A Diverse Detail of Mathematics An Artifact for Standard #1
Although mathematics is seldom a subjective study, its logic and judgments can be founded upon unnecessary stereotypes to begin with. For instance in our study of statistics in Algebra I, students recognized the danger of biased surveys and convenience sampling. Furthermore, in statistics, it is of prime importance to both the surveyor and those surveyed that the least amount of bias is available for either party's gain. Documented here below are some artifacts that show how some stereotypes are broken down by the logical rationale of mathematics. A conclusive reflection is provided at the end.
On March 3rd, 2009, the U.S. Census Bureau released two separate Facts for Features articles: one for Asian/Pacific American Heritage Month, and another for Older Americans Month. Both specifically focused on those core groups of Americans, but also expanded their comparative statistics to the rest of the nation. For example, the above screenshot shows how “this group [Asians] comprised about 5 percent of the total population”. Additionally, the idea of this statistic being drawn from a sample is reinforced by the vocabulary choice—“about” and “population estimates” are strong signs that although the data is approximately right, it is not perfect and definitely not a simple random sample. Note that this statistic was also taken from 2007—a non-census year.
From the same website, the breaking news from January 2008 about more young women having Bachelor's degrees more than young men demolishes some huge stereotypes in society— largely the traditional view where daughters were brought up to study home economics. Moreover, this recent data also shows that naturalized citizens are more likely to have a college degree than Americans-by-birth. At the last bullet point, Asians are shown to be the highest earning members of society, although they are the second smallest minority group. Conclusive Reflection Both of these files, released by the Census Bureau, play an important part of the Algebra I or Statistics classroom not only because of their mathematical quality, but also because of their construction to our social perspectives. Given this pre-prepared resource, we should affirm Johann Pestalozzi's vision of how to let children deduce their own conclusions from objective evidence: “Children should learn through activity and through things. They should be free to pursue their own interests and draw their own conclusions.” Perhaps the narratives from the U.S. Census Bureau that accompany the statistics throw off the latter part of that vision, but Pestalozzi's views can still be fulfilled if we simply look at the numbers and answer mathematical questions with mathematical answers. Johann Pestalozzi was also a proponent of educating the whole child—heart, hand, and head. By exposing children to this raw information, they are able to make it meaningful to their hearts, experience it hands-on, and cognitively process a rational conclusion from these statistics, not from stereotypes.