Social Education 59(1), 1995, pp. 14-16
National Council for the Social Studies

Social Math in the History Classroom

Bernard C. Hollister
In the seventies there was talk of social math. This was an attempt to wed mathematical concepts with the social studies. In particular, we were seeing significant numbers of teachers with majors or minors in sociology, psychology, economics, political science, and other social sciences entering the social studies classrooms. Since many of these teachers had some background in statistics, it seemed natural that links between math, particularly statistics, and the social studies would become stronger. Unfortunately, this did not happen to any great degree, and it certainly did not happen in the history classroom.
With the advent of computers and spreadsheets, there is now another chance to make the kind of "naturaquot; connections that must be made between the math classroom and the social studies classroom, particularly the history classroom. Over the past five years, a colleague and I have developed literally hundreds of files of data relevant to American and world history classrooms. These data include files on the male/female ratio in the United States from 1790-1990, disease patterns both nationwide and worldwide, the length of terms of members of the Cabinet, numerous data on the American presidency, winning percentages in American professional baseball from 1900 until today, and many more. I mention these only because the computer now allows us to look at raw historical data as never before. In fact, we can now begin actually to question the very generalizations and assumptions the textbook makes. For example, if we graph out the times the United States actually committed troops abroad, we find a very interesting high point in the 1920s and 1930s. This is exactly the time the textbooks tell us was the Period of American Isolationism; the data powerfully contradict this interpretation.

Perhaps of even more interest to students might be the ratio of females to males in the United States since the first census was taken in 1790. A chart can show how many females there are in the United States for every 100 males. Here we seek to ask questions of the data. For example, why does the ratio of males to females fall in 1870 and not rise to the level of 1860 until 1890? What better way to explain the tragic impact of the Civil War than the ratio of females to males in this country? Why is there such a dramatic fall in the ratio beginning with the early part of the twentieth century? Discussion here might center on the issues of medicine, sanitation and the creation of the hospital as a middle class institution. Should the United States Senate and House of Representatives represent the majority of Americans? Therefore, should the Senate and House reflect the male/female ratio of the United States?

Included here is an in-depth activity to be used as a model for using math, science, and social studies in the classroom. We will attempt to analyze the North American bison population from aboriginal times until contemporary times. Data of the kind presented can be displayed in the classroom either through a big-screen television hooked to a computer or through overhead projection. When we use data in the history classroom, there are actually three different subsets of questions being asked. One is a methodological series of questions, such as: Where did we get the data? How reliable are the data? Could I use other sources of information than statistics? What is the best way of graphing or displaying the data? What is the best way of interpreting the data?

Another set of questions is more substantive, questions about history in particular. For example, do the data support or refute the textbook interpretation of the American bison's decline? Can I make a different interpretation from the historians? How can the data both help us and hinder us in interpreting what happened "historically?"

A third set of questions deals with metacognitive questions: How can graphs and spreadsheets better help me to learn about the time period or event in question? How can they hinder my learning? How do I learn best?

For the last set of questions, it should be noted that one assumption we make in teaching history to young people is clearly wrong. This assumption is that students cannot grasp intellectually the abstractions of time such as "century," "millennium," or "ten thousand years." If these time periods are graphed and presented visually to students, I have found that not only can they grasp them but they can also ask some very intelligent questions about the data presented over these time periods.

Let's try the three subsets of questions by "interpreting" the bison data. First, let us examine Chart A: "North American Bison Population, Estimated 1885-1983."

This chart seems to show a dramatic story of environmentalism in action, namely, the North American plains bison being saved from virtual extinction. By 1895, there were fewer than 1,000 bison left in North America, according to the estimates of the Department of Interior. Methodological questions arise immediately: How does the government arrive at such figures as these? How reliable are they? Even if the figure is more like 2,000 or even 5,000, the decline of the bison from 1885 when there were approximately 20,000 is still significant. But the "bounce back" to 46,000 plus in 1983 is an even more dramatic story. Substantive questions also arise: How did the decline happen, and how and why did the increase in bison numbers happen? What, in particular, happened between 1902 and 1983 to cause the numbers to increase? Another methodological question arises here: The data points are not consistent in this chart. We have the periods 1885-1889 (four years), 1889-1895 (six years), 1895-1902 (seven years), and most significantly 1902-1983 (eighty-one years). How, and how significantly, will this "distort" the data? Can we establish different mathematical rates of decline for the bison?

If we examine Chart B, "North American Bison Population, Estimated 1865-1889," we find that there is a deliberate overlap between this chart and the previous one. These are the data to which most textbooks, either very explicitly or at least implicitly, refer when they mention the decline of the bison. In 1865, we have approximately 15,000,000 bison, and only ten years later, their numbers have fallen to fewer than 2,000,0000. The substantive issue here is what some textbooks call "The Opening of the West," or the coming of the white settlers, and more particularly their technology, to the plains area. That technology may be the railroad, the steel plow, the rifle, or barbed wire-all had a significant impact on the decline of the bison. Again, that old methodological question about the data points arises, but here there is at least only a four- or five-year gap between the data. Does this make the data methodologically less suspect?

With Chart C, "North American Bison Population, estimated 1800-1870," the data become very interesting. They perhaps begin to challenge, if only implicitly, the usual textbook accounts. We can see that in 1800 there is a projected estimate of 40,000,000 bison in North America. By 1850, their numbers have fallen precipitously in half to 20,000,000 and by 1870 by another 5,000,000 plus. No one seriously questions that there were insignificant numbers of whites in the plains area by 1800, but the bison population has already begun to plunge, if the data are "accurate." What is happening here? Can the Native Americans be responsible for this? When were the eastern Native Americans relocated to the plains area? Can we get an idea of how many whites were in the area at this time? How many Native Americans? Can we establish a ratio between the land area of the bison range and the proportion of Whites/Native Americans in the area for the various data points? What will this tell us?

Using a formula from the Excel program on my computer, I was able to quickly make a mathematical projection based on the bison population in 1800 and 1850 for the years 1900, 1950, and 2000. (Chart D, "Projected North American Bison Population Based on Figures from 1800 and 1850.") Even if the whites had not occupied the plains area as dramatically as they did, the mathematical model tells me that the bison population would have continued to decline.

The picture of the bison decline from aboriginal times until 1983 is shown graphically in Chart E, "North American Bison Population from Aboriginal Times Until the Present." Of course, a methodological question looms immediately: How do we estimate bison, or for that matter anything else in "aboriginaquot; times? It is here that mathematicians, anthropologists, demographers, population experts, and archaeologists, to mention just a few, help us.

It is here that we also must begin to raise some science questions in the social studies classroom. Is it possible that homo sapiens almost delivered the coup de grace to the bison but was not the sole or even primary cause of its dramatic decline? Is it possible that disease might play a role here? Do we see disease patterns or cycles in either the animal or human worlds that could help us construct a model here? Is it possible that abiotic forces such as climate, soil, precipitation, etc., could play a role here? Was the plains area undergoing long-range cycles that could help explain the decline of the bison?

If we look at the giant or great mammals of North America, such as the giant beaver, giant elk, or mammoth, they were all extinct by the time the settlers came into the plains area. Is it possible that extinction theories can help us better understand the decline of the bison? Is it possible that the bison were already well on their way to extinction before the whites appeared?

You will note that we have raised far more questions than we have given answers. This is one of the hallmarks of the so called new paradigm of learning/teaching: We will ask more questions and, therefore, create more problems for students than we will give answers. Furthermore, these questions will lead us on a trail across disciplines.

An effective way to begin to sensitize students in the classroom to the relevance of statistics and/or social math is to do a statistical analysis of the classroom itself. This may be done with a computer or without. The following questions are only examples:

How many of the class were born in this state? Another state?

What month were you born?

How many pets do you have? Dogs? Cats? Fish? Birds? Other?

What birth position are you in your family?

How many of you are left handed? Right handed?

The idea here is not only to compile some hard data for the class, such as birth months, but also to demonstrate to students that data are human constructs to be used and controlled by them. Furthermore, students must be able to create their own containers-categories-to store the data in. For example, if we ask about birth months, might it be better to construct "containers" or categories that allow students to decide what seasons their class was born in?

I have had students become passionately interested in how many of their classmates are right handed or left handed. How many children in your school are left or right handed? In the other schools in the community? What percentage of the people in the United States are left or right handed? What ratio can we establish between your school and the nation?

These are not trivial questions, nor are these trivial skills we seek to develop, because when students must deal with larger questions of statistics, they will be more comfortable when they see such categories as "Below the Poverty Line" or "Middle Class". They will begin to ask the important questions about not only the data but also the categories the data have been slotted in.

If our students are truly to begin to think across disciplines, we must constantly model for them that they can do this. I have used the bison model in elementary, middle, and secondary schools, as well as colleges. Students too frequently are asked to do worksheets or homework that are particular to math, science, or social science; they are used to being told, "This is math time;" "This is social studies time." We must struggle to find problems for them that "naturally" cut across the old disciplines and allow them to think statistically.

Bernard C. Hollister teaches at the Illinois Mathematics and Science Academy in Aurora, Illinois.