Data Modeling supports the growth of statistical reasoning by engaging middle school students in the construction of data, the invention of statistics, and the development of models of chance, all of which ground inference about data. Construct maps portray conceptual stepping-stones in statistical reasoning, organized by forms of reasoning, such as Conceptions of Statistics and Modeling Variability. Seven curriculum units are tools to support learning. Each unit features classroom activities, formative assessments, and related resources, including teacher-designed extensions to the curriculum units.
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Data modeling is an approach to learning and teaching statistics that engages students in ways of thinking about variability that approximate how professionals in the discipline of statistics think about variability. Traditionally, data and statistics have been taught apart from chance and probability. Data Modeling integrates these two strands, so that learning about data and statistics helps students think about chance, and learning about chance helps a student interpret statistics and data. The two strands come together as students invent and revise models that explain variability in data that they have generated. Like professionals in data analysis, students invent and adapt representations, measures and models of variable data. The Data Modeling curriculum is a story. It is the combined account of the unique histories of students and their teachers from many districts engaging with fundamental ideas of statistics and probability over a series of designed events that build on student understanding. The story is based on these essential themes:
- Data Modeling creates opportunities for students to construct data by engaging in simple processes that generate variability, such as repeated measurement of the same attribute or production of a product. By participating in these processes, students link process to variability.
- Students invent visual displays, measures and models of the data generated by these variability-producing processes.
- During small-group and whole-class conversations, student inventions are compared and contrasted with an eye toward the mathematical ideas that guided their creation.
- Conventions, such as forms of display used to visualize data or statistics used to measure characteristics of a distribution, are solutions to problems of visualizing, summarizing, and modeling the variability inherent in chance processes. Student inventions help make the rationale for these mathematical conventions more accessible and visible. Conventions typically solve problems that students encounter as they invent.
- As students progress in the curricular sequence, initial understandings of visualization, measures and models of data are extended and elaborated to explain new contexts of variability. Once initially learned, core concepts are re-used and re-contextualized, never abandoned.
- Construct maps describe typical progressions of student thinking about core concepts of visualization, statistics, chance, and modeling. These constructs provide the foundations for formative (during instruction) and summative (after instruction) assessments,so that assessments are geared toward inferring states of student knowledge from student responses, rather than simply focusing on "right" or "wrong."
- Teachers use student responses to formative assessments to plan and conduct formative assessment learning conversations. During these whole-group conversations, selected student responses are compared and contrasted to emphasize mathematical ways of thinking,so that all students have opportunities to revise and refine their thinking.
These themes underlie the type and order of investigations students encounter during 7-8 weeks of instruction. The investigations are organized into units that position students to participate in ways of acting and thinking that are characteristic of how statisticians act and think. A snapshot of each of the units provides a brief introduction to the curriculum, but if we refer to unfamiliar concepts in these snapshots, don’t worry. We developed Data Modeling in partnership with teachers, and teachers now lead our professional development. They will be available to help you learn about these ideas and to help you develop them with your students. Each unit contains a section, entitled Mathematical Background, which highlights the mathematical concepts and procedures that are the focus of that unit. Other supporting materials, including classroom video illuminations of the expected evolution of student thinking described by each construct map and teacher-developed supplements to the units, are found on this site.