THE PROBLEM WITH NUMBERS: WORD FREQUENCY

-What surprises for you about the word-frequency of the number words on the list below?

-What do you notice about the frequency of these numbers and number-related words?

-What activities do you do to help your students acquire and retain number vocabulary?

A Frequency Dictionary of Spanish, by Mark Davies (also available in all other major languages) can be the language teacher’s best friend. Take numbers, for instance. Being aware of the frequency with which number vocabulary is used can help us understand what to teach and can also explain why students can have trouble remembering all of the words in our amazing numbers units. The higher frequency the word, the more often students will see and hear that word—and the more often the word will be reinforced in natural speech and reading. And the opposite is also true–the less frequent the word, the less often it will occur and the fewer exposures learners will have to it.

Numbers are a traditional part of level 1 curricula. Beginning students expect to learn the numbers. and no wonder: numbers are extremely helpful when traveling, which beginners often dream of doing. Beginning programs always include numbers, but problems arise because those number words are not reinforced often enough for students to truly acquire them once they’ve moved on from the numbers unit.

For example, take a look at the number-related words in the top 100 most frequently used Spanish words (these frequencies are similar in other languages). Wouldn’t you think that there would be a few more common numbers among the top 100 words? This has always surprised me.

más (#24)          more, plus

dos (#56)           two

primero (#60)    first

uno (#72)           one

menos (#98)      less, minus

Here is another way to look at number word frequency. The frequency numbers of some of these number words is not what I would have predicted:

• 0 and 1 are thousands of places apart in usage.

• 2 is used more often than 1.

• 14 and 15 are more than 1,000 places apart in frequency number. Seems like those two would be closer.

• 100, 700 and 900 don’t even make the top 5,000 most-used words in the language.

• The word for 1,000,000 is used far more often than the word for 13. Seems like 13 would be more common and more useful than that.

So many counter intuitive findings! Here’s the listing of numbers by frequency compiled from Davies:

cero (#2284)                   0

uno (#72)                         1

dos (#56)                         2

tres (#119)                       3

cuatro (#188)                 4

cinco (#231)                    5

seis (#375)                       6

siete (#470)                     7

ocho (#492)                     8

nueve (#786)                   9

diez (#436)                      10

once (#1455)                   11

doce (#823)                     12

trece (#2115)                   13

catorce (#2278)              14

quince (#1033)                15

veinte (#582)                   20

treinta (#722)                  30

cuarenta (#943)              40

cincuenta (#782)            50

sesenta (#1306)               60

setenta (#1773)               70

ochenta (#2120)             80

noventa (#3417)             90

cien (not in top 5,000)    100

ciento (#300)                  100+

quinientos (#3426)         500

setecientos (not in top 5,000)  700

novecientos (not in top 5,000)  900

mil (#300)                        1,000

millón (#523)                  1,000,000

There are also many more number-related words that beginning students are often expected to know that are not high-frequency at all. The words for 8th and 9th, octavo & noveno, for example, do not even make the top 5,000. Students are likely to come across them only on a level 1 numbers test. Those words are not likely to appear anywhere in the average student’s Spanish-speaking sphere for years and years. Beginning learners will memorize them, take the test, and then forget them.

Unless we purposefully use the number words, students will not be exposed to them often enough to acquire them. Few of these words come up in the everyday speaking, listening and reading situations in which novices and even intermediates find themselves. Most novice language learner literature, for example, focuses on the top 200-300 words, and even intermediate-low and intermediate-mid texts often use no more than the top 700-1,000 words.

We don’t want students in level 2 and 3 saying, “Yeah, we covered numbers in level 1, but I don’t remember them anymore,” which my students used to say before I consciously began using numbers all the time.

Here are some ways to reinforce number-related vocabulary in your program with little-to-no preparation or materials:

USE NUMBERS EVERY DAY

Build numbers into your daily class routine as you speak to your students in the target language.

• Write Out the Date: Assign a student job of writing out the date in words on the board every day. Students will see it as they look around the room. Some teachers do a calendar talk every day. If you can pull that off without it being tedious, do it.
• The Date Is Part of the Grade: Have students write out the date with words in the target language on every assignment, quiz or test, including their daily warm-up and on their weekly timed writing. Make writing out the date a small part of the grade for the assignment or assessment–just an extra point or two. 5/12 does not count. It must be written out with words in the TL: el doce de mayo.
• Write Out Numbers: When you say a number, pause and write the numeral and write out the TL word to reinforce it. Otherwise, the number word will just zip right by most students.
• Announcements: Announcements and activities almost always have numbers in the form of dates and times. Talk about school upcoming school activities in the target language and be sure to include numbers as you do. Ask about scores of athletic events.
• Everyday Activities: When folding a piece of paper to create rectangles to draw a story, for example, ask about the number of rectangles folds will make. 1 fold = 2 rectangles, 2 folds = 4 rectangles, 3 folds  = 8 rectangles. This is a hands-on way to teach base numbers and exponents that even young students or students that claim to be bad at math can get. One fold is 2 to the 1. two folds is 2 to the 2, etc. This is more intuitive in Spanish because “to fold” is doblar, to double.
• Events: Use numbers when talking about events that excite students. How much does it cost to go to prom? Is it fair? Is it reasonable? What is the range of expenses?
• Pi Challenge: Challenge students to recite as many digits of pi as they can. 20 to 40 digits is common and doable. One girl named Everett memorized 100 digits and said them in Spanish in front of the class–a bit of overkill, but impressive nonetheless. The class listened to her and followed along, reading the numbers that were projected behind her on the projection screen as she rattled them off.
• Add 20 years to your age:  This is a fun one. When students ask how old you are, casually claim that you are 20 or even 30 years older than you really are, and then resume the lesson. They will not let it go. They will keep asking numbers-related questions for a long time to clarify and to try to trip you up. the round number makes it easy to calculate your fictitious year of birth and graduation. I love this one! Kids sneer and ask what is was like growing up in the (First) Great Depression.

USE NUMBERS WITH YOUR REGULAR CURRICULUM

Purposefully use numbers when talking about:

• Stories: Make numbers parts of the details in stories that you expect students to remember.
• Geography: Distances, degrees of latitude on maps, altitude, population size, density and climate can all be naturally discussed with numbers.
• History: Ask about dates and years. Numbers of people involved in events.
• Small c Culture: Be on the lookout for ways to compare practices between cultures with numbers. The number of tortillas eaten at a typical meal, for example. Compare kilos to pounds, and kilometers to miles.
• Big c Culture: Include numbers when you talk about art, music, architecture and other high culture topics
• Literature: Mention the year of the time period in the text to give it historical context. Whenever anything having to do with numbers is mentioned in the text, casually talk about it.
• Student Interviews: (a la Persona Especial): Students’ lives are filled with potential numbers. You will naturally use numbers if you remember to ask about birthdays, plans for vacation, estimated costs of prom, of college, etc.
• Timed Writing: Have students count the number of words in their weekly timed/speed writing and report the number aloud in the target language, or if there is wide variation in ability, have each student report only the difference in their number from last week.

PLAY GAMES WITH NUMBERS

Here are a couple of number-based games my students have always liked.

• El bebé malo (The Evil Baby)

Joe Neilson of Tucson used to tell a story about a bad baby. The image was simultaneously slightly disturbing and compelling to students so I have always used it in other classroom activities—sort of an anti-mascot for Spanish class.

El bebé malo is a counting game like the old “Hide the Thimble” parlor game (ask your grandmother, or great grandmother). One student leaves the room. Another student hides a doll, the evil baby, which has been creatively and often horrifically marked up by students in the class. The first student returns, and the whole class begins to count out loud in the target language: softly when the student is far from the hidden doll, louder when she is closer to it, and they are all screaming when she is right by it. The number the class is on when she finds it is her score and it is written on the board. This game is loud, rowdy and fun.

There are no prizes. It is just for pride, but often competitions between classes develop for the lowest scores, which indicates the most skill from the class in delivering the volume cues, and highest scores for the most skill in hiding the doll.

You will discover some devilishly clever individuals in your classes when you do this game. The creativity of students in hiding something is remarkable. Some of the wildest places that students have hidden it: In the microwave, in the ceiling tiles, in the parking lot (visible from the classroom, but unexpected), and out in the hallway (it was surreptitiously tossed out as the door was opened to let in the seeker).

Modifications:

-Use an unmodified, cute, little, plush toy with younger students. A scary-looking marked-up doll with mean eyes, scars and tattoos may be a bit much for young students.

-Have younger students or beginners count just up to 10 or 20 and then keep repeating that sequence rather than pushing on to higher numbers they are not ready to use. Assign a student to make tally marks on the white board to mark off every set of 10 or 20 to keep track of the score.

• Arroz y frijoles

  (Rice and Beans—for other languages, substitute any two words that go together)

This is a drinking game adjusted to become a cooperative counting game. Have students stand in two circles, three circles for large classes. The objective is to count to 35 in the target language. Students count off around the circle.

Here’s the cooperative part: when a student makes a mistake, he goes to the other circle. The circle with the error-maker has to start over at 1. The new circle that the error-maker enters lets him in, and continues counting. That circle does not have to start over. So, a student can be a “loser” in one circle, but be part of the winning team in the new circle. Here’s how to play:

-Round 1: Substitute the word “arroz” for multiples of 5. This round goes: 1, 2, 3, 4, arroz, 6, 7, 8, 9, arroz, 11, etc., all the way to 35. First circle to 35 wins the round.

-Round 2: Substitute the word “frijoles” for multiples of 7. So, 1, 2, 3, 4, 5, 6, frijoles, 8, 9, 10, 11, 12, 13, frijoles, 15, etc., all the way to 35.

-Round 3: Like round 2, plus add “frijoles” for words with a 7 in them: 17 and 27.

-Round 4: Combine all of the elements of the previous 3 rounds. So, this round would sound like this: 1, 2, 3, 4, arroz, 6, frijoles, 8, 9, arroz, 11, 12, 13, frijoles, arroz, 16, frijoles, 18, 19, arroz, frijoles, etc., all the way to 35. This last round is hard. Even teachers and native speakers have a tough time with it.

These rounds could be done on four consecutive Fridays as a treat. Since each round will take 10 minutes or so, doing all 4 of them at once would be too much. We’ve got to always keep them wanting more.

The secret to winning this game is this: the circle whose members help one another the most wins. Letting students discover this is powerful and preferable, but if you have a slow or overly competitive group, spell it out to them. Tell them explicitly: “If you help each other, you will win,” which is also not a bad motto for our lives.

I love this game because of all the overlapping components in it. It teaches by experience many of the qualities that go into becoming a good language learner:

-Cooperation: Some students will need more help. We need to help one another.

-Concentration: Each student has to be aware of what is going on in the game.

-Involvement: There is no sitting on the bench. All are playing and all are valuable.

-Anticipation: Everyone needs to be thinking ahead.

-Repetition: The numbers are repeated, but students are also rehearsing in their minds.

-Social Awareness: Paying attention to others is built into the game.

-Numbers: Oh yeah, that’s what this article is about…

             • El número mágico

This is a number guessing game. Pick a # and students take turns guessing it. You can use más de and menos de (more than or less than) to give them clues. Thanks to Leslie Davisson for reminding me of this one. I had a student teacher that did this one remarkably well having students guess her age when they were asking  her questions for a Persona Especial interview. See it here

A variation on the number guessing game from Janet Fettinger Holzer (who says she forgot where she got it):

Teacher thinks of 2 (or more) digit number. Students guess. Teacher responds based on place value. Ex. Secret number: 87. S guesses 12 T says no/no (TL of course) S guesses 27 T says no/yes S guesses 85 T says yes/no. I don’t tell them how the game works the first time because part of the fun is figuring out how the clues work.

Awareness of frequency can help us to remember that students need more meaningful exposure to numbers. I have also cataloged other number-related words by frequency, but that will be in another blog…