# Term Paper: Low Math

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In the book, Ma provides an example of a Chinese teacher who has this profound understanding.

This teacher prepares for their lesson by considering what they will teach and what it means. They link the lesson that will be taught to the underlying concepts they want the students to learn, to the other concepts the information should link to, and to the actual mathematical skill involved. In this way, the student gains several things. They gain the mathematical skill, they gain an understanding of the mathematical concepts, and they add this knowledge to what they already know about mathematics. With this approach, the student is able to grow their knowledge and understanding. Each new concept the student learns adds to what they already know, creating a more comprehensive and deeper understanding. This knowledge also makes it easier for the student to continue learning, as they are able to link the information to what they already know.

In contrast, an American teacher would be more likely to be focused on only providing the mathematical ability. The student learns how to complete a mathematical task, but does not learn why it is done this way. Without this understanding, the student is not linking the new knowledge to past knowledge. Rather than having a comprehensive and deep understanding, the student has a wide range of information to recall, without any of it being linked together. This approach is least efficient for learning.

This same point is supported by other research, including one book where the importance of number sense is described. The book is titled Beyond Arithmetic: Changing Mathematics in the Elementary Classroom and focuses on why the National Council of Teachers of Mathematics (CTM) called for a shift in the way mathematics is taught. According to the book, "to have 'sense' about numbers means to understand how numerical quantities are constructed and how they relate to each other" (Mokros, Russell, and Economopoulos 5). This 'sense' requires an in-depth understanding, not an approach based on memorizing. The book describes how the emphasis in mathematics is shifting from just being able to complete mathematical problems, to being able to solve problems and apply reasoning to situations. This type of thinking requires not that students have formulas and methods memorized, but that they are able to think of their own methods and apply them. This was the kind of thinking seen in the Chinese teachers of Ma's study, with them able to explain things and apply them. It was also the kind of thinking particularly lacking in the American teachers. This second book then, leads to the same conclusion; that the problem lies in the teaching approach. If the teachers are not able to do what is necessary in modern mathematics, then they will not be able to teach this ability to students. Clearly, the problem needs solving at the teacher level.

The same book also discusses the general American approach, saying that mathematics is generally approached as a 'tidy' subject. Mathematics is described as a subject that is considered to be black-and-white and to consist of simple rules to be followed. This view is rejected, just as Ma rejected it. Instead, the authors suggest that students should work on non-routine problems. As the authors describe, "students should expect 'messiness.' There may be different paths to a solution, and there may be several different good solutions to a problem" (Mokros et al., 53). This aspect leads back to the idea that the teachers are not the base cause, but rather, the American approach to mathematics.

It is also worth noting that the Chinese and American teachers looked at it in Ma's study had studied mathematics for similar amounts of time. The Chinese teachers had the equivalent of a bachelor's degree. If anything, the American mathematics teachers were actually more qualified, many having master's degrees. Despite these education levels, the Chinese teachers achieved much better results. This indicates that it is not a lack of training that is the problem with the American teachers; instead it is what they are trained in.

Another aspect revealed in the study related to the Chinese focus on teachers having both subject knowledge and the ability to teach it. Ma suggests that in American elementary schools, teachers are focused more on the ability to teach than the subject knowledge. However, as seen earlier, in mathematics, in-depth subject knowledge is required to adequately teach the subject. Without this in-depth knowledge, teachers are not able to give adequate explanations of mathematics.

This fact may explain why American elementary students do not have the same problems with other subjects like English and geography. In these subjects, in-depth knowledge is not essential to the teaching of them. In fact, it may be more beneficial to focus on improving teaching methods, than improving teacher knowledge.

Consider a teacher who is teaching about the countries of the world. A teacher who knows everything about the countries of the world is not necessarily in a good position to teach it because too much information will only make the subject too difficult for students. Teaching about one aspect of a country and not another does not impact the meaning of the information for the student. There is not a specific link between two sets of information, as there is in mathematics. You can understand the currency of a country, without having to know about the country's rivers and mountains. A teacher with a greater amount of information is therefore, not in a much better position than one that knows only what has to be taught. However, if two teachers have different teaching abilities, there is a major difference. A teacher that has a greater number of teaching methods at their disposal and a greater understanding of how to teach can teach the material in a way that is understood. In most elementary subjects, teaching ability may be more important than having an in-depth understanding of the material.

As noted, mathematics is an exception to this. In the case of mathematics, in-depth understanding is equally as important as teaching ability. This is another reason why the teaching of mathematics in America is inadequate; there is not enough focus on this aspect. To solve this problem, it may be necessary for mathematics teachers to be treated differently than teachers of different subjects. Mathematics teachers may need to specialize in their specific area. Interestingly, this is exactly what Ma reports in her study of Chinese and American teachers.

Conclusion

The problem of low math scores for American elementary students has now been considered in detail. It has been seen that there are considerable differences between Chinese and American teachers, and that these differences account for the poor performance of American students. At the same time, it has been seen that the problems go beyond the teachers themselves, with the base cause being the American approach to mathematics. Firstly, mathematics has to be recognized as a subject that requires understanding, not just memorizing. The whole approach to learning mathematics has to be altered. Secondly, teachers need to learn the subject in-depth so they are capable of teaching students this knowledge. In doing this, it is also important to note that mathematics is a subject with different qualities than other elementary subjects. While in other subjects, teaching skill may be critical, in mathematics, in-depth knowledge is at least as critical. This requires the teaching of mathematics and the training of mathematics teachers to be treated as a different process than of other subjects. With these steps put in place, America can expect to produce mathematics students with a greater understanding and ability in mathematics. In turn, some of these students may become teachers themselves, passing their own greater knowledge to more students. Once put in place then, the system builds on itself, until American students will be at least equal with the world's best.

Works Cited

Ma, L. Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates, 1999.

Mokros, J., Russell, S.J., and Economopoulos, K. Beyond Arithmetic: Changing…
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