Math Perceptions of Taiwanese and American children

The objective of this article critique is to review and evaluate several empirical studies which have examined mathematics perception cross-culturally. The main study that focuses on examining mathematics perception cross-culturally is a study that was done in 2004 by Dr. Yea-Ling Tsao. In this study, researchers proved that Taiwanese students consistently score higher in cross-national studies of achievement than American students.

Several other studies were done that also support this theory. Therefore, the main purpose of this article critique is to evaluate Tsao’s study in order to properly assess both the validity of Tsao’s design and the inferences drawn from the study. This critique will also show that, while different studies were done at different times, researchers still have come up with one consistent hypothesis: American students are constantly scoring below the national average in academic testing.

In order for Tsao to complete her study, she came up with specific research questions and hypotheses for her study. The study done in 2004 was to determine why is it that Chinese students are constantly amongst the top scorers in cross-national studies of achievement and American students are constantly below the national average. Dr. Yea-Ling Tsao gives an example early on in her article about how different studies have shown that American students are consistently performing poorly on tests of mathematics and science.

She also gives an example of how in a recent national study of mathematics achievement, American students in the middle school grades were performing lower than the national average in problem solving, geometry, algebra, calculus, and other areas of mathematics. In contrast, Japanese students from the same grade level had significantly higher average scores. In this study, Dr. Yea-Ling Tsao is trying to understand the reasons for the different perceptions of mathematics of Taiwanese children compared to American children.

Tsao is concerned in taking a deeper look at the cross-cultural differences in mathematics perception and attitudes of younger children. Those tested were 21 students in Denver, Colorado, and 37 students in Taipei, Taiwan. The researcher’s main concern in the study was to determine if attitudes and beliefs have a noticeable effect on American student’s performance in mathematics. In order to obtain answers to this problem, the researcher felt that it would be necessary to compare American students to Taiwanese students.

The researcher’s main concern was to investigate differences in math perception between those students scoring highly versus those students scoring poorly on national exams. The researcher thought that the solution would be due to cross-cultural differences in achievement. For this particular study, a survey including 39 closed questions (developed by Alan Schoenfeld in 1989) was used. All items on the survey were in the form of a seven point rating scale, with 1 being “strongly agree” and 7 being “strongly disagree”. The questionnaire was determined to be extremely consistent with an alpha of 0. 468.

The survey contained questions associated to student’s perception of what mathematics is and how to do well in it, what mathematics solutions should be, how math problems can be solved, how mathematics is learned, and student motivation. For the first 33 questions, the students were asked to rate them on the seven point scale described above. The last six questions on the survey dealt with grades, gender, and perception of the children’s parent’s attitudes towards mathematics. The researcher also used a two-tail t-test to compare the mathematical perceptions of Chinese and American students.

The average of each cateogry in the survey was also compared. As stated above, there were six main categories being compared: what mathematics is, how to do well in it, what mathematics solutions should be, how math problems can be solved, how mathematics is learned, and student motivation positive vs. negative. During the study, Tsao had to deal with different quality control issues. The two cities, Taipei and Denver, are very comparable in size and demographics. Researchers chose Denver due to the residents coming from native-born, English-speaking, economically fit families.

Researchers chose elementary school children as the subject for the study for two reasons. First, the researchers wanted to know if cross-cultural differences in achievement emerged during early years of schooling (Tsao 2004). Tsao also focused on elementary school students to achieve some understanding of the early background of the large differences that appear later in middle and senior high school (2004). For this study, a small sample was used in order to complete the study: one classroom from two public schools (one located in Denver; the other located in Taipei).

As for the size, these two cities are reasonably comparable. The classroom in Taipei had 37 students and the classroom in Denver had only 21 students as subjects for the study. From the questionnaire, researchers found remarkable differences in the beliefs of Taiwanese and American students and their overall perception of mathematics. The data showed major differences in the means (averages) for the category of what mathematics is. This shows that to start off, American and Taiwanese students do not even share the same view of what mathematics is.

The Taiwanese students were apt to disagree or even feel neutral about math being “mostly numeral”. However, most American children were apt to agree with this idea of mathematics. For the second category of how to do well in mathematics, there were also considerable differences in the average scores. Data for the American students reflected that memorization was the key to being successful in mathematics. The data collected from the Taiwanese students was just the opposite; they wanted to know the rules of how, for example, 1 + 1 = 2 and not just memorize that as a rule.

For the third category of what math solutions should be, there was also a noticeable difference in the average scores. American students simply believed the solution to be the right answer, while, their counter-parts strongly disagreed with that idea. For the fourth and fifth categories, how math problems can be solved and how mathematics is learned, there were not many noteworthy differences amongst the two cultures. For the last category, the researcher decided to break down the subject of student motivation into two partspositive and negative.

For the negative motivation subcategory, the researcher was trying to include the idea of learning math because it was required or because they feared punishment if it was not learned. Interestingly, the Taiwanese students were affected by this negative motivation. The American students were predisposed by positive motivation such as wanting to do well in the class. Tsao’s data was analyzed using correlations and a two tailed t-test. The researcher made six categories of related questions to assess each student’s perception of math.

The categories were arranged as follows: what mathematics is, how to do well in it, what mathematics solutions should be, how math problems can be solved, how mathematics is learned, and student motivation positive vs. negative. The results from the self-questionnaire revealed significantly noticeable differences in the average scores of each category except for the fourth and fifth categories of how math problems can be solved and how mathematics is learned. The results showed that 24 of the 33 questionnaire items had considerable differences between the two different cultures.

The data from the study revealed that there was a significant difference in the perception of mathematics in each culture. The data collected revealed that American students believe that solving mathematics problems depends on knowing the rule. On the other hand, the data reveals that Taiwanese students feel that good teaching practice in mathematics consists of showing students many different ways in solving the same problem. The researcher also found that Taiwanese students really do believe that math is useful in real life.

This study also showed that the Taiwanese students had an overall more positive perception of math than their American cohorts. However, this was due to the Taiwanese students learning math because of fear of punishment. The Taiwanese students’ more positive perception was suggested to have come from the fact that their culture places a very high value on mathematics achievement. In conclusion, the data collected shows that the two culture’s perception on mathematics is clearly different, but that math is useful inside and outside of a classroom setting. There are several studies have data which is in line with the findings of Tsao (2004).

One of these studies was done on the mathematics achievement of Chinese, Japanese, and American children (Stevenson, Lee & Stigler 1980). For this particular study, researchers collected data from children in China, Japan, and America. They tested children shortly after entering elementary school and again near the end of their elementary education. The data collected from this study revealed that the American children’s scores were significantly lower than those of the Japanese children in kindergarten and at grades 1 and 5, and lower than those of the Chinese children’s at grades 1 and 5 (Stevenson, Lee, Stigler 1986).

Therefore, similar to Tsao’s study, scores of the American children present a consistent decline compared to those of the Chinese and Japanese children. Another study that is similar to Tsao’s study is a study done in 1990 by Stevenson, Lee, and this time, Chuansheng Chen. The researchers returned to the same school as in 1980, the year of the original study, and tested a third sample of fifth graders. Again, Japanese children were found to be consistently more advanced than their American cohorts. The difference between the performance of the Japanese and American children was actually greater in 1990 than in 1980.

Clearly, researchers have consistently found that East-Asian children seem to always out-perform American children in mathematics achievement (Tsao 2004, Stevenson, Stigler, Lee 1986, Chen). Different students from different cultures are raised differentlythat’s what makes a “culture” a “culture”. Within Tsao’s study, researchers found that there are quite a few differences in the student’s attitudes and beliefs of the two cultures toward mathematics and in the parent’s attitudes and beliefs towards mathematics.

There are many different reasons as to why there is such a vast difference in mathematics achievement between the two cultures. For example, Dr. Tsao points out that it could be a negative attitude of the American culture that could be producing the low international achievement scores in mathematics. But this isn’t something that is going to be easily fixable. Like Tsao points out, the whole negative motivation of American children stems from different cultural values and systems, which comes from differences in the amount of investment of children, parents, and teachers in the learning of mathematics.

The latter is likely to be the most crucial foundation of the mathematical ability differences when comparing East Asian and U. S. children. Researchers also felt a need to look at the mathematics classrooms in Japan, Taiwan, and the United States. There was a study done in 1987 to offer objective and concrete data on the organization and behavior of classroom activities. This study was done on 20 fifth-grade classroom in three locations: Minneapolis, Japan, and Taiwan. Researchers James W. Stigler, Shin-Ying Lee, and Harold W. Stevenson decided to observe the activities being completed in the mathematics classrooms.

Large cross-cultural differences were found in many variables related to classroom structure and management. These vast differences paralleled diversity in achievement in mathematics among the three countries. A large number of these variables were very much related to the average level of mathematics achievement within the American classrooms. Based on the research that has been examined, it is clear to me how important it is to incorporate different cultures in the classroom.

Every child is different and every child learns differently. Mathematics is important, yes, but is it more important than being artistic in school? Every student that is a part of your classroom is going to be unique, both personality-wise and learning style-wise. Students learn things in different ways, and as educators, we should able to recognize this and embrace it. This study can also provide teachers an opportunity to understand their students’ math perception. By recognizing that cultures may have different opinions about mathematics and education, teachers can better appreciate their students.

This study can also be beneficial because if the teacher recognizes and understands the students’ perceptions, she can offer individualized teaching styles for students when needed. After evaluating these studies, I do feel that future study is necessary is future study is most likely going on right now. If I could design a study to test the research findings further, I would design a study for parents and care-givers. The category of care-givers would include anyone that had anything to do with the growth and education of a child. Parents are of a huge interest to me because they are essentially where the learning begins for a child.

If we start off the research on the parents, and then maybe work our way down to teachers and so on, then researchers will know exactly where the different perceptions come from. All of the studies that were analyzed were given to young subjects. While we do need the relevancy of young children, we also need to see the effect of the parent and care-givers of the young children. As we all know, most thoughts and perceptions of children stem from their parent’s thoughts and perceptions. That is why it is absolutely vital for researchers to first study how children are taught and who better to show this than their parents.

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