Shakila, Jetty. (2012). Learning of Mathematical Concepts in relation to spatial ability and problem solving skills among secondary school pupils. Unpublished. Ph.D., Education. Acharya Nagarjuna University,Guntur,Andhra Pradesh.

Is the learning of the mathematical concepts related to the spatial ability of IX class pupils. ii)Is learning of the mathematical concepts related to the problem solving skills of IX class pupils. iii)Does the learning of Mathematical concepts differ with respect to gender, academic achievement and type of concepts? iv)Does the learning of mathematical concepts differ with respect to the environmental variables like status of the school, its location, educational background and economic background of the parents? v)Does the learning of mathematical concepts differ with respect to the frequency of usage of teaching aids in classes?1. Secondary school pupils differ in their levels of achievement in mathematical concepts. 2. Secondary school pupils differ in their levels of achievement in different areas of learning of mathematical concepts. 3. Secondary school pupils differ in their levels of learning of spatial ability. 4. Secondary school pupils differ in their levels of learning of problem solving skills. 5. There would be no significant relationship between the learning of mathematical concepts and spatial ability of secondary school pupils. 6. There would be no significant relationship between the learning of mathematical concepts and problem solving skills of secondary school pupils. (a) There would be no significant relationship between the learning of mathematical concepts and approach avoidance character of secondary school pupils. (b) There would be no significant relationship between the learning of mathematical concepts and problem solving confidence of secondary school pupils. (c) There would be no significant relationship between the learning of mathematical concepts and personal control of the secondary school pupils. 7. There would be no significant relationship between the learning of mathematical concepts, spatial ability and problem solving skill of secondary school pupils. 8. There would be no significant relationship between the learning of mathematical concepts and academic achievement of the secondary school pupils. 9. There would be no significant difference between boys and girls in learning of mathematical concepts of secondary school pupils. 10 (a). There would be no significant difference between the rural and urban secondary school pupils in learning of mathematical concepts. (b) There would be no significant difference between secondary school pupils of different schools in learning of mathematical concepts. (c) There would be no significant difference between the pupils of parents with different educational background in learning of mathematical concepts. (d) There would be no significant difference between the secondary school pupils of different economic backgrounds in learning of mathematical concepts. 11 (a) There would be no significant difference in the learning of mathematical concepts in relation to the type of concept. (b) There would be no significant difference in the learning of mathematical concepts in relation to the use of teaching aids.

For the present study the investigator has taken up a stratified random sample of 31 schools and 620 pupils from IX class in Krishna District.1. A test was constructed on mathematical concepts in practical situations on three areas containing 60 problems from VIII class mathematics text book by the investigator. 2. A Standardized tool on spatial ability, a differential aptitude test containing 40 questions was used. 3. Problem solving skills scale was framed by C.G.Venkatesha Murty of R.I.E Mysore and used by him. It is including approach avoidance character of the person in problem situations, problem solving confidence and personal control, containing 22 questions was used.The researcher thought that normative survey method is suitable to collect data through questionnaires and tests to pupils on learning of mathematical concepts, on spatial ability and problem solving skills.The statistical techniques that are employed are given as the following. Objective 1 :Mean, S.D, Percentage of mean, 1/5th of mean, comparison with normal distribution, classification scale. Objective 2 :Mean, S.D, Percentage of mean, Area wise mean, 1/5th of mean, comparison with normal distribution, classification scale. Objective 3 :Mean, S.D, Percentage of mean, 1/5th of mean, comparison with normal distribution, classification scale. Objective 4 :Mean, S.D, Percentage of mean, 1/5th of mean, comparison with normal distribution, classification scale. Objective 5 :Analysis of variance (r), Chi Square (χ2) test. Objective 6 (a) :Analysis of variance (r). Objective 6 (b) :Analysis of variance (r). Objective 6 (c) :Analysis of variance (r). Objective 7 :Multiple correlation. Objective 8 :Analysis of variance (r), Chi Square (χ2) test. Objective 9 : Mean, S.D, Percentage of Mean, t-value. Objective 10 (a) : Mean, S.D, t-values, F-Value. Objective 10 (b) : Mean, S.D, t-values, F-Value Objective 10 (c) : Mean, S.D, t-values, F-Value. Objective 10 (d) : Mean, S.D, t-values, F-Value Objective 11 (a) : Mean, S.D, t-values. Objective 11 (b) : Mean, S.D, t-values, F-Value

1. Secondary school pupils are to have an average level of learning of mathematical concepts. 2. Nearly half of the sample has average level and about two fifths has low level of learning of mathematical concepts in learning sets, mensuration and symmetry. The pupils are found heterogeneous in all the three areas of learning of mathematical concepts. 3. The secondary school pupils are found having average spatial ability. They are found heterogeneous in their spatial ability. Two fifths of the sample of pupils are found to have high spatial ability. 4. The pupils are found to have high problem solving ability and the sample is found homogeneous in problem solving skill. The noteworthy feature of the sample is that none of them is found to have very low problem solving skill. 5. There is significant positive relationship among the learning of mathematical concepts, problem solving skills and spatial ability of secondary school pupils; between learning of mathematical concepts and spatial ability of secondary school pupils; and between the learning of mathematical concepts and problem solving skills of secondary school pupils. 6. Significant positive relationship is found between the learning of mathematical concepts and approach avoidance of the problem; between the learning of mathematical concepts and problem solving confidence and also personal control in the problem situation of secondary school pupils. 7. Significant positive relationship is found between learning of mathematical concepts and academic achievement in mathematics of secondary school pupils. 8. Boys and girls did not differ significantly in their learning of mathematical concepts. 9. Significant difference was found in the learning of the type of concept in secondary school pupils. The learning of conjunctive concepts is better than the learning of disjunctive concepts and relational concepts but such difference is not found when the learning of disjunctive and relational concepts are compared. 10. There is significant influence of use of teaching aids on the learning of mathematical concepts of secondary school pupils. 11. Rural pupils have significantly better learning of mathematical concepts than that of urban secondary school pupils. 12. There is significant influence of the status of the school on the learning of mathematical concepts of secondary school pupils.

1.This study will enable the pupils to identify the need and importance of learning of mathematical concepts. 2.This study will help to find out ability of the high school pupils in different areas of learning of mathematical concepts. 3.This study will enable the teacher to identify the need and importance of spatial ability. 4.This study will help the teachers to know about the ability of the high school children in applying the mathematical knowledge in problem solving skill. 5.This study will help the mathematics teachers to focus their attention on their teaching of mathematical concepts. 6.This study will direct the teachers to develop better teaching strategies to care the pupil’s comprehension of mathematical concepts. 7.This study will catch the attention of curriculum framers and text book writers to keep their mind on the development of concepts through different subjects of education. 8.The pupils can be given the task of framing the mathematical problems analogous to the problems given in the text books. 9.Real life related approach in understanding many mathematical concepts can facilitate better learning of them. 10.Mathematics teachers can remove some of the wrong attitudes in pupils towards mathematics, develop confidence in them tapping their abstract abilities.

Keyword(s): Mathematics Education