ICOTS-7, 2006: Kranendonk 1 A QUANTITATIVE STUDY OF COUNTRIES USING POPULATION DATA AND PYRAMID GRAPHS
Henry Kranendonk
unpublished
While an equation can be solved manually or by the click of a button in multiple ways, the information this equation communicates should also be a reason why students study it. Although the "how to's" are important, they must be balanced with "why?" and "for what purpose?" The latter questions are essentially more meaningful, more interesting, and more engaging for many students. It is critical that students learn how to communicate their thinking to others. The project outlined in this paper
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... s specifically designed for middle and high school students to improve their skills in posing quantitative questions and in articulating "why?" and "for what purpose?" these questions are asked. INTRODUCTION Students in the 8 th and 9 th grades from Milwaukee, Wisconsin were involved in a project entitled "People Count!" The first part of this project began with unpacking data displayed in population pyramid graphs that, at first glance, were simply viewed as "odd graphs" by students. Although pyramid graphs are used in biology, geography, and economics to study various conditions of countries, this project connected the shapes of pyramid graphs to basic numeric summaries that generated an understanding of population data. The first lesson asked students to examine data displayed in a simplified population pyramid graph (see Figure 1). This type of graph displays a side-by-side histogram of the count of people by specific age categories and gender. Figure 1 summarizes a group of people attending an event. Students' conjectures identifying the event became more focused as they read or calculated the number and percent of females and males, the number and percent of various age categories, the number and percent of teenagers, and the mean and median ages of females and males. Throughout this lesson, students were connecting the population data to several calculated number summaries and the "shape" of the pyramid graph. Initially students developed verbal explanations of the connections they observed. Their explanations were later incorporated as written summaries for questions presented in the project activities.
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