Teaching resources: How ancient cultures shaped mathematics
From the ancient origins of zero to the paradox of motion, NOVA’s teaching resources immerse students in the wonder of math.
The numeral system of 0 through 9 known as the Hindu–Arabic system, recognizes both the Hindu origin of the numerals and the role of Arab mathematicians in the Middle East who introduced it to Europe. Image Credit: NOVA/GBH
In NOVA’s new documentary Zero to Infinity, mathematician Talithia Williams takes viewers on a global journey to discover how the concepts of zero and infinity revolutionized mathematics across different cultures over thousands of years. Now, the Zero to Infinity collection on PBS LearningMedia features excerpts from the film contextualized with background readings, teaching tips, and discussion questions to help students understand the history of these fundamental concepts. For example, many of the numeral systems used by ancient cultures did not include the number zero. The earliest documented use of zero is believed to be in a manuscript from India dated to as early as the third or fourth century.
Students also have the chance to learn about the work of Persian mathematician Muhammad ibn Mūsā al-Khwārizmī, who conducted his research out of the “House of Wisdom” (a.k.a. the Grand Library of Baghdad) more than a thousand years ago. In a book on arithmetic al-Khwārizmī wrote in about 825 CE, he explains the Hindu–Arabic numbers and how to perform addition, subtraction, multiplication, division, doubling, and halving as well as how to calculate with fractions.
A good thing in [math] education would be to cut down the content a bit and savor these ideas.
“A good thing in [math] education would be to cut down the content a bit and savor these ideas,” mathematician Manjul Bhargava said during a Zero to Infinity live-streamed panel on the NOVA YouTube channel. “We just had a whole hour show on zero and infinity talking about the beauty of it. We never get to do that in school, and we should really appreciate these concepts.”
Eugenia Cheng, another mathematician featured in the film, wishes teachers had the chance to be more expansive with math curriculum, and focus on the wonder of math, as opposed to teaching content optimized for standardized test score performance.
“Most of the math we are going to learn in school we are not going to directly use,” Cheng said during the panel discussion. “It’s important that we learn to use our brain in a rigorous, systematic, and efficient way that enables us to take in different points of view and make connections between things.”
Mathematicians Talithia Williams, Manjul Bhargava, and Eugenia Cheng answer questions about the concepts of zero and infinity during a live conversation on Youtube following the premiere of NOVA's latest documentary, Zero to Infinity.
Whether students are curious about where today’s number system and basic math functions came from, or want to solve real-world problems to better understand number and quantity, geometry, algebra, or statistics concepts, this collection of math resources from NOVA can help bolster learning for grades 6-8!
Hindu-Arabic Numerals and Algebra | Zero to Infinity (Grades: 9-12)
Learn where today’s widely used number system and basic math functions came from, and how the decimal system was developed. The set of ten numerals—0, 1, 2, 3, 4, 5, 6, 7, 8, 9—that you have used all your life make up the Hindu-Arabic system, also known as the decimal system or base-ten system. It is a place value (or “positional”) system, meaning that the value of a numeral depends on its position. The values increase by powers of ten. For example, in the number 3,286, “6” is in the ones place while “3” is in the thousands place; the value of each numeral is its value multiplied by the value of the place—the “3” in the number represents 3,000.
The History of Zero | Zero to Infinity (Grades: 6-8)
Although it’s easy to take the concept of zero for granted, this digit representing “none” actually had to be invented. Learn about when and where the zero we use today originated.
Calculating the Area of a Circle Using Pizza Slices | Zero to Infinity (Grades: 6-12)
Finding the area of a circle is easy with a simple formula involving pi. But how could people have done it before they knew about pi? Learn how the concept of infinity can help convert a circular pizza into a rectangle, making it much easier to measure. Use this resource to help students reason abstractly and construct an argument about the formula for the area of a circle.
Zeno’s Paradoxes and Limits in Calculus | Zero to Infinity (Grades: 9-12)
In the fifth century BCE, the Greek philosopher Zeno of Elea thought deeply about time and motion. Zeno is most famous for describing several paradoxes where if one assumes space and time are infinitely divisible, then it follows that motion is an illusion. More than a thousand years after Zeno’s death, a new branch of mathematics called calculus helped make sense of his paradoxes. Use this resource to provide opportunities for students to calculate how fast an object is moving at a particular instant using limits in calculus.