TEACHERS’ AND STUDENTS’ ATTITUDES TOWARDS MATHEMATICS …shodhganga.inflibnet.ac.in/bitstream/10603/5444/10/10_chapter 6.pdf · TEACHERS’ AND STUDENTS’ ATTITUDES TOWARDS MATHEMATICS

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CHAPTER 6

TEACHERS’ AND STUDENTS’ ATTITUDES TOWARDS MATHEMATICS

6.1 INTRODUCTION

This chapter raises the issue of the relationships between students’

mathematics achievement and the attitudes of both the student and the teacher toward

mathematics. There is now a widespread recognition that affective factors play a

critical role in teaching and learning of mathematics. (Mcleod 1992, 1994). A number

of researchers have investigated the relationship between affective and cognitive

domains. In general attitudes, beliefs and emotions are the major descriptors of the

affective domain in mathematics education. Traditionally mathematics education

researchers have taken the relationship between attitude towards mathematics and

achievement in mathematics as a major concern in their research work. Aiken (1970)

referred to attitude as a learned predisposition or tendency on part of an individual to

respond positively or negatively towards some object, situation, concept or another

person. Neal (1969) defined Attitude towards Mathematics as a tendency to engage in

or avoid mathematical activities, a belief that one is good or bad in mathematics and a

belief that mathematics is useful or useless.

In both theory and practice a strong relationship between Attitude towards

mathematics and Achievement in mathematics has been taken implicitly for a long

time. Hazma Mukhtar (1952) demonstrated the relation of motivational and attitudinal

factors to the problems of learning mathematics. Behr A N (1973) , Rajput( 1984),

Singh (1986), found attitudes to be related to mathematics achievement. Factors

predominant among school failures studied by Jain (1979) were mathematical

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background, attitude towards mathematics and low motivation. Tuli (1979) found

aptitude for mathematics and achievement in mathematics were significantly and

positively related to mathematical creativity.

Students' concerns about mathematics can significantly affect their ability to

learn and understand the subject. Furthermore, their anxieties and attitudes may

greatly affect how they perceive their own mathematical competence (Hopko R. D.

1998). For instance, students may perceive mathematics as an incomprehensible set of

abstract procedures and methods to follow, not being aware that there are reasons

underlying these methods. Frustration due to the lack of in-depth understanding may

discourage students from pursuing studies in mathematical sciences. Through

observations and interviews with high school students as they were solving

mathematical problems, Schoenfeld (1985) concluded that part of the problem-solving

process is influenced by students' beliefs about the nature of mathematical knowledge

and learning. The affective factor of math anxiety is greatly related to mathematics

achievement in the negative direction. Gender is also considered as a basic factor

which is largely related to both affective and cognitive math anxiety. Ho. H. Senturk

et al (2000),Saha (2007) conducted a study on gender, attitude to mathematics,

cognitive style and achievement in Mathematics. It was found that all the three

contribute to statistically significant difference in achievement in mathematics.

Thomas (2006) conducted a study to determine the Attitude towards Mathematics and

achievement by combining co-operative learning strategies with instruction delivered

using an Integrated Learning System (ILS).

Teachers are the key to improving mathematics education. The preparation,

certification, ongoing professional development and attitude of teachers define the

outcome of their teaching experience on their students. Research into the


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mathematical understandings of teachers indicate that even when teachers (both pre

service and in-service) appear to be adequately prepared, their mathematical

knowledge base is shallow and compartmentalized (Ball, 1990; Bloom, 2001; Bryan,

1999; Post, Tirosh D and Graeber, 1990). A rich, well-connected knowledge base

allows teachers to conduct the kind of inquiry and discourse that students need to

develop to have a proper understanding of mathematics concepts. McSheffrey

K,(1992).suggests that teachers' ability to connect math to real-life situations affects

female students' math experience. The influence of teachers' behaviors on students

(teachers who made students feel important, cared for, etc...), the influence of parents

(their support or lack of support), personal decisions regarding attitudes towards math,

and the attitudes of boys toward girls were found to be factors affecting the

achievement of school students in mathematics. Teachers' attitudes are almost as

important as those of students. Reports show that minority teachers may themselves

express negative attitudes about math, encouraging their students to pursue higher

levels of education but not in math or science. Majority teachers may tend to shield

minority students from failure by holding lower expectations and not recommending

higher-level math classes. (Cocking and Chipman 1989).Researchers have indicated

that teacher attitude may affect student achievement.(Brophy and Good 1974,Cooper

and Good 1983)

Attitude towards mathematics among students does affect achievement in

mathematics.(Aiken LR,1971). If school students have a strong belief that

mathematics is not useful in their lives or future careers, they may resist spending

time or effort needed to be successful at it .Several investigators have developed

scales to measure attitude towards mathematics and also discovered a relation

between attitude and achievement. Kolhe (1985) compared boys and girls and urban


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and rural population on attitude towards mathematics and indicated significant

differences between the attitudes of urban and rural students towards mathematics

irrespective of sex. Mishra (1978) developed a scale to measure attitude towards

mathematics and indicated a relationship of attitudes with some socioeconomic

factors. Children from better homes had a favorable attitude when compared to

children from poor homes. K. K. Perkins, W. K. Adams and others (2005) found

positive correlations between particular student beliefs and conceptual learning gains,

and between student retention. They saw that students who come into a course with

more favourable beliefs are more likely to achieve high learning gains

Another area which has been studied is belief about future careers Pettitt,

Lisa(1995)Accordingly it is seen that middle school students do not recognize the

subjects that they must study in order to have specific careers. They tended to choose

sex-stereotyped careers when filling out the survey. Girls felt that they would be

capable of becoming doctors or veterinarians, but they did not want to have science-

related careers as adults. Boys stated the opposite. Neither the boys nor the girls

recognized the relation between the study of math and science and their future career

aspirations. Because this study indicates that girls may not realize that their preferred

future careers can require course work in science and math, it seems prudent for math

and science teachers to discuss with students the many professional fields that require

math and science.

The records of these studies highlights the significance of attitude toward

mathematics and directs the attention of mathematics educators to the relationship

between attitude and achievement in mathematics .It is seen that teachers’ personal

beliefs and experiences effect how they teach, Thompson (1992) pointed out that

there are numerous ways of interpreting the idea of a belief. Integrating the


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frameworks for change, researchers Smith, Z.S., Williams, S.R & Smith, M.E. (2005)

provided the components of a model for analysis of the essential elements and

processes of changing beliefs which included Teachers’ interests in change, the

extents to which they problematize current practices and pose possible solutions, their

activities in exploring and testing these alternative practices and their reflective

analyses of the benefits of these changes for students, leading to lasting changes in

beliefs and practices

This study seeks to find the influence of teaching practices on student beliefs

and their achievement in mathematics, the relationship between student beliefs about

mathematics and their conceptual learning in the mathematics course, the relationship

between students’ beliefs about mathematics and their decisions about whether to

continue on in mathematics in their future studies.

6.2 DATA

Attitudes of students’ and teachers’ were collected by administering a

mathematics attitude scale in a questionnaire prepared for the same purpose. The

attributes for students ’attitude towards mathematics consists of a set of 14 statements

to which students respond using a five point Likert scale. The questions related to

their self confidence in learning mathematics, the usefulness of mathematics, the

importance of conceptual understanding in mathematics, the relation between effort

and ability in mathematics, parents’ and teachers’ attitudes towards their ability in

mathematics,understanding of the classroom lecture, the perception of the students

towards their teachers liking of the subject ,the importance of mathematics in their

future career choices.


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The questions were worded both in the positive and negative sense ranging

from “strongly agree to “strongly disagree”. For the positive sense questions a value

of 5 was assigned to “strongly agree” ,decreasing values of 4,3,2,1 were given to the

other questions, where “strongly disagree was assigned the value 1. For the negative

sense questions the values were assigned in the opposite sense. The maximum score

for the students’ attitude was 70 while the minimum score was 14. The median score

was 41 so the scores between 36-46 was taken as indicating indecisive attitude. On

the basis of this students were categorized as

Scores Attitude

14-24 Highly Negative attitude

25-35 Negative attitude

36-46 Indecisive attitude

47-57 Positive attitude

58-70 Highly positive attitude

The attributes for teachers’ attitude towards mathematics consists of a set of

16 statements to which teachers’ responded using a five point Likert scale. The

questions related to their liking for teaching the subject, job satisfaction, and attitude

of the students towards mathematics, the importance of conceptual understanding in

mathematics and the usefulness of mathematics

The questions were worded both in the positive and negative sense ranging

from “strongly agree to “strongly disagree”. For the positive sense questions a value

of 5 was assigned to “strongly agree”, decreasing values of 4,3,2,1 were given to the

other questions, where “strongly disagree was assigned the value 1. For the negative

sense questions the values were assigned in the opposite sense. There were other


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questions which brought to light opinions of the teachers towards mathematics

education.

.The maximum score for the teachers’ attitude was 80 while the minimum

score was 16.A high score would likely indicate a positive attitude towards learning

and teaching mathematics by both the students and teachers. The median score was

48 so the scores between 42-54 was taken as indicating indecisive attitude On the

basis of this the teachers were categorized as

Scores Attitude

16-27 Highly Negative attitude

28-41 Negative attitude

42-54 Indecisive attitude

55-67 Positive attitude

68-80 Highly positive attitude

6.3 STATISTICAL ANALYSIS

The scales administered to the students for testing attitude were checked for

internal consistency through reliability analysis .Spearman-Brown co-efficient

formula for equal lengths test was calculated Cronbach's alpha measurement of

homogeneity was calculated. The Guttmann’s split-half technique for reliability of the

instrument was also calculated. The values given below all reveal high reliability

coefficients

Class Groups Reliability coefficients

Cronbach's alpha Spearman-Brown Guttman's split-half

VII Students .953 .945 .942

IX Students .959 .946 .945

VII Teachers .927 .937 .933

IX Teachers .751 .887 .887


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The combined score of the students of classes VII and IX have been taken as

the dependent variables. The student attitude and teacher attitude were taken as the

probable independent (predictive) variables.

The mean and standard deviation of the combined scores were calculated,

ANOVA ( Analysis of Variance) has been used to test the variance in the mean of the

combined score for the different classes of students’ attitude and teachers’ attitude

This has been followed up with a post reliability test to asses the consistency

of the results. The results of the test are as follows

Variation of combined weighted scores (Mean+SD, count) (Mathematical

achievement, concept and ability) of students of various schools of Bongaigaon

district grouped by students’ attitudes have been shown below . Values having

different superscripts (a,b,c,d, e ) differ significantly (P<0.05) between groups/levels

in a class.

Attitude group (Students)

class Highly Negative Negative Indifferent Positive Highly Positive F

VII

Mean+SD 11.377 a ± 3.8 15.78 b ± 5.08 26.107 c ± 7.69 38.358 d ± 9.62 50.06 e ± 8.044 153.66 **

N 13 72 95 84 26

IX

Mean+SD 8.35 a ± 4.2 16.6 b ± 6.42 26.77 c ± 6.43 41.81 d ± 10.9 57.1 e ± 9.21 205.15 **

N 23 66 79 94 28

TABLE 6.1 Mean scores of students divided on basis of student’s attitude

0

10

20

30

40

50

60

Scores

VII IX

Class

Achievement Scores

Highly Negative

Negative

Indecisive

Positive

Highly Positive

Figure 6.1 Mean scores by student’s attitude


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class

Attitude Groups(Teachers)

1(Negative) 2(Indecisive) 3(Positive) 4(Highly Positive) F

VII

Mean+SD 13.51 a ± 5.54 23.49 b ± 10.397 32.47 c ± 11.48 44.07 d ± 12.60 59.818 **

N 4 8 14 3 3

IX

Mean+SD a ± 22.91 b ± 13.88 33.22 c ± 14.50 51.09 d ± 11.78 52.73 **

N 12 14 3

TABLE 6.2 Mean scores of students divided on basis of teacher’s attitude

Figure 6.2 Mean scores by teacher’s attitude

Following ANOVA , correlation co-efficients between attitudes and combined scores

of students were derived with the following results. Co-relation is significant at P <

0.01 level

Pearson Correlation

Sig. (2-tailed)

Student Attitude Teacher attitude

Class VII-Combined Scores .857* .650*

Class IX-Combined Scores .888* .502*

TABLE 6.3 Correlation between attitudes and combined score

0

10

20

30

40

50

60

Scores

VII IX

Class

Achievement Scores

Negative

Indesisive

Positive

Highly Positive


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Lastly stepwise regression has been performed to carry out a choice (subset) of

independent variables from the set of predictor variables taken initially. All predictor

variables were taken initially and tested one by one for statistical significance,

deleting any that were not statistically significant.

Taking the dependent variable Y as the combined score of the students and X1

students’ attitude and X2 teachers’ attitude as the independent variables the

regression equation for both class VII and class IX is assumed to be of the form

Y = α + ß1 X1 + ß2 X2 +ε where α is the intercept and is a constant, ß1, ß2 are the

slopes and ε the error term which reflects other factors influencing Y

Regression has been carried out on the data of the class VII and class IX .

Model Summary for class IX

R R Square Adjusted R Square Std. Error of the Estimate

.893 .797 .796 7.36510

Predictors: (Constant), STUDENTS’ ATTITUDE,TEACHERS’ ATTITUDE

R2 = .797 implies that regression explains 79.7% of the variation on the combined

score due to the two predictor variables, student attitude and teacher attitude

ANOVA

Sum of Squares df Mean Square F Sig.

Regression 61247.244 2 30623.622 564.545 000

Residual 15568.247 287 54.245

Total 76815.491 289

Predictors: (Constant), ), STUDENTS’ ATTITUDE,TEACHERS’ ATTITUDE

Dependent Variable: COMBINED SCORE

F= 564.54 is highly significant at P<.001


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Coefficients

Unstandardized Coefficients Standardized Coefficients T Sig.

B Std. Error Beta

(Constant) -35.902 4.050 -8.864 .000

STUATT 1.178 .042 .837 27.800 .000

TEACHATT .292 .082 .108 3.571 .000


The individual contribution of each predictor to the model is given by their coefficient

B. The positive value of the co-efficients for student attitude and teacher attitude

indicate positive relationships. An increase in the value of each of these predictors

will show an increase in the combined scores of the students. For this model the t

values for student attitude and teacher attitude are highly significant (P<.001). The

standardized Beta values show that the attitude of the student towards mathematics

has a higher impact than the attitude of the teacher on the combined scores.

Hence the regression equation for class IX is given by

Y = -35.902 ++ .837 X1 +.108 X2

That is , Combined Score= -35.902 + .837 (Students’ attitude) +.108(Teachers’

attitude).

Fig 6.3 Graphical representation of regression equation for Class VII


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Model Summary for class VII

R R Square Adjusted R Square Std. Error of the Estimate

.867 .752 .750 6.78018


R2 = .752 implies that regression explains 75.2% of the variation on the combined

score due to the two predictor variables, student attitude and teacher attitude

ANOVA

Sum of Squares df Mean Square F Sig.

Regression 39930.564 2 19965.282 434.303 .000

Residual 13193.627 287 45.971

Total 53124.191 289



F= 434.30 is highly significant at P<.001

Coefficients

Unstandardized Coefficients Standardized Coefficients T Sig.

B Std. Error Beta

(Constant) -24.610 2.376 -10.359 .000

STUATT .939 .048 .748 19.491 .000

TEACHATT .251 .057 .170 4.416 .000


The individual contribution of each predictor to the model is given by their coefficient

B. The positive value of the co-efficients for student attitude and teacher attitude

indicate positive relationships. An increase in the value of each of these predictors


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will show an increase in the combined scores of the students. For this model the t

values for student attitude and teacher attitude are highly significant (P<.001). The

standardized Beta values show that the attitude of the student towards mathematics

has a higher impact than the attitude of the teacher on the combined scores.

Hence the regression equation for class VII is given by

Y = -24.610+ .748 X1 +.170 X2

Combined Score= -24.610+ .748(Students’ attitude)+ .170 (Teachers’ attitude).

Fig 6.4 Graphical representation of regression equation for Class IX

Examination of the data on future studies of mathematics in relation to the attitudes of

the students revealed that negative attitudes hamper the choice of mathematics as a

subject in higher studies

0%

20%

40%

60%

80%

100%

Positive Negative

Attitudes

Response to future study of mathematics

Negative

Indecisive

Affirmative

Fig 6.5 Response to future study of mathematics based on attitude


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6.4 DISCUSSION

The above results are consistent with the theory that attitudes are a factor of

student learning.The result of this study is in keeping with other studies of a similar

type which are conducted on how performance is affected by attitude. Xin Ma and

Jiangmin (2004) conducted a study to determine the causal ordering between Attitude

towards Mathematics and achievement in mathematics of secondary school students.

Results showed the achievement demonstrated causal predominance over attitude

across the entire secondary school. Studies carried out by by Yara (2009)showed that

attitude of students can be influenced by the attitude of the teacher and his method of

teaching. These factors greatly accounted for the students’ positive attitude towards

mathematics and that, without interest and personal effort in learning mathematics by

the students, they can hardly perform well in the subject These findings are similar to

those of Thiagarajan et al. (1995) who found significant correlation between teachers

attitudes and academic achievement of the children. Similarly Gyanani and Agarwal

(1998) found that classroom climate, teachers’ behaviour and attitudes account for

variations in the academic achievement of the pupils.

The above model addresses the issue of how student performances are affected

by teachers’ and students’ attitudes towards mathematics. There is seen that there are

significant differences in the means of the combined scores for different attitude

levels .Thus the associations among the attitudes of students for both class VII and IX

and their attainment in mathematics is significant The students and teachers’ attitude

towards mathematics are important factors in mathematics education. The attitudes of

the students towards mathematics are themselves influenced by other factors which

are again interrelated like school environment providing opportunities for intellectual


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growth , parents’ influence, social environment the importance they attach to

mathematics in the growth of their career, motivation, peer group effect.

It is worth noting the majority (63.5%) of the students with positive attitudes

towards indicated they would pursue mathematics in their future studies, while 30.7%

remained indecisive and only 5.8% did not want to pursue mathematics later on. On

the other hand there is predominance ( 81.3% )of students with negative attitudes

towards mathematics indicated they would not take up mathematics as a subject in

their future studies, the rest remaining indecisive. This would suggest that attitudes

towards mathematics have an impact on the future study of the students. This in turn

also reflects their career choices. What is important is that school students may not

realize the role of mathematics as it is used in many career areas like physical science,

life sciences, social sciences, actuarial science, technical fields and even medicine.

The competition and the opportunities in the career world become a serious problem

for students if they do not have a good knowledge of mathematics, because then they

are excluding themselves from the many career paths that need mathematics.

ANOVA showed that the average of the combined scores was not the same for

all groups .There is seen that there are significant differences in the means of the

combined scores for different attitude levels both in case of students and teachers.

Also a study of the trends in the relationship between attitudes and combined

mathematics scores show that positive attitudes on the part of the student and teacher

towards mathematics show higher combined scores in mathematics. There is a high

positive correlation between attitudes of students and their scores in mathematics and

a moderate positive correlation between attitudes of teachers and the scores of their

students in mathematics. This suggests that more positive attitude creates the


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opportunity for learning and motivation that leads to success in mathematics

performance.

Comparison of means between different groups which show significant

differences indicate that negative attitudes discourage, limit, and even prevent

learning, positive change, and growth. Research has indicated that student attitudes

and achievement-related behaviors are important in understanding the causes of

disparity in mathematics achievement .The basic premise underlying any teaching

therefore should be that the pupil has the capacity to learn and change and wants

these things to happen regardless of past performance.

However this relationship between attitudes and mathematics achievement is

not simple and often interdependent. The relationship between attitude and ability is

seen to be dynamic and interactive. Highly positive attitudes indicate strong

performances in mathematics; on the other hand they may also be the effect of doing

well in mathematics. This interdependent relationship of interest in mathematics

affecting achievement and high achievers showing positive interest has been seen in

studies by Koller O and Baumert J (2001).Regardless, the strong link between them

indicates that attitudes are important outcomes in themselves. The more students

succeed in mathematics the more likely they are to believe that they can succeed; the

more students believe they can succeed the more engaged they will become with

learning mathematics.

Teachers and parents and guardians should promote positive attitude towards

mathematics among school children. Attitudes towards mathematics are important as

they are associated with actual achievement as well as enrollment in higher level

mathematics courses. As is seen there are external factors of mathematics learning

like school environment and socio-economic status. Though attitude itself is


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dependent on these and other factors, it is also an internal and individual quality. A

conscious effort on part of the teacher and parents can bring about a constructive

change in the attitude towards mathematics of the students. This more positive

attitude creates the opportunity for learning and motivation that leads to success in

math regardless of past performance. This together with the important role

mathematics education plays in the school education of a child makes it necessary to

undertake measures to positively affect attitudes and achievements in school level

mathematics.

------------------------------------------------------------------------------------------------------- Discussion of this chapter is based on our paper entitled “A Study on Attitudes Towards Mathematics and Its Impact on the Mathematics Achievement of School Students” which is published in the International Journal of Mathematics Education, Volume 1, Number 1 (2010), pp-1-12.


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TEACHERS’ AND STUDENTS’ ATTITUDES TOWARDS MATHEMATICS …shodhganga.inflibnet.ac.in/bitstream/10603/5444/10/10_chapter 6.pdf · TEACHERS’ AND STUDENTS’ ATTITUDES TOWARDS MATHEMATICS