The objectives of the study were: (1) To study the relationship between problem solving ability and demographic factors, such as, area, sex, community parental occupation, parental income, father’s educational qualification, mother’s educational qualification of the students and category of the schools. (2) To study the selection of sub-test, giving required ordering and weightages. (4) Establishment of influencing factors in the development of problem solving ability. (5) Diagnosing the errors which contribute for the reduction of problem solving ability.

The hypotheses of the study were: (1) There is no significant difference in the problem solving ability in mathematics of students of different areas (urban and rural). (2) There is no significant difference in the problem solving ability in mathematics of boys and girls. (3) There is no significant difference in the problem solving ability of students in mathematics with different community backgrounds. (4) There is no significant difference between different parental economic backgrounds and the problem solving ability in mathematics of their words. (5) There is no significant difference between the performance of the students whose fathers work difference in occupations and solving ability of their wards. (6) There is no significant difference in the problem solving ability in mathematics of students whose fathers are of different educational levels. (7) There is no significant difference in the problem solving ability in mathematics of students whose mothers are of different educational levels. (8) There is no significant difference in the problem solving ability in Mathematics of students with different category of schools.

The sample consisted of 1000 boys and girls of X grade drawn from the schools under the control of different management, Zilla Parishad, state government, Kendriya Vidyalaya, Samithi’s A.P. Residential School Society (State Government and Navodaya Vidyalayas), private selected on the basis of clustered, and rural and urban background.

The problem solving ability test in mathematics for students of X class consisted of 100 items of objective type questions (multiple choice, true/false) with 5 sub-tests of 20 questions per subject was constructed by the investigator.

For this investigation, normative survey method was used.

The data were analyzed with the help of  t-test.

The findings of the study were: (1) There is a significant difference in the problem solving ability in mathematics of students of different areas. Urban students’ performance was found to be significantly better than rural students. (2) There was no significant difference between the performance of boys and girls regarding problem solving ability in mathematics. (3) There was a significant difference in the problem solving ability of students in mathematics with different community background. (4) The increase in parental income was associated with higher performance regarding problem solving ability in mathematics. (5) The subjects whose fathers were gazetted officers or intellectuals excelled in performance with reference to problem solving ability in mathematics. (6) The higher the qualifications of the parents (father/mother) the better was the performance of the students with reference to problem solving ability in mathematics. (7) The school climate had a direct influence on the performance of the students. The performance of the group of students, who were studying in Kendriya Vidyalaya was found to be superior to students in all the other types of schools. Kendriya Vidyalayas, private schools and residential schools had far better infrastructural and better physical facilities and staff pattern when compared to government and Zilla Parishad schools. Better educational climate led to better results. This opened up an important issue of improving the conditions of government and Zilla Parishad high schools.