Analysis on Attributions Affecting Junior Middle School Teachers in
Execution of New Mathematics Curriculum
Liaoning Province Basic Education & Teaching Research Training Center
Teachers School of Huanggu District, Shenyang, Liaoning
In this article, a cluster analysis is made by means of qualitative research on the abundant first-hand data
accumulated in the continuing observations of and probing interviews with four mathematics teachers in junior
middle schools, and many elements that have been hindering the execution of new mathematics courses in junior middle schools have been summarized. Based on this and in virtue of the well-known Cognitive Dissonance
Theory, the elements are further analyzed and root causes affecting teachers in teaching new mathematics courses
in junior middle schools are exposed.
Key words:course concept, class teaching behavior, Cognitive Dissonance, attribution analysis
Ever since the new curriculum is started, the educational & teaching notation and behaviors of teachers in class have changed to a certain extent. However, the teaching concept of most teachers has not changed distinctly, and the behavior in class is basically a formality, namely, the so-called “to guide the students to make thorough
inquiries” is actually to influence the thinking of the students so they will follow the teachers; the so-called “to
cultivate the creative ability of the students” is that, in fact, all the strategy for problem solving is still done by the
teachers alone, the so-called “to divide the students into groups for discussion and cooperation” is nothing but to
make the students sit together without any communication or mutual assistance; the so-called “to promote the
connection of mathematics with real life and other subjects” is that, in fact, the context of questions are far beyond
the students‟ experience.
Why have the behaviors of most teachers not changed essentially after they have been trained on the new curriculum? What are the elements that have been hindering the improvement of class behaviors of mathematics teachers in junior middle schools? It was the above puzzles that made the authors start the research, which shall be illustrated in this essary.
2，Design and Procedure of the Research
2.1 Research Method
A qualitative research Method is mainly adopted in the research. Data are collected through probing interviews with four mathematics teachers and classroom observations on them. Then the data are analyzed, summarized and clustered by using the Grounded Theory(2；！from which major elements that affect the improvement of the
teachers‟ behaviors are discovered.
2.2 Research Instruments
Major tools used for this research are Outlines of Pre-class and Post-class Interviews, Classroom Observation Instrument？COI，, Codes of Mathematics Tasks and video tape analysis technique, of which, Classroom Observation Instrument？COI，and Framework of Mathematics Tasks for Instruction are developed in“QUASAR”
program by the Study, Research and Development Center of Pittsburgh University, so they are more reliable and effective(3；.
According to the research method, four mathematics teachers are principally recommended by three schools with
their agreement. At the request of the four teachers, they are named as Teacher A, Teacher B, Teacher C and Teacher D in this essary. Their rèsumès are stated as follows:
Teacher A has ten years of teaching experience and is one of the leadership teachers in the district. Since 2002
when she started her experiment on the new curriculum, she has been teaching two classes mathematics and has
been the teacher-in-charge of one of the two classes. In October 2004, she presented a demonstration class in the
annual meeting of the Northeastern Mathematics Education Seminar. The school where she works is making a
teaching experiment in which students are divided into multi-levels according to their mathematics ability.
As one of the leadership teachers in the district and the leader of the mathematics teaching group of the school,
Teacher B has nine years of teaching experience. Since 2003 when she started her experiment on the new course,
she has been teaching two classes mathematics and has been the teacher-in-charge of one of the two classes. In
April 2004, she won the first prize in the all-China evaluation activity for mathematics teachers in junior middle
Teacher C has ten years of teaching experience, she is one of the leadership teachers in the district, the leader of
the grade and the leader of mathematics teaching group of the grade. She started the new course experiment in
Teacher D has 2 years of teaching experience. In 2003 she started the new course experiment and ever since she
hasbeen teaching two classes mathematics and has been the teacher-in-charge of one of the two classes.
2.4 Data Collection
Between September and December, 2004, we made a one-week continuing observations of and interviews with the above four teachers respectively. In order not to lose any information, all the pre-class and post-class interviews were audio taped and all the teaching processes observed in class were video taped with their consent. The teaching process analyzed after each time of video taking and then a post- class interview is conducted. The audio record of each interview was then dictated into words, which is added to it with notes, date and environment when the video was taken.
After the repeated analysis of what the teachers said and how they behaved in class teaching, the main factors that affect the improvement of behaviors of the teachers are discovered gradually. The factors described below are mentioned by at least two of the teachers, who have identical opinions of the same factors. Factor 1: The Workload Is Too Heavy for a Teacher In-Charge-Of aClass
Of the four teachers interviewed, three are teachers-in-charge. All of them mentioned in the interview that much of their time is spent on their work as a teacher-in-charge of a class.
Teacher A: “Every day I take care of my students outside of classes as well. The management of the school is very
strict. Scores are deducted from my class when something wrong happens, therefore I cannot be at ease in the
office, even when the teaching group is preparing lessons together.”
Teacher B: “Nearly all the mathematics teachers in our school are teachers-in-charge of a class. Every day we
must be in the classroom when the students have self-study in the morning and afternoon. It takes us a lot of time. In addition, every day we have to deal with a lot of trifles of the class. Sometimes we cannot have our own time at
home in the evening, because we must communicate with the students‟ parents or answer their phone calls.”
Teacher A: “Besides teaching during the daytime, I have to deal with the problems of my class and all the routine
affairs assigned by the school. If I want to prepare my lessons perfectly, I have to work late into the night.”
Furthermore, all of them mentioned that they must spend a lot more time studying the new textbook. And the new instruction method requires that the teachers should spend more time on preparing teaching aids and learning aids before teaching. Also,there are lots of open questions in the homework that take more time for the teachers to correct.
Factor 2: Students’ Ability
The school where Teacher A works is conducting a teaching experiment on students who are divided into levels according to their learning ability, i.e.the teaching classes are formed according to the students‟ performance of the
subject. The classes taught by Teacher A belong to two levels. One is Level A and the other is Level B. When asked why Level A class and Level B class are taught with different teaching behaviors, she said: The content of the new textbook is more favorable for good students. For the students with a lower score, they are just funny. If you ask the students what they have learned, they will tell you they have only seen something funny but nothing from the mathematical point of view. For a lower-level student, you must teach her one if it is one, and two if it is two. Only in such a case can she get a score. In Level A class, if the students can understand, you may leave the problem for them. But in Level B class, you have to give them a more detailed explanation. A problem needs to be explained bit by bit.” “ The teachers who teach students of Grade 8 do not have so many problems as we do,
because their students are much cleverer. Whenever you raise a question, the students will response quickly. But the students we are teaching are not so smart as the current Grade 8 students. When our students saw that the exhibition board showing the work of that class was good, they also made one, but it was not so good.”
Teacher B believes: “Bright children can learn from games, because they are bright. Slow children are only interested in the fun, and we have to explain a lot in the end.”
When a teacher talked about the benefit she got from the cooperation with her colleagues, I asked: “ Have you
ever thought that this cooperative method can be used in your teaching?”
Teacher A answered: “It should be helpful. It should be useful if the students can take it seriously. But the students
do not think deeply or seriously. They can not concentrate in class. If you let them work together, What they think is that they can talk something unrelated to the work .That is difficult to control.”
I asked further: “ Why don‟t they think deeply or seriously?”
The teacher answered: “ This is what I cannot resolve. This is brought forward from the primary school. It is caused by primary education, That is why they do not have a good study habits.”
Factor 3: Various Examinations
In the interviews, all the teachers repeatedly mentioned that it is all kinds of and all levels of examinations that have constrained their choice of teaching behaviors in class.
Teacher C: “You give the students an opportunity to work out the solution to a problem by themselves, and
probably it is good for them to understand new knowledge, but if they have not mastered the knowledge completely, what will they do in the examinations?”
Teacher B: “The students like to use their calculators very much, so it is obvious that their manual calculating ability is not as high as that of the students before. What can they do if they are not allowed to use calculators in
examinations in the future?” “I heard it shall not be allowed to use calculators in the compulsory nine year middle school graduation examinations next year, so now I have stopped the students from using calculators.” “The new
course requires less ability of inference proof. However, can the problems to be solved in the future examinations be of the same level?”
Additionally, the supplementary materials for students also affect the teachers‟ behaviors. Some teachers fail to teach the students according to the requirements of the new textbook, one of the reasons is that the supplementary materials of the students have some exercises that are beyond the required range of the new textbook. Therefore, the teachers tend to think that more explanations in class are better than fewer explanations. Basically speaking, this also means that a pressure is imposed on teachers by the examination.”
Factor 4: Class Size
When talking about group activity in class, all the four teachers thought that there are too many students in each class to organize group activity.
Teacher A: “ The students are too many, that‟s why a lot of activities designed in the new textbook cannot be done
in class. It is very difficult to control the situations when they are free to do the activities, and the class is out of control.”
Teacher B: “It will be easier to organize activities and the discussion will be more fruitful if they are all good
students. But the difference between the ability, study habits and self-control of the students in the same class is too big, so it is difficult to organize them.” “ The poor students think that they are free to talk about anything in
the discussion, so it is difficult to maintain class discipline.”
Factor 5: Contents and Requirements of Teaching Do Not Match the Teaching Hours
The new course stresses the students‟ participation and experience while they are acquiring knowledge. (参与或体
验知识的发生发展过程), However, when compared with the syllabus, the contents in new curriculum have not been reduced clearly. Furthermore, the teachers are just in a phase to explore new teaching techniques, therefore it often happens that they cannot finish their teaching tasks. All the four teachers interviewed mentioned that the teaching hours are not sufficient.
Teacher A: “Some of the problems are open to such an extent that the students will argue about them endlessly. Normal teaching tasks cannot be fulfilled in the short 45 minutes”, “I intend to let the students discuss some
contents freely, but they cannot have any result in a class. For example, „the conditions of similarity triangles‟ can be discussed among the students themselves. It is not necessary to teach as it is arranged in the textbook, i.e. to consider equal angles in the first class, to think about three corresponding sides in proportion and two corresponding sides in proportion with equal included angles in a second class and so on and so forth. But the current situation is that the students could possibly reach no conclusion in the free discussion in class, because their schedules are different.” Teacher B said: “ The existing textbook calls for students‟ activities in almost every
class, either think over something, or discuss something, or do something by hand. Once the students begin such activities, the teaching tasks shall probably not be fulfilled.”
Factor 6: Teaching Resources Are Not Sufficient
All the four teachers mentioned that every time they organize hands-on activities, they have to spend a lot of time looking for and making teaching aids. They hope to have readily-made teaching aids and learning aids. In addition, the students are lack of supplementary materials that are in conformity with the new course. A vast majority of the materials on the market are concentrated on training the students‟ skills of resolving problems, therefore the teachers must spend a lot of time and energy searching for or developing some exercises to bring up the students‟
ability to solve problems.
Factor 7: Cognizance of Teaching and Learning
To manipulate, to think independently, to discuss and exchange and to sum up are the main ways of teaching in class with students‟ participation, and is the important cognition process for students to realize creation and construction of significance. But in the following statements, it can be seen that the teachers are still short of complete cognizance of it.
Teacher A: “The students are very much interested in practicing by hand, but it‟s a waste of time. Some of the students only play. When you ask them what they feel about it, they would say nothing.”
Teacher B: “When you want the students to make a summary by themselves, they just cannot come to the point,
time is wasted when they turn about here and there. Very few students can make a good summary, so at last the teacher has to give them an exact conclusion.”
Teacher C: “ The research on ways of thinking gives results too slowly. Since it is something recessive, it could be
better to do more exercises.”
Teacher D said: “She doesn‟t understand even if I explain it, let alone exploring by herself.” “It is good to let the students discuss, but in some of the groups there is only one student speaking, and nothing can be discussed in some groups, they still do not understand what they did not understand, so at last I have to explain it to them in detail. ”
Factor 8: Previous Teaching Experience
In the process of sorting the data, we discovered that the teachers use different techniques to teach different contents. As for the new teaching contents newly added in this curriculum reformation, most of the teachers will use the technique designed for the new textbook (at least formally). But for some traditional contents, those included in the syllabus, most of the teachers just use to the traditional teaching method again. Teacher B: “Some problems are discussed among the students at the beginning, but after I walk around the classroom, no result is achieved, so I wonder if I can finish my teaching task and I start my explanation again.”
Teacher C: “The student can‟t learn anything in the exploration if he can‟t understand what the teacher explains to him.”
Teacher D mentioned: “ It is hard to control the students‟ activities in class. It will affect the teaching schedule, so
it is easier to keep the teaching rhythm by my explanation.”
Factor 9: The System for Evaluation of Teachers
All the four teachers talked of the influence on the teaching in class produced by the evaluation of teachers made by the school. For example, Teacher A: “The principals of the school just look at students‟ score, they do not care
about your teaching methods. You will be a good teacher only if your students get high scores in the examination.”
Teacher B: “High scores are enough, no matter how you teach. All kinds of evaluations of teachers are based on the marks of the students.” Teacher C: “It‟s merely a nice but false appearance. What will happen if the score drops at the end of the term? The principal will be unhappy, and the parents will be unhappy. The class was just so good, but after you teach them…so we have to gaze at the marks of the students every day.” “The principal are interested in nothing but your score. A high score can make everything good. That‟s why we are only concentrated
on the marks of the students.”
Factor 10: Hardware Conditions
All the existing hardware conditions of the school have influence on the teaching behaviors of the teachers. In the interviews, I have inquired about the teachers‟ comments on CAI. They all agree that computer-aided instruction
is good for increasing the students‟ interest and providing more information. However, they all say that the
existing computers cannot meet the requirement for teaching. There are very few chances to have a class in the multi-media classroom. It is apparent that the existing conditions of schools limits the teachers‟ awareness of modern information technology and the formation of their operating skills.
4，Discussion and Conclusion
Based on the interviews, observations and analysis, we have summed up the above ten factors that are hindering the execution of new mathematics curriculum in junior middle schools. Some of the factors are those that are discovered by the teachers themselves. Some are obtained after analysis of the teachers‟ behaviors and their understanding. Besides these, are there any further factors hindering the teachers‟ execution of the new course? For this purpose, we shall make a further analysis by means of Cognitive Dissonance Theory. 4.1 Theoretical Basis of the Analysis
Cognitive Dissonance Theory was founded by Leon Festinger, a famous American social psychologist, in 1957.
The theory has brought significant influence to the field of social psychology. The essential concepts of the theory are “cognition” and “cognitive dissonance”. The so-called “cognition” refers to everything that a person can
realize, which may be a person‟s cognition of his own behavior, his own psychological state and the
characteristics of his personality, or may be his cognition of external objective affairs(1；, such as a teacher‟s
cognition of his or her teaching concept and the understanding of his or her teaching behavior. The so-called “cognitive dissonance” means that if a cognitive element leads to the negative of another cognitive element, the two cognitive elements shall be distorted. For instance, if a teacher knows that the new course encourages students‟ exploration by themselves, exchange and cooperation, and he still uses the explanatory mode with new
curriculum, then he has a cognitive dissonance in his mind.
In terms of cognitive dissonance, the theory has presented two basic assumptions: (1) “ The distortion is caused by the psychological malaise, which drives people to reduce the distortion with effort to reach a balance.” (2) “ When there is a distortion, apart from making efforts to reduce it, people will positively avoid the scenes and information which may increase the distortion.” (1；.
In order to reduce or eliminate the distortion, people generally use three methods as follows: The first is to change the behavior so that it is in conformity with the attitude and therefore eliminate the distortion thoroughly; the second is to change the attitude so that it is in conformity with the behavior and therefore eliminate the distortion thoroughly; and the third is to introduce a new cognitive element so that it is coordinated with one of the cognitive elements, and increases the importance of this cognitive element in the distortion and therefore relatively reduces the importance of the other cognitive element to reduce the extent of distortion as a whole(1；.
4.2 Cognitive Dissonance of Teachers
From what is observed in class, the four teachers involved have tried to a different extent the teaching behavior encouraged by the new course. Their operating levels are basically at a mechanical operating level. After they have tried the new teaching behavior in class, the teachers believe that the new behavior results in disorder of the class, the teaching schedule being out of control, nothing learned by students and possibly more serious polarization. This means that the teachers have realized that the new behavior is not in disaccord with their original teaching belief. This “disaccord” is the major form of cognitive dissonance of the teachers at present.
4.3 Possible Route to Reduce or Eliminate the Cognitive Dissonance
According to the theory, when the teacher has realized that his new behavior is in distortion with the original teaching concept, he will try every effort to reduce or eliminate the distortion. In the following context, we shall probe into the possible routes for the teachers to reduce or eliminate the distortion from three aspects. 4.3.1 Abandon or Parry the Ttrial of New Behavior
Presently, cognitive dissonance mainly emerges between the new behavior and the original teaching belief. Among the three methods in the theory for reducing or eliminating the distortion, to change the behavior means to abandon the trial of the new behavior, which should be an easy way to reduce the current distortion. As viewed from the present actual teaching, some teachers have returned to the original state of teaching after a period of execution of the new course. So it can be seen that this method is really an effective method which the teacher can use to eliminate the distortion.
4.3.2 Introduction of New Cognitive Element
As viewed from what has been discovered in the research, when facing the distortion caused by using the new behavior as required by the new course, all the four teachers have cited a lot of objective reasons as the basis for their argument. This type of behavior in their argument falls into the third method for elimination of the distortion, i.e. to introduce new cognitive element. In other words, the above-said objective reasons are the reasons why the teachers introduce new cognitive elements which are identical to their original behaviors (such as “to fill the class with the teacher‟s explanation” and “to put the class under the teacher‟s control”). Through the introduction of
these new cognitive elements, the number of cognitive elements that are identical to the original teaching beliefs is increased, and the proportion of the two types of cognitive elements is changed, as a result, the extent of cognitive dissonance is reduced. Even though this method can in no way eliminate the distortion thoroughly, it can reduce the extent of the distortion temporarily and relieve the teachers of their psychological pressure. So it is clear that to introduce new cognitive elements is also an effective method for teachers to use to eliminate the distortion. 4.3.3 To Change the Attitude
According to this theory, the third method for eliminating distortion is to change the attitude. Now let‟s probe into the feasibility for teachers to adjust the cognitive dissonance.
One of the important contributions of Cognitive Dissonance Theory to the social psychology is that it has fully affirmed the decisive function of behavior to the movement of cognitive contradiction and discovered the relations between new behavior and cognition. That is, the behavior is changed first and the concept is changed later with disaccord effect as the medium, and it is behavior that makes external reality re-emerge through cognition, which leads to cognitive disaccord. Therefore, the change to cognition is not the direct result of the coordinating effect, the purpose of which is merely to make the behavior significant so that it is rationalized.
This is to say, against the background of course reformation, once the teacher has tried the new behavior encouraged by the course reformation, his understanding of the new behavior will enter into his original world of cognition. At this moment, the understanding of the new behavior will be in conflict with his original teaching concept, and therefore the balance of the original world of cognition is broken, that is, cognitive dissonance is produced. In view of the identical psychology which people seek after cognition, the teacher will endeavor to give a reasonable explanation to this new behavior in order to reduce or eliminate the distortion. It should be noted that the explanation of the new behavior may be positive or negative. If the teacher can get positive support, he will try and improve this behavior continuously, realize the positive function of the behavior, complete the process of creating his own concept of teaching the new course, and therefore complete the change from the old to the new teaching concept. Meanwhile, the cognitive dissonance is eliminated thoroughly. Without positive external support, the teacher will give a negative explanation to the new behavior, and therefore he will parry or abandon the trial of the new behavior.
The above analysis results in two viewpoints: firstly, the relations between behavior and conceptual change are clarified, i.e. behavior is changed first and concept is changed later; secondly, the change in behavior is a positive way for the teacher to eliminate the current cognitive dissonance.
4.4 The Root Cause Affecting the Teachers’ Execution of the New Course Is Shortage of Good Social
Course reformation is the process to abandon the original course concept and behavior and to unify the new concept and the behavior. This process will definitely start from breaking the balance between the original concept and the behavior and proceed to establishing the balance between the new concept and the behavior. The schematic diagram below is a brief description of the process from the original balance to the new balance. To try the new behavior is the first step to change the teaching behavior. Once a new behavior is tried, a cognitive
Abandon new behavior
Try a new Cause cognitive Reduce or
eliminate behavior dissonance Explain the new behavior dissonance positively
distortion between the new behavior and the original concept will be caused. Then the teacher will make effort to reduce or eliminate this distortion in such a way, either to abandon the new behavior or to introduce new cognitive elements, or to emphasize the positive aspect of the new behavior. When the teacher chooses positive explanation of the new behavior as the route to eliminate the distortion, he will try the new behavior continuously and feel the new course concept contained in the new behavior. And finally, a balance shall be established between the new behavior and the new concept.
In the above-mentioned process, when the balance between the new behavior and the new concept is established, the route the teacher chooses to reduce the distortion is a critical link related to whether he can try the new behavior for the second time. According to Cognitive Dissonance Theory, “To obtain other people’s consent and
support for establishing a social reality is one of the main methods for a person to change his cognition when he is facing the pressure to change.” This is to say, the support of the school leader and the students‟ parents, the mutual help of the colleagues and timely guidance of specialists and so on can have positive influence on the teacher for his positive explanation of the new behavior. Therefore, the social environment where the teacher is situated (school, teaching group) is the direct factor that affects the change to the teacher‟s behavior.
Leon Festinger. A Theory of Cognitive Dissonance, Stanford University, Stanford, Calif., 1957. Chen Xiangming. Qualitative Research Techniques, Education Science Publishing House, 2000 Mary Kay Stein, Margaret Schwan Smith, Marjorie A. Henningsen, and Edward A. Silver Implementing
Standards-based Mathematical Instruction: A Casebook for Professional Development Teachers College Press