Math Perceptions of Taiwanese and American Children

Article Critique

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 0.8468. 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 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

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