Teaching Mathematics Using Primary Sources: Analyzing Population Pyramids

This post was written by Peter DeCraene, the 2020-21 Albert Einstein Distinguished Educator Fellow at the Library of Congress.

Results from the 2020 decennial census are becoming available, providing an opportunity to study earlier census data and explore population trends in the United States from the late 19th century. By observing, reflecting on, and questioning graphs known as population pyramids, students can hone their graph analysis skills at the same time they study immigration patterns. The Statistical Atlas from 1890 has a number of these types of graphs.

Consider the population pyramids showing the percentages of people in the U.S. by age, gender, and ethnicity.

Population Pyramid from 1890 Census showing percentages of people in the United States by age, gender, and ethnicity.

Population pyramid from 1890 Census showing percentages of people in the United States by age, gender, and ethnicity.

Ask students to note their observations, reflections, and questions about this chart, perhaps recording their thinking on the Primary Source Analysis Tool. First, ask the students to speculate why the first shape is wider at the bottom than at the top, and prompt them to explain their reasoning using details like the title of the image and the meaning of the labels on the axes. Some may wonder what the shapes mean, and how to read the charts; encourage them to share their interpretations, perhaps in small groups or with partners.

Others might wonder why four of the graphs have long bars at the bottom and get shorter, but one graph has more of a bulge, or why two graphs appear more bottom heavy. Answers to these questions may be found in the immigration patterns from the last part of the 19th century, and may spur further research in this area, or provide numeric evidence supporting what students have already read. A similar set of graphs from 1880 provides an opportunity to compare and contrast the percentages over time.

Another set of population pyramids from the same statistical atlas shows the populations of each state, organized by gender and age.

Percentage of the aggregate population in each age group, by gender and age from 1890

Percentage of the aggregate population in each age group, by gender and age: 1890

Divide the class into small groups, assigning each group a different row from the page, to discuss what they see, think, and wonder about these charts. Ask them:

  • Do the shapes match the previous chart showing the entire U.S. population?
  • How do they differ from that graph and from each other?
  • What might account for these differences?

After the groups have explained their thinking, ask the class to identify any overall patterns.

Alternatively, provide each group with a complete set of the state charts (separated onto individual state cards) and ask the students to sort the states into two or more groups, and to write a title for each group to explain why the states were included. It may be useful to keep some states out of the initial set (the last column of the page would work well) and ask the students to decide and explain which group each of these additional states belongs to.

Comparing and contrasting population pyramids highlights the ages and genders of the population in ways that other representations might not. Students may be interested in exploring other ways to represent this data, such as pie charts or side-by-side bar charts and discuss whether or not the pyramids are the best way to represent this kind of data. Alternatively, students might find data about their own town or school they can represent in this way.

Learning to read charts and graphs is an important data literacy skill, and these examples provide real historical connections for students. Let us know what connections your students make!

3 Comments

  1. Derrick Bell
    August 10, 2021 at 1:12 pm

    As a student and Math Major and possible future educator, Thank You for this interesting post.

  2. Derrick Bell
    August 10, 2021 at 1:14 pm

    As a student and Math Major, Thank You for this interesting post.

  3. Alison Noyes, Emerging America program at the Collaborative for Educational Services
    August 12, 2021 at 3:41 pm

    I really love these examples of spurring student inquiry. I will suggest them to teachers who are teaching about immigration, or human geography, or any of a variety of topics as ways to engage, especially students who enjoy puzzles and graphics. Using primary source methods developed for math and science are often great ways to expand teaching styles to offer more options to capture student curiosity.

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