4 minute read
Math Past
Yoruba Counting Words
Where do number words come from? Do other people use different words to represent numbers? What do other people’s number words mean?
Write the word nineteen and ask students why they think we use that word to mean 1 ten and 9 ones. It may help to add space between nine and teen, or to underline the two parts of the word as you read it. Students should point out that the word nine is in nineteen. Some may notice that teen kind of looks and sounds like ten.
In the first four modules, students learned how different people have represented and written numbers throughout history. The ways we write numbers can affect our number sense and the kinds of calculations we can perform. For example, adding and subtracting with Roman numerals is notoriously difficult!
The words we use for numbers are also connected to our number sense. The connection between words and number sense is deep. We learn the words for numbers before we learn to write them, and words for numbers developed earlier in human history than written numerals, since spoken language developed first.
Tell the class you met someone who says that where they grew up, they say “5 before 20” to describe a number. Ask students what number they think this person is describing. A number path can be used to help students answer this question. Tell the class that this is how the Yoruba people of western Africa describe the number 15. The Yoruba people form a large ethnic group, and the Yoruba language is the native language of between 30 and 40 million people! In addition to having deep mathematical traditions dating back centuries, they are also famous for their music, which features advanced drumming techniques.
Unlike our decimal or base-10 system, the Yoruba number system is a vigesimal, or base-20 system. Many people in different regions of western Africa use base-20 systems, and they are used in the Americas too. For example, the Maya system, which we saw in modules 3 and 4, is also a base-20 system. The different and interesting aspect of the Yoruba system is its reliance on subtraction.
Remind students how we use tens to make our numbers, making as many groups of 10 as we can, and then saying how many ones are left. Ask students why they think we use 10 this way. Hint: What do most people have 10 of that you can use to count? Fingers!
When counting from 10 to 20 in Yoruba, the number words start out with a similar meaning to ours. They also describe 10 and some ones, which can be roughly translated as follows.
11 12 13 14
1 past 10 2 past 10 3 past 10 4 past 10
Then, at 15, the numbers start to be described differently.
15 16 17 18 19
5 before 20 4 before 20 3 before 20 2 before 20 1 before 20
Ask students if they can think of a reason the Yoruba people use 20 this way. Hint: Just like most people have 10 fingers, most people also have 10 toes. Put them together and that’s 20.
Things get more complex as you move past 20. For example, the word for 35 translates roughly to five before two twenties, and the word for 45 is described as five from ten from three twenties or three twenties minus ten minus five. This goes beyond first grade learning but could be a good challenge for advanced students with the aid of the 1–120 number path.
Remember, between 30 and 40 million people describe their numbers this way! Children who grow up learning to count this way can use these numbers fluidly. They learn the numbers through hands-on activities that use objects like pebbles or beans, and through traditional games like Ayo, or Oware, a version of Mancala seen here.
How did the Yoruba people come to count this way? One theory is that this number pattern was developed so that if the multiple of 10 is understood, you can count on one hand. For example, knowing that you’re counting from 20 to 30, you can put up fingers one at a time to count 21, 22, 23, and 24. When you put the fifth finger up, the understanding is that now you mean 5 before 30, or 25. To get from 25 to 30, you put fingers down one at a time, counting 4 before 30 (26), 3 before 30 (27), 2 before 30 (28), 1 before 30 (29), and finally when all fingers are down, you have reached 30.
Use one hand to count from 20 to 30 the Yoruba way as a class.
Ways of describing numbers that differ from our own can seem counterintuitive at first. In a sense, to understand the Yoruba number words, you need to understand the basics of addition and subtraction. However, each of the words tells you what it means.
Consider the English number words twelve and fifty. Neither of these words is descriptive of the number it represents. Fifty derives from the Old English words for five (fif) and group of ten (tig). Similarly, twelve comes from the Old English word twelf, which means two left, as in two left after 10. Since we no longer speak Old English, these descriptions are lost on us and on our students!
In fact, research shows that this lack of descriptiveness hinders young learners’ number sense. In many other languages, number words are more descriptive. For example, in Mandarin Chinese, thirteen is said “ten-three.” Understanding the limits of our point of view and incorporating other cultures’ perspectives into our thinking can only make us stronger as we work with math!
