Culturally Responsive Mathematics Instruction for All: 
An Example of Using a Korean Traditional Game

Ji-Eun Lee
Auburn University-Montgomery
U. S. A.

What I Saw
What We Can Do
Instructional Idea
Looking Forward
Endnotes
References

What I Saw

My university has offered a Summer Enrichment Program for several years. Students in local elementary schools have voluntarily participated in this program with their parents' permission. Both teacher candidates and students have benefited from this program. Teacher candidates experience various classroom situations in the program. Students are also presented with ample opportunities to review and preview curricular materials. [paragraph 1]

Last summer, teacher candidates in my mathematics methods course encountered an unusually large Korean student population. Recently, a Korean automobile company built an assembly plant in the city of Montgomery, Alabama, and many Korean workers and their families have moved to this city to set up the plant. Due to the influx of Korean children and their parents' extraordinary support for their children's educational success (Adams & Gottlieb, 1993; Bailey & Lee, 1992), an unprecedented number of Korean students participated in the Summer Enrichment Program.  [paragraph 2] .

One day I witnessed a moment of cultural connection, which drew Korean students' attention. Mr. Cochrane¹, a teacher candidate, was scheduled to teach grades 4 - 6 students the concept of "theoretical and experimental probability" on the second day of the program. After observing the first day's lesson, he wanted to add a special comment for Korean students. He asked me if I knew any probabilistic games with which the Korean students were familiar. I gave him some information about "Yut-nori," one of the popular traditional games in Korea. Mr. Cochrane used this information in the introductory part of his lesson. He posed several questions about the probabilistic materials and briefly mentioned Yut-nori as one of the examples. Korean students were very surprised to hear that their American teacher mention their traditional game familiar to them. Yut-nori was not a main instructional activity in the lesson. However, Mr. Cochrane's attempt to address another culture in mathematics classroom provided a great emotional support to the students from a foreign country. Later, Mr. Cochrane positively reflected on his teaching, saying, "I think I connected with the Korean students well." [paragraph 3]

What We Can Do  

I believe that various items from different cultures can be developed as mathematically meaningful lessons incorporating mathematical concepts beyond just mentioning and introducing the names. For instance, the concept of probability and statistics can be found in traditional games in many cultures. If we consider the historical development of the study of data analysis and probability, it becomes obvious that many societies have developed games and rituals of chance out of eagerness to predict the future. For instance, many fortune- telling techniques and diviners' predictions were made based on chance and probability. Even in the present days, probabilistic games are an important and interesting part of our lives from simple card games to popular TV game shows such as Wheel of Fortune and various lotteries. [paragraph 4]

The growing emphasis on multicultural education in the education community calls for an attention to the diversity of our society and educators' understanding of the role of various cultures in teaching and learning mathematics (Ubiratan, 2001; Zaslavsky, 1991). Mathematics lessons that utilize various traditional games can be important vehicles through which mathematical concepts can be taught while showing respect for different cultures. [paragraph 5]

Instructional Idea

In this article, I would like to provide an example of a mathematics lesson using Yut-nori, a traditional Korean game of chance and probability.

Lesson Title: Yut-nori - a game of chance and probability

Grade Levels: 6 - 8

Goal: The goal of this lesson is for students to understand the basic principles of probability.   

Students should know: 

1. The meaning of simple events;

2. How to represent the probability of events that are neither certain nor impossible using common fractions;

3. Theoretical probability and experimental probability  

Objectives: As a result of this activity, students will be able to:

1. conduct an experiment

2. display data

3. find the probability of an event

4. interpret the game rules in relation to the principles of probability

5. search for traditional probabilistic games in other cultures and analyze the similarities and differences

Interdisciplinary Connections: Social studies-History

Materials: one Yut-nori game set for each group of four students [paragraph 6]  

Procedures:

1. Review the previous learning.
    

2. Introduce the Yut-nori game set. Show the game set and briefly explain it: 

Yut-nori is one of the traditional folk games played in Korea. It has four sticks, each with a flat side and a round side, just like a head and a tail of a coin. Each player tosses four sticks at a time onto a mat and counts the number of sticks that fall on the flat side or the round side. Depending on this number, each player (or each team) can move a marker on the game board. Each player or team takes turns until one player/team brings all of the markers back to home first. 

Figure 1. Yut-nori Game Set	Figure 2. A Family Playing Yut-nori

3. Ask students what they know about Korea. Allow students to have a short discussion. If Korean students are in the class, they would be good resource persons. 
    

4. Distribute the game sets and let the students have free playing time.
    

5. Ask the students how many different combinations are possible when they toss four sticks at a time. Ask them to represent outcomes on a list, chart, or picture. The results will be five different combinations:
    

• One flat side and three round sides (F, R, R, R )

• Two flat sides and two round sides (F, F, R, R )

• Three flat sides and one round side (F, F, F, R)

• Four flat sides (F, F, F, F )

• Four round sides (R, R, R, R)   

Figure 3.  All Possible Combinations of Yut-nori
Do (F, R, R, R)	Gae (F, F, R, R)	Gull (F, F, F, R)

6. Explain more game rules in relation to this result: 

Each combination has a special name which represents an animal, and the movement of markers also represents how fast each animal is (e.g., a pig is the slowest and a horse is the fastest). Table 1 shows the name of each combination and the rules of movement:    

Table 1. Basic combinations and movements of Yut-nori

7. Ask the students to find out theoretical probability for each combination. Ask them to represent outcomes on a list, chart, or tree diagram. The result will be the following:

Table 2. Tree  Diagram

Table 3. Theoretical Probability ²

8. Ask more discussion questions about this result in connection with Yut-nori game rules:
    

• In Yut-nori, if you have "Yut" or "Mo," you can have another chance to throw the sticks. Do you think this rule is reasonable or fair? Why or why not?

• In Yut-nori, if your marker ends up at the spot, with an exact count, where another marker of yours rests, you can move the markers together from the next move. If your marker ends up on a dot, with an exact count, where the other team's marker rests, you can remove the other's marker from the game board and earn another chance to to toss the sticks.  The other team's marker has to start over from the beginning.  How do these rules and the results of theoretical probability affect your decision on the movement of your marker? 

• If your marker ends up on one of the five big dots, with an exact count, you have a choice of taking a shortcut to the goal.

9. Have each group of four students play the game. 
    

10. Share the experiences: What was your strategy? What was the riskiest moment you had? What made the situation risky?
     

11. Have a follow-up discussion: How is probability used in the world? What are the similarities and differences between Yut-nori and other popular probabilistic games in the US such as throwing dice, tossing coins, black jack, drawing lots, and so on? [paragraph 7]  

Extensions/Modifications:

1. Investigate international probabilistic games. Compare similarities and differences.

2. Investigate cultural and historical factors in relation to several cultural games.  [paragraph 8]

Looking Forward