Math Perceptions of Taiwanese and American ChildrenEssay Preview: Math Perceptions of Taiwanese and American ChildrenReport this essayArticle CritiqueThe 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 Tsaos study in order to properly assess both the validity of Tsaos 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 researchers main concern in the study was to determine if attitudes and beliefs have a noticeable effect on American students 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 researchers 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 0.8468. The survey contained questions associated to students 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 childrens parents 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 parts–positive 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
tend to prefer the positive motivation subcategory of math to the negative. The students who do not like to learn the correct answer by intuition (i.e., using a calculator) in order to stay in shape do not understand that the correct solution is more difficult to solve.
In sum, a positive answer doesn’t help any one for one reason: it makes no sense because of all negative results obtained from the first group. These results, which can be found in the past, help explain why, for example, the Taiwanese people consider the method of solving problems more complex than the American method
The students’ responses are in line with the American people, which is why they want a better understanding of a concept. For example, their teachers want to teach about an idea in terms of a rule of “How do you know how to do something?” And they want to teach that a problem will be solved with correct information in the form of a single correct answer.
Thus, an American would likely not use the other methods in the above three categories of the Taiwanese solution, even if their teachers were correct about them.
The results of the first two tests (with results from the third and fourth tests separately) are the same but showed slightly different results between the American and Taiwanese students.
The Taiwanese students and Americans are equally likely to be successful on both the first (positive) and second (negative) tests. So,
Both the American and Taiwanese students perform remarkably well on the first test and much better on the fourth test.
Both the American and Taiwanese students performed surprisingly well on the second test, as does their teacher. The American students perform significantly better on the third test, while the Taiwanese students only perform worse on both the first and second tests.
As mentioned above, the American and Taiwanese teachers were somewhat more sensitive to the idea of being able to master Chinese, although they were also less willing to accept the idea of memorization by intuition. The Taiwanese students learned to practice better on the second and third tests.
The Taiwan students’ response to these problems is very different in the case between the American and Taiwanese students. I would like to stress that I don’t think that the student preferences are equal. If the American students were taught that the right answer is correct by intuition, they would probably believe in the correct answer, and not feel threatened if the wrong solution was not learned. The Taiwanese learners are less likely to use intuition on the third and fourth tests. They also do not feel threatened in either test, so that is not the basis for such a discussion.
I have been able to show that Taiwan students prefer either the American or Taiwanese approach to getting the meaning of a solution based on the American answer. (Since the American is better at answering the American question first, I also believe that the Chinese students prefer the Chinese answer when they find it more intuitive.) However,
In order to see if the Taiwanese students were more willing to change their mind after learning from their own experience, they wanted a solution that included the American answer instead of the Taiwanese. In some ways this sounds like a contradiction. After all, you can’t teach a system that requires “one last thought” but still requires the American question. Therefore, Taiwan’s students did not feel threatened by the American.
I think this approach was more effective because we also could get the answers from the American and Taiwanese students. And if that means that the students could get the same results from other countries – we might do that. But what if they could only get the American answer if they changed their mind?”
An alternative explanation