ATTITUDE OF SECONDARY SCHOOL STUDENTS TOWARDS MATHEMATICS IN RELATION TO THEIR PROBLEM-SOLVING ABILITY IN MATHEMATICS By Sourav Paul[1]

Abstract

The present investigation has been designed to verify the strata-wise (sex and caste) comparison between the variables like Problem-solving Ability in mathematics and Attitude towards Mathematics. It also enquires the interrelationship between the variables and how Problem-solving Ability in mathematics can be predicted from Attitude towards Mathematics. It is found from the study that in case of Problem-solving Ability in mathematics, gender factor plays a significant role but in case of Attitude towards Mathematics almost no significant difference has been observed between the cross sections of the strata. Analysis of the study reflects that the studied variables are highly associated to each other.

Keywords: Attitude, Attitude towards Mathematics, Problem-solving ability.

INTRODUCTION

In modern psychology, attitude is crucial, distinctive and important concept. Attitude connotes a neuropsychic state of readiness for mental and physical activity. A lot of research has been done on attitude towards mathematics, but theoretically the concept needs to be developed. A simple definition of attitude, that describes it as the positive and negative degree of affect associated with a certain subject. According to this point of view the attitude towards mathematics is just a positive or negative emotional disposition towards mathematics (Mcleod, 1992; Haladyna, shaughnessy J. & Shaughnessy M, 1988).

The issue of underachievement in mathematics has come to research focus of most mathematics educators. In particular, the relationship between attitude towards mathematics and achievement in mathematics had traditionally been a major concern in mathematics education research (Ma and Kishor, 1997). Neale (1969) described the relationship between the two as one of a reciprocal influence. There is also research evidence showing that students’ high performance in mathematics is not necessarily positively associated with their attitudes about mathematics and mathematics learning. There is lot of factors like fear, anxiety etc. affecting success in mathematics. (Baloglu, 2001).

Problem- solving plays a crucial role and has a special importance in the study of mathematics. A primary goal of mathematics teaching and learning is to develop the ability to solve a wide variety of complex mathematics problems (Wilson, Fernandez, and Hadaway (1993).  Stanic and Hilpatrik (1988) emphasized the role of problem- solving in school mathematics and showed a rich history of the topic. To many mathematically literate people, mathematics is synonymous with solving problems – doing word problems, creating patterns, interpreting figure, developing geometric constructions, proving theorems, etc. On the other hand, persons not enthralled with mathematics may describe any mathematics activity as problem- solving (Wilson, Fernandez, and Hadaway: 1993).Problem solving is an integral part of all mathematics learning. In day to day life and in the workplace being able to solve problems can lead to great advantages. However, solving problems is not only a goal of learning mathematics but also a major means of doing so. Problem- solving means engaging in a task for which the solution is not known in advance. Good problem solvers have a “mathematical disposition”– they analyze situations carefully in mathematical terms and naturally come to pose problems based on situations they see.

School education has long focused on problem- solving (Dillon 1982; Ramirez 2002). Cognitivism and constructivism, both of which have been providing a basic framework for school education , stressing the importance of improving students problem- solving ability , NCTM (2000 ) standards suggests that , in order to prepare for the 21st century , today’s students should identify themselves with the ability to use mathematical knowledge for problem- solving , with the ability to communicate mathematically, and with the ability to reason mathematically and a mathematical propensity .

Affective responses are seen to be extremely complex, consisting of much more than the expression of positive and negative feelings in the exhibition of confidence, they entail structures of intimacy, integrity and meta affect that promote deep mathematical inquiry and understanding. Complex networks of affective pathways both contribute to and detract from powerful mathematical problem- solving ability (de Bellis and Goldin, 1999).

NEED FOR THE STUDY:

Research has shown that students’ achievement may be influenced by attitude towards problem- solving. According to Ma and Kishor (1997), the variable “attitude” is one of the most important factors that relates to achievement. Borasi (1990) adds that the conceptions, attitudes, and expectations of students regarding mathematics and mathematics teaching have been considered to be very significant factor underlying their school experience and achievement.

A student needs to think and make decisions using appropriate strategies to solve mathematics problems (Effandi and Normah, 2009). Patton et al. (1997) propose that learning to solve problems is a primary objective in learning mathematics, as problems are an inevitable fact of life. They also said, students’ success in achieving their goals encourages them to develop positive attitudes towards mathematics and other problem solving activities. Positive attitudes are assumed to have significant relationship with students’ achievement.

Slovin (2000) stated that students who possess a positive attitude towards mathematics will succeed at higher educational and professional levels. Salleh (2004) found that students attitudes towards problem – solving are considerably favourable. Patterson et al. (2003), in their study of attitude towards mathematics, found that male students have a more positive attitude than female students.

Ishak (2000) found that there was no significant difference in mean problem-solving achievement between male and female students though; several studies show that male students perform better than female students. This performance difference is apparent in difficult subjects, such as mathematics and physics. According to Fennema (1985), males perform better than females when tasks involve the cognitive skills used in mathematics. He also stated that starting from secondary school male students demonstrate better mathematical skills than do female students. Usually, male students are able to solve implicit problems and problems that do not require specific strategies (Gallagher & Lisi, 1994). Many students believe that males are more successful at mathematics in comparison to their female counterparts.

There has been a plethora of researchers on “attitude towards mathematics”, “achievement in mathematics” and the relation between the two. No conspicuous relationship could be observed by the researchers. Problem-solving ability has natural positive relation with achievement in mathematics. Now it appears worth-studying whether attitude towards mathematics and problem-solving ability in mathematics bear any significant relation so that they can predict each other.

Past researches suggest that more research needs to be done on attitude towards mathematics and problem- solving ability in mathematics or mathematics problem- solving skills, especially between the complex chemistry of two variables and particularly in students at the secondary level. A study was, therefore, designed as “Attitude of secondary school students towards mathematics in relation to their problem – solving ability in mathematics”.

OBJECTIVES OF THE STUDY

  1. To find the score of the students in attitude towards mathematics scale.
  2. To find the score of the students in problem–solving ability test.
  3. To tabulate the scores in each test sex-wise and caste-wise, and find the corresponding mean.
  4. To determine the significance of difference in each test (sex-wise and caste-wise).
  5. To determine the inter-relationship between the two variables: attitude towards mathematics and problem- solving ability in mathematics i.e. to find the co-efficient of correlations (r) between the score obtained by the students in attitude towards mathematics scale and problem- solving ability test.
  6. To ascertain whether problem-solving ability scores in mathematics could be predicted from the attitude towards mathematics scores.
  7. To find the significance of difference in mean scores in problem-solving ability in mathematics of the students belonging to high and low attitude  towards mathematics groups.

HYPOTHESES OF THE STUDY

  1. These exists a significant difference between mean attitude towards mathematics scores of boys and that of girls.
  2. There exists a significant difference between mean attitude towards mathematics scores of general caste students and that of other caste students.
  3. There exists a significant difference between mean attitude towards mathematics scores of general caste boys and that of other caste boys.
  4. There exists a significant difference between mean attitude towards mathematics scores of general caste girls and that of other caste girls.
  5. There exists a significant difference between mean attitude towards mathematics scores of general caste boys and that of other caste girls.
  6. There exists a significant difference between mean attitude towards mathematics scores of other caste students and that of other caste students.
  7. There exists a significant difference between mean problem- solving ability scores of boys and that of girls in mathematics.
  8. There exists a significant difference between mean problem- solving ability scores of general caste students and that of other caste students in mathematics.
  9. There exists a significant difference between mean problem- solving ability scores of general caste boys and that of other caste boys in mathematics.
  10. There exists a significant difference between mean problem- solving ability scores of general caste girls and that of other caste girls in mathematics.
  11. There exists a significant difference between mean problem- solving ability scores of general caste boys and that of general caste girls in mathematics.
  12. There exists a significant difference between mean problem- solving ability scores of other caste boys and that of other caste girls in mathematics.
  13. Attitude towards mathematics scores obtained by the students was highly correlated with their problem-solving ability scores in mathematics.
  14. Problem-solving ability scores in mathematics could be predicted from attitude towards mathematics scores.
  15. The high and low achievers in attitude towards mathematics scale would respectively score high and low in problem-solving ability test in mathematics.

 

DELIMITATIONS OF THE STUDY

  1. The study considered two variables:  attitude towards mathematics and problem-solving ability in mathematics.
  2. The study was confined to students of west Bengal of Class-IX of Bengali medium schools (just promoted) under WBBSE.
  3. No. of students comprised 118 boys and 98 girls.

METHODOLGY

In the study, the population is the entire students of West Bengal who have just passed Madhyamik Examination – 2012 under West Bengal Board of Secondary Education (WBBSE) in Bengali medium and admitted in class-IX under West Bengal Council of Higher Secondary Education (WBCHSE) without considering their stream of study.

The researcher used cluster sampling in which they selected first 6 (six) districts from North and South Bengal in the ratio 1:2 randomly. Then the researcher selected higher secondary (H.S) schools from the selected districts preserving randomness as far as possible. The researchers selected 12 students from each 3 schools out of each selected district. So the sample size of the study was (12x3x6) = 216The selected districts are: Malda and CoochBehar from North Bengal and Howrah, North 24-Parganas, Purbo Medinipur and Birbhum from South Bengal.

Table 1. Strata-wise Classification of Total Sample

Caste/Sex General Caste Other Caste Total
Boys 76 42 118
Girls 67 31 98
Total 143 73 216

Tools Used:

  1. “Attitude Towards Mathematics Scale” which was developed and standardized by Dr. S.C. Gakhan & Rajni (2004), for measuring attitude towards mathematics among the students. It has in all 46 items with eight dimensions. Each item forms with five options with scores ranging from 1-5 for positive statements and 5-1 for negative statements. The five points were quantified by giving score ranging from 1 for strongly disagree to 5 for strongly agree for positive statements and reverse for negative statements. As the test was culture free and culture fair the test was simply translated into Bengali. The reliability of the scale was found to be 0.78 under split – half method. The test consists of 46 items.
  2. Problem Solving Ability Test which was developed and standardized by L.N. Dubey (2008). In this study researcher modified and restandardized the test identifying three dimensions (namely, Elementary Algebra, Arithmetic and basic Numerical Ability) and added a few new problems in the test and deleted a few problems from the main test. The final draft contained 20 items each with 4 alternative responses with one correct answer, for scoring all or none principle (0/1) was considered. The restandardized test translated into Bengali with reliability of 0.92 by test-retest method.

Collection of Data:

Typed standardized questionnaire of Attitude towards mathematics scale and Problem- solving ability test in Bengali version (adapted, translated and restandardized) were given to every selected student in a plenary session and necessary directions and examples were given at the very outset. Then the researchers instructed to students for giving responses on the given two tools within set time limit.

After completion of the test answer scripts were checked by the researchers on the basis of specified scoring key. The score obtained by each student will be tabulated. The score will be treated as data for statistical analysis for the study.

Presentation of Data:

Table-2 shows that the mean score of PSA, in case of Boys, General Caste Boys and Other Caste Boys lies above and Other Caste Girls lies lower in compare to all other strata. Other Caste showing largest variability and Other Caste Girls has lowest variability in respect to all other strata.

Table 2 also shows that mean score of ATM in case of Other Caste Boys lies above and General Caste Boys lies lower in respect of all other strata. General Caste and General Caste Boys showing largest variability and Other Caste Girls lowest variability in compare to all other strata

Table 2. Number of Students (N) Strata-wise and their Respective Mean, Median and S.D. of Problem-Solving Ability and Attitude towards Mathematics

Strata N      Mean       S.D.
PSA ATM PSA ATM
Boys 118 12.525 175.92 4.067 19.04
Girls 98 9.673 176.62 3.612 18.35
General Caste 143 11.385 175.23 4.108 20.13
Other Caste 73 10.932 178.21 4.134 15.41
General Caste Boys 76 12.566 173.08 4.113 20.19
Other Caste Boys 42 12.452 181.05 4.032 15.72
General Caste Girls 67 10.045 177.67 3.695 19.94
Other Caste Girls 31 8.871 174.35 3.344 14.35
Total Sample 216 11.231 176.24 4.113 18.69

.ANALYSIS AND INTERPRETATION OF THE DATA

It is evident from the Table 3 that there is a significant difference of mean scores of problem-solving ability in mathematics between the pairs Boys-Girls, General Caste Boys-General Caste Girls and Other Caste Boys-Other Caste Girls. So, the hypotheses 1, 5 and 6 are retained at 1% level of significance.  Other hypotheses viz. 2, 3 and 4 are rejected even at 5% level of significance.

It is evident from the Table 4 that there is a significant difference of mean scores of attitude towards mathematics between the pair General Caste Boys – Other Caste Boys. So, the hypothesis 9 is retained at 5% level of significance but not at 1% level of significance. Other hypotheses viz. 7, 8, 10, 11 and 12 are rejected even at 5% level of significance.

 

 

Table 3. The t-values between Different Strata of Problem-Solving Ability Scores in Mathematics

SL. No. Strata N Mean S.D. t-value P -value Level of Significance
1. Boys

Girls

98*

98

12.63

9.67

4.20

3.61

 

5.29

 

0.000

 

S at 0.01

2. General Caste

Other Caste

73*

73

11.12

10.93

3.90

4.13

 

0.29

 

0.773

 

NS

3. General Caste Boys

Other Caste Boys

42*

42

11.83

12.45

4.10

4.03

 

– 0.70

 

0.487

 

NS

4. General Caste Girls

Other Caste Girls

31*

31

10.29

8.87

3.51

3.34

 

1.63

 

0.109

 

NS

5. General Caste Boys

General Caste Girls

67*

67

12.34

10.04

4.21

3.69

 

3.36

 

0.001

 

S at 0.01

6. Other Caste Boys

Other Caste Girls

31*

31

12.16

8.87

4.07

3.34

 

3.48

 

0.001

 

S at 0.01

 

Table 4. The t-values between Different Strata of Attitude towards Mathematics Scores

Sl. No. Strata N Mean S.D. t-value p-value Level of Significance
1.

 

Boys

Girls

98*

98

174.2

176.6

19.2

18.3

 

-0.89

 

0.375

 

NS

2. General Caste

Other Caste

73*

73

175.0

178.2

21.4

15.4

 

– 1.05

 

0.297

 

NS

3. General Caste Boys

Other Caste Boys

42*

42

171.6

181.0

20.9

15.7

 

– 2.33

 

0.022

S at 0.05 but NS at 0.01
4. General Caste Girls

Other Caste Girls

31*

31

179.1

174.4

17.2

14.3

 

1.17

 

0.246

 

NS

5. General Caste Boys

General Caste Girls

67*

67

172.4

177.7

20.7

19.9

 

– 1.49

 

0.137

 

NS

6. Other Caste Boys

Other Caste Girls

31*

31

179.1

174.4

16.2

14.3

 

1.22

 

0.228

 

NS

* Sample size is reduced to equalize with the other stratum for the sake of conformity of the distributions.

 

Correlation and Regression:

It is found that there is a moderate (r = 0.421) linear relationship (P-value = 0.000) between the two variables viz.  attitude towards mathematics and problem-solving ability in mathematics.

                        Regression equation of PSA on ATM is

PSA = – 5.08 + 0.0926 ATM

PSA could be predicted from the scores of ATM (beta co-efficient is significant,        P < 0.01).

Table 5. Significance of Difference between the Means of Problem-Solving Ability Scores as Obtained by High-Score Group and Low-Score Group in Attitude towards Mathematics Scale

N Group M SD t – value p -value Level of Significance
30

 

High

Low

13.03

8.23

3.31

2.42

 

– 6.42

 

0.000

 

S at 0.01

From Table 5 it is evident that there is a significant difference between high and low achievers in attitude towards mathematics scale would respectively be the high and low in problem-solving ability test in mathematics.

FINDINGS

  1. Following results revealed from the testing of the studied hypotheses:
Strata Problem-solving ability in Mathematics Attitude towards Mathematics
Boys

Girls

S at 0.01 NS
General Caste

Other Caste

NS NS
General Caste Boys

Other Caste Boys

NS S at 0.05 but NS at 0.01
General Caste Girls

Other Caste Girls

NS NS
General Caste Boys

General Caste Girls

S at 0.01 NS
Other Caste Boys

Other Caste Girls

S at 0.01 NS

 

 

  1. In case of attitude towards mathematics, there is no significant difference for all caste and sexes. The significant difference (at 0.05 level of significance) on attitude towards mathematics between General Caste Boys and Other Caste Boys.
  2. The two variables are highly correlated (df = N-2, p<0.01, r=0.421)

CONCLUSION

  • Among all the strata, significant difference exists in problem-solving ability in mathematics only sex-wise. Cast has no significant role here.
  • No caste-wise difference exists in problem-solving ability in mathematics.
  • The problem-solving ability in mathematics and attitude towards mathematics are significantly correlated.

Discussion:               

In order to do more justice to the investigation, the sample size should have to be increased sex-wise, caste-wise, grade-wise. The cluster sample with more cautiously prepared standardized test could unearth the objective reality between the variables. The present study was conducted to one class level only, better validation; investigation in different class levels should have been undertaken. For several constraints the above ideal condition could not be achieved by the investigator.

The relation between attitude towards mathematics and problem-solving ability in mathematics could not be uniquely determined by different investigators Findings of the first group of investigators were proximal proportions of the students consider mathematics as a crucial subject which has relevance in their daily life. This notion needs to be sustained among students for learning mathematics .Grouws, Howald and Calangelo (1996) asserts that students’ experiences, attitude, beliefs and conception of mathematics influence their learning of mathematics. Grootenboer (2002) suggests that if students experiences of learning mathematics in school is positive then they develop a positive attitude towards mathematics and this supports in reducing mathematical anxiety, for promoting this viewpoint , the curriculum of mathematics should include concepts and topics that are pertinent and have a close connection to children’s daily life experience . With this, it is necessary to engage students in problem – solving tasks so as to provide them with the concrete experience that mathematics is effective and useful in addressing issues and concerns that come across in the daily life.

According to Anku (1996), students’ dispositions towards mathematics affect their learning. He reported that developing mathematical concepts from real – life experiences or through problem – solving promotes students interest and confidence in doing mathematics.

Aikens (1970, 1976) found only low positive correlations among elementary school children. There may be sex differences in attitude towards mathematics. Schofield (1983) found that attitude and achievement were more strongly related for boys than girls. Again the above discussion shows that relationship between attitude and mathematics achievement is not sufficiently concrete.

REFERENCES

Akinsola, M. K. (2008). Relationship of some psychological variables in predicting problem-solving ability of in-service mathematics teachers, The Montana mathematics Enthusiast, 5, No.1, 79-100.

Amirali, M. (2010).  Students’ conceptions of the nature of mathematics and attitude towards mathematics learning, Journal of Research and Reflections in Education, 4, No.1, 27-41.

Buchanan, N. K. (1987).  Factors contributing to mathematical problem-solving performance: An exploratory study, Educational Studies in Mathematics, 18, 399-415.

Carlson M. P. and Bloom, I. (2005). The cyclic nature of problem-solving: An emergent multidimensional problem-solving framework, Educational Studies in Mathematics, 58, No.1, 45-75.

Garrett, H. E. and Woodworth, R. S. (2007). Statistics in psychology and Education, Paragon International Publishers, New Delhi.

Hannula, M. S. (2002). Attitude towards mathematics: emotions, expectations and rules, Educational studies in mathematics, 49, 25-46.

Lee, S. K. et al. (2003). A development of the test for mathematical creative problem-solving ability, Journal of the Korea society of mathematical Education – Series D: Research in Mathematics Education, 7, No. 3, 163-189.

Lianghuo, F. et al. (2005). Assessing Singapore students’ attitude towards mathematics and mathematics learning: Finding from a survey of lower secondary students, Nanyang Technological University, Singapore.

Maat, S. B. M and Zakaria, E. (2010). The learning environment, teachers’ factor and students’ attitude towards mathematics amongst engineering technology students, International Journal of Academic Research. 2, No.2, 16-20.

Mohd, N. and Mahmood, T. F. P. T. (2011). The effects of attitude towards problem-solving in mathematics achievements, Australian Journal of Basic and Applied Sciences, 5(12), 1857-1862.

Murat, P. and Seref, M. (2008). Pre-service elementary school teachers learning styles and attitude towards mathematics, Eurasia Journal of Mathematics, Science and Technology, 4(1), 21-26.

Rastogi, S. (1991). Mathematics weakness: causes & remedy, Mittal Publication, New Delhi.

Wikipedia – Online Encyclopedia.

Zakaria, E. and Yusoff, N. (2009).  Attitude and problem-solving skills in algebra among Malaysian matriculation college students, European Journal of Social Sciences, 8, No.2, 232-245.

Zan. R. and Martino, .P. D. (2007). Attitude towards mathematics: overcoming the positive/negative dichotomy, The Montana Mathematics Enthusiast, Monograph 3, 157-168.

 

ACKNOWLEDGEMENT

Authors gratefully acknowledge the suggestions given by Dr. Kamal Krishna De, Former Principal, David Hare Training College , Kolkata – 19 and Professor , R.K.M. Shikshanamandira, Belurmath, Howrah – 2, Dr. Bishnupada Nanda, Associate Professor, Department of Education, Jadavpur University, Kolkata-32 and Kiranmoy Chatterjee, Research Fellow, Bayesian and Interdisciplinary Research Unit, Indian Statistical Institute, Kolkata -108.

 

 

 

[1] Research Scholar, Department of Education, Rabindra Bharati University, Kolkata