Abstract
The present investigation has been designed to verify the stratawise (sex and caste) comparison between the variables like Problemsolving Ability in mathematics and Attitude towards Mathematics. It also enquires the interrelationship between the variables and how Problemsolving Ability in mathematics can be predicted from Attitude towards Mathematics. It is found from the study that in case of Problemsolving 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, Problemsolving 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 21^{st} 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 problemsolving 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. Problemsolving ability has natural positive relation with achievement in mathematics. Now it appears worthstudying whether attitude towards mathematics and problemsolving 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
 To find the score of the students in attitude towards mathematics scale.
 To find the score of the students in problem–solving ability test.
 To tabulate the scores in each test sexwise and castewise, and find the corresponding mean.
 To determine the significance of difference in each test (sexwise and castewise).
 To determine the interrelationship between the two variables: attitude towards mathematics and problem solving ability in mathematics i.e. to find the coefficient of correlations (r) between the score obtained by the students in attitude towards mathematics scale and problem solving ability test.
 To ascertain whether problemsolving ability scores in mathematics could be predicted from the attitude towards mathematics scores.
 To find the significance of difference in mean scores in problemsolving ability in mathematics of the students belonging to high and low attitude towards mathematics groups.
HYPOTHESES OF THE STUDY
 These exists a significant difference between mean attitude towards mathematics scores of boys and that of girls.
 There exists a significant difference between mean attitude towards mathematics scores of general caste students and that of other caste students.
 There exists a significant difference between mean attitude towards mathematics scores of general caste boys and that of other caste boys.
 There exists a significant difference between mean attitude towards mathematics scores of general caste girls and that of other caste girls.
 There exists a significant difference between mean attitude towards mathematics scores of general caste boys and that of other caste girls.
 There exists a significant difference between mean attitude towards mathematics scores of other caste students and that of other caste students.
 There exists a significant difference between mean problem solving ability scores of boys and that of girls in mathematics.
 There exists a significant difference between mean problem solving ability scores of general caste students and that of other caste students in mathematics.
 There exists a significant difference between mean problem solving ability scores of general caste boys and that of other caste boys in mathematics.
 There exists a significant difference between mean problem solving ability scores of general caste girls and that of other caste girls in mathematics.
 There exists a significant difference between mean problem solving ability scores of general caste boys and that of general caste girls in mathematics.
 There exists a significant difference between mean problem solving ability scores of other caste boys and that of other caste girls in mathematics.
 Attitude towards mathematics scores obtained by the students was highly correlated with their problemsolving ability scores in mathematics.
 Problemsolving ability scores in mathematics could be predicted from attitude towards mathematics scores.
 The high and low achievers in attitude towards mathematics scale would respectively score high and low in problemsolving ability test in mathematics.
DELIMITATIONS OF THE STUDY
 The study considered two variables: attitude towards mathematics and problemsolving ability in mathematics.
 The study was confined to students of west Bengal of ClassIX of Bengali medium schools (just promoted) under WBBSE.
 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 classIX 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 24Parganas, Purbo Medinipur and Birbhum from South Bengal.
Table 1. Stratawise 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:
 “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 15 for positive statements and 51 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.
 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 testretest 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:
Table2 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) Stratawise and their Respective Mean, Median and S.D. of ProblemSolving 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 problemsolving ability in mathematics between the pairs BoysGirls, General Caste BoysGeneral Caste Girls and Other Caste BoysOther 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 tvalues between Different Strata of ProblemSolving Ability Scores in Mathematics
SL. No.  Strata  N  Mean  S.D.  tvalue  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 tvalues between Different Strata of Attitude towards Mathematics Scores
Sl. No.  Strata  N  Mean  S.D.  tvalue  pvalue  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 (Pvalue = 0.000) between the two variables viz. attitude towards mathematics and problemsolving 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 coefficient is significant, P < 0.01).
Table 5. Significance of Difference between the Means of ProblemSolving Ability Scores as Obtained by HighScore Group and LowScore 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 problemsolving ability test in mathematics.
FINDINGS
 Following results revealed from the testing of the studied hypotheses:
Strata  Problemsolving 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 
 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.
 The two variables are highly correlated (df = N2, p<0.01, r=0.421)
CONCLUSION
 Among all the strata, significant difference exists in problemsolving ability in mathematics only sexwise. Cast has no significant role here.
 No castewise difference exists in problemsolving ability in mathematics.
 The problemsolving 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 sexwise, castewise, gradewise. 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 problemsolving 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 problemsolving ability of inservice mathematics teachers, The Montana mathematics Enthusiast, 5, No.1, 79100.
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, 2741.
Buchanan, N. K. (1987). Factors contributing to mathematical problemsolving performance: An exploratory study, Educational Studies in Mathematics, 18, 399415.
Carlson M. P. and Bloom, I. (2005). The cyclic nature of problemsolving: An emergent multidimensional problemsolving framework, Educational Studies in Mathematics, 58, No.1, 4575.
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, 2546.
Lee, S. K. et al. (2003). A development of the test for mathematical creative problemsolving ability, Journal of the Korea society of mathematical Education – Series D: Research in Mathematics Education, 7, No. 3, 163189.
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, 1620.
Mohd, N. and Mahmood, T. F. P. T. (2011). The effects of attitude towards problemsolving in mathematics achievements, Australian Journal of Basic and Applied Sciences, 5(12), 18571862.
Murat, P. and Seref, M. (2008). Preservice elementary school teachers learning styles and attitude towards mathematics, Eurasia Journal of Mathematics, Science and Technology, 4(1), 2126.
Rastogi, S. (1991). Mathematics weakness: causes & remedy, Mittal Publication, New Delhi.
Wikipedia – Online Encyclopedia.
Zakaria, E. and Yusoff, N. (2009). Attitude and problemsolving skills in algebra among Malaysian matriculation college students, European Journal of Social Sciences, 8, No.2, 232245.
Zan. R. and Martino, .P. D. (2007). Attitude towards mathematics: overcoming the positive/negative dichotomy, The Montana Mathematics Enthusiast, Monograph 3, 157168.
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, Kolkata32 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