teachers in the study did not rely on traditional statistical terminology and measures as much as anticipated, the words they did use illustrate that through more informal descriptions of distributions, they were able to express rich views of variation and distribution. This paper details these descriptions, categorizing them into three major areas: traditional notions, clumps & chunks (distribution subsets), and notions of spread. The benefits of informal language in statistics is outlined.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education