This post was written by Peter DeCraene, a 2021-22 Albert Einstein Distinguished Educator Fellow at the Library of Congress.

Mathematics is, I believe, a creative, human endeavor at its heart. Human beings have invented a variety of ways to represent quantities and describe the geometry of the cosmos. We’ve also used visual art and poetry to try to capture the essence of mathematics. Mathematics instruction that focuses on procedures and rote memorization, which has been a trend since the publication of early 19^th century arithmetic books, does not often expose students to these human and creative aspects of mathematics.

Each of these sources provides a different view of the purpose and nature of mathematics and can broaden students’ perspectives about the subject. Organize students into groups and ask each group to analyze one of the items using the Observe-Reflect-Question protocol, pointing out that they all show some aspect of mathematics.

Balanced account, Cuneiform tablet no. 32	Sphaera mundi, 1488.
Mathematics	Poetry 180

Encourage students to use the Primary Source Analysis Tool to record their initial discussions. The discussion may reveal a variety of student conceptions and teachers can spark additional discussion by asking some focus questions:

• What details in these items were most interesting or surprising?
• How did the creators of these items view mathematics? Why do you think that?
• When was the item created, and how might that time period have influenced its creator?
• What does the item tell you about mathematics?

Ask each group to share some of their thinking with the whole class. Encourage students to support their ideas with references to the items or the item record. Once each group has presented, ask some more general questions about the history and purpose of math, as well as students’ views about learning the subject:

• How did humans decide which symbols to use to represent numbers?
• In what ways has mathematics changed over the course of history? Why have those changes occurred?
• What are the best ways to learn mathematics?
• And what really constitutes the subject of mathematics, anyway?

These are all huge questions that math educators and researchers continue to grapple with. It is important to acknowledge the breadth and depth of mathematics beyond what students typically see in their textbooks. Different students connect (or disconnect) with math in different ways and for different reasons and asking students to observe, reflect, and question topics provides more opportunities to engage all students at multiple levels, and to demonstrate the rich history and humanness of mathematics.