Low Math Scores of American Elementary Students

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 statement provides reasoning for why American teachers do not have an understanding of mathematics, and why they are unable to teach it effectively. 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.