Low math scores of American elementary students has been a major issue in education for some time. The Third International Mathematics and Science Study (TIMMS) conducted in 1995 showed the extent of the problem. The TIMMS study compared students in 42 countries, allowing American students to be compared with international students. The study rated the math ability of American students as adequate in fourth grade and poor in twelfth grade compared to other countries. This study was not the first time that concerns had been raised about American students achieving poorly in science and math. It was however, the largest and most comprehensive look at the real extent of the problem. The study made people realize the significance of the issue and resulted in the awareness of the public, the government and education and mathematics researchers. The major question that needs answering is why the low math scores occur, and consequently, what can be done to change it.
To begin answering this question, it is first necessary to consider some of the many reasons that have been proposed. A consideration of the issue and the reasons proposed will show why some do not provide a logical answer. It will then be seen that there is one reason that has been proposed that does adequately explain the situation. This reason is based on how teachers teach mathematics and is supported by various research projects. Based on this research, the problem can be linked to the skill and methods of American elementary school teachers. A close look at this research will reveal the problems with American mathematics teachers and the base causes of these problems. This will lead to a final conclusion suggesting the changes necessary for overcoming the problem.
Possible Explanations for Low Math Scores
The problem of low math scores became an issue of interest to everyone, from parents, to teachers, to child psychologists. It is not surprising then that a wide range of reasons were proposed.
Some believed that it was a product of American society and related to changes in the American family. In short, the mother and father both work, the child does not have a good role model or someone to help them study, and so the child's learning suffers.
Others believed it was a result of the many distractions present in children's lives. Children were playing video games, watching television and not studying like they should be.
Others believed that the problem was based on the pressures of the school system. Schools were understaffed, funding was low and so the schools did not have the ability to teach children as well as they should.
While all these may be contributors to the problem, there is one issue that they do not provide an adequate answer to. The issue is why student's results are low specifically in math. There are no similar problems reported in student's results in English, geography, or history. Instead, this is a problem specific to the study of mathematics.
This aspect suggests that the problem is not based on the students, since any impact on the students should affect their results in all subjects. This leads to a conclusion that the problem must be subject-based. It must be based on teaching methods, the curriculum, or the teachers themselves.
A suitable theory was proposed by Liping Ma in the book Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States. Research described in the book shows that there is a major gap between the knowledge and the teaching ability of American and Chinese mathematics teachers. It is also worth noting that China is a good means of comparison because Chinese elementary students scored very high in the TIMSS.
A consideration of Ma's results and conclusions will provide a suitable reason for the gap seen between American and Chinese students, and thus provide an answer to the question of why American elementary students compare so poorly on an international scale.
Comparing Elementary Mathematics Teachers
Ma's comparison of American and Chinese elementary mathematics teachers shows that they differ significantly in their mathematics ability, their understanding of mathematics, their ability to teach, and their approach to teaching. It is worthwhile to consider each of these areas in turn.
Comparing Mathematics Ability
Ma conducted much of the research by interviewing elementary mathematics teachers. The comparison involved 23 American teachers and 72 Chinese teachers. Ma asked each teacher four mathematics questions to determine their ability, with each of the questions becoming increasingly more difficult. For the first two questions, all the teachers arrived at the correct answer. However, for the third question only 43 per cent of American teachers were able to complete the question correctly, while all the Chinese teachers were correct. The fourth question also showed a significant gap, with a much higher percentage of Chinese teachers arriving at the correct answer.
This part of the research shows that American teachers do not have the same level of mathematics ability as Chinese teachers.
Comparing Mathematics Understanding
Another important aspect of Ma's research was based on investigating whether Chinese and American teachers had the same level of mathematics understanding. The four questions were each designed not only to assess whether the teacher could arrive at the right answer, but also to determine if they were able to grasp the concepts involved. In this area, the results were even more dramatic.
In the first question, 10 per cent of American teachers had a conceptual understanding, compared to 86 per cent of Chinese teachers. In the second question, 40 per cent of American teachers had a conceptual understanding, compared to 90 per cent of Chinese teachers.
The findings here suggested that American teachers could complete mathematics problems equivalent to what their students would be learning. However, they could do this without being aware of the basic underlying concepts. In short, they might be able to remember how to work something out, but they did not why it was worked out that way.
This gap in understanding the concepts involved in mathematics then impacted significantly on the third aspect of Ma's study, the ability to teach mathematics.
Comparing Ability to Teach
The main purpose of the study was to consider why American elementary students were not learning mathematics as effectively as Chinese students. It is logical then, that a major part of the study is based on considering not just what the teacher knows, but whether they can teach it.
The questions of the study did not only ask the teachers to perform the calculations, they also asked them to explain how to do the calculations. Again, the results showed a significant gap between the American and Chinese teachers. Question three of the study asked teachers to complete a question and make up a story problem that could be used to teach students how to complete the problem. Only one of the American teachers was able to make up the story problem, while 90 per cent of the Chinese teachers were able to. The other three questions showed the same overall results, American teachers had a much lesser ability to adequately and correctly explain what they were doing.
This finding is significantly linked to the American teacher's inability to grasp the key concepts. A teacher may be able to remember the correct way to complete a problem, but without an understanding of the key concepts, they do not have the ability to explain why. This leads to the situation where teaching is based on memorizing facts. This leads to the final aspect revealed by Ma's research, a difference in the approach to teaching mathematics.
The American Approach to Teaching Mathematics
Ma argues that the American approach to teaching mathematics is based on teaching procedurally, not conceptually. According to Ma mathematics is approached as a collection of facts and rules where mathematics means following set procedures step-by-step to arrive at answers. This American approach appears to be a correct definition of how mathematics is seen. Unlike subjects like English and geography, the emphasis is not on understanding, but on remembering. Students do not have to know why a certain number is the area of a shape. Instead, all they have to do is remember the formula for calculating the area.
The problem then, comes down, not to a deficiency in the teachers themselves, but to a deficiency in the whole system that then impacts how the teachers are taught. If the why of mathematics is not considered important, then teachers do not learn why, and in turn, they do not teach why.
The first three problems identified with American teachers were: the lack of mathematics ability; the lack of mathematics understanding; and the inability to teach mathematics effectively. Each of these three problems can be seen as having its base cause in the approach to teaching mathematics.
The Problem With American Mathematics
Ma summarizes the findings of the study saying that American teachers lack what she describes as a "profound understanding of fundamental mathematics." This…