Mathematic

# Educating sources: How historical cultures formed arithmetic | NOVA

Discover ways to apply these classroom-ready sources in a webinar hosted by NOVA Training and GBH Training on December 7, 2022 at 7pm (ET). Register for the Zoom webinar right here.

In NOVA’s new documentary Zero to Infinity, mathematician Talithia Williams takes viewers on a worldwide journey to find how the ideas of zero and infinity revolutionized arithmetic throughout completely different cultures over hundreds of years. Now, the Zero to Infinity assortment on PBS LearningMedia options excerpts from the movie contextualized with background readings, instructing suggestions, and dialogue questions to assist college students perceive the historical past of those elementary ideas. For instance, lots of the numeral techniques utilized by historical cultures didn’t embrace the quantity zero. The earliest documented use of zero is believed to be in a manuscript from India dated to as early because the third or fourth century.

College students even have the possibility to be taught concerning the work of Persian mathematician Muhammad ibn Mūsā al-Khwārizmī, who carried out his analysis out of the “Home of Knowledge” (a.ok.a. the Grand Library of Baghdad) greater than a thousand years in the past. In a ebook on arithmetic al-Khwārizmī wrote in about 825 CE, he explains the Hindu–Arabic numbers and easy methods to carry out addition, subtraction, multiplication, division, doubling, and halving in addition to easy methods to calculate with fractions.

A great factor in [math] schooling could be to chop down the content material a bit and savor these concepts.

“A great factor in [math] schooling could be to chop down the content material a bit and savor these concepts,” mathematician Manjul Bhargava mentioned throughout a Zero to Infinity live-streamed panel on the NOVA YouTube channel. “We simply had a complete hour present on zero and infinity speaking about the fantastic thing about it. We by no means get to try this at school, and we must always actually recognize these ideas.”

Eugenia Cheng, one other mathematician featured within the movie, needs lecturers had the possibility to be extra expansive with math curriculum, and deal with the marvel of math, versus instructing content material optimized for standardized check rating efficiency.

“A lot of the math we’re going to be taught at school we aren’t going to immediately use,” Cheng mentioned in the course of the panel dialogue. “It’s necessary that we be taught to make use of our mind in a rigorous, systematic, and environment friendly method that permits us to soak up completely different factors of view and make connections between issues.”

Whether or not college students are interested by the place at the moment’s quantity system and fundamental math capabilities got here from, or need to resolve real-world issues to raised perceive quantity and amount, geometry, algebra, or statistics ideas, this assortment of math sources from NOVA can assist bolster studying for grades 6-8!

### Hindu-Arabic Numerals and Algebra | Zero to Infinity (Grades: 9-12)

Be taught the place at the moment’s broadly used quantity system and fundamental math capabilities got here from, and the way the decimal system was developed. The set of ten numerals—0, 1, 2, 3, 4, 5, 6, 7, 8, 9—that you’ve used all of your life make up the Hindu-Arabic system, also called the decimal system or base-ten system. It’s a place worth (or “positional”) system, which means that the worth of a numeral is determined by its place. The values improve by powers of ten. For instance, within the quantity 3,286, “6” is within the ones place whereas “3” is within the hundreds place; the worth of every numeral is its worth multiplied by the worth of the place—the “3” within the quantity represents 3,000.

### The Historical past of Zero | Zero to Infinity (Grades: 6-8)

Though it’s simple to take the idea of zero with no consideration, this digit representing “none” really needed to be invented. Study when and the place the zero we use at the moment originated.

### Calculating the Space of a Circle Utilizing Pizza Slices | Zero to Infinity (Grades: 6-12)

Discovering the realm of a circle is simple with a easy system involving pi. However how might folks have accomplished it earlier than they knew about pi? Find out how the idea of infinity can assist convert a round pizza right into a rectangle, making it a lot simpler to measure. Use this useful resource to assist college students motive abstractly and assemble an argument concerning the system for the realm of a circle.

### Zeno’s Paradoxes and Limits in Calculus | Zero to Infinity (Grades: 9-12)

Within the fifth century BCE, the Greek thinker Zeno of Elea thought deeply about time and movement. Zeno is most well-known for describing a number of paradoxes the place if one assumes house and time are infinitely divisible, then it follows that movement is an phantasm. Greater than a thousand years after Zeno’s dying, a brand new department of arithmetic referred to as calculus helped make sense of his paradoxes. Use this useful resource to offer alternatives for college students to calculate how briskly an object is transferring at a specific prompt utilizing limits in calculus.

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