The objectives of the study: (1) To identify the percentage of high school students who have attained formal operational abilities of Proportionality; Propositional logic and combinatorial analysis. (2) The ascertain the differences in the development of abilities of Proportionality; Propositional logic and combinational analysis abilities across sex. (3) To study the differences in the development of abilities of Proportionality, Propositional logic and combinational analysis among high school urban and rural students. (4) To examine the nature and extent of relationship of Proportionality,  Propositional logic and combinational analysis with academic achievement in science. (5) To determine the predictive efficiency of Proportionality, Propositional logic and combinational analysis both individually and conjointly for science achievement of high school students. (6) To identify the factorial structure underlying proportionality, propositional logic and combinational analysis and achievement in science in terms of general and group factor/s. 

The hypothesis of the study were: (1) Majority of the high school students do not attain the formal operational abilities proportionality, propositional logic and combinational analysis. (2) There are significant differences in the development of Proportionality, Propositional logic and combinational analysis abilities between high school boys and girls. (3) There are significant differences in the development of Proportionality, Propositional logic and combinational analysis abilities between urban and rural high school students. (4a) The formal operational ability of proportionality is significantly related with academic achievement in science. (4b) Propositional logic has a significant relationship with academic achievement in science. (4c) There is a significant relationship between combinatorial analysis and science achievement. (5a) Formal operational abilities, namely, proportionality, propositional logic and combinational analysis are significant predictors of science achievement of high school students. (5b) The conjoint contribution of proportionality, propositional logic and combinational analysis towards science achievement is greater than their separate predictive efficiency. (6) The variables of proportionality, propositional logic and combinational analysis cluster together in general/group factor/s with science achievement at formal operational stage.

The sample comprised 409 Students of Grade X from Various High Schools of Punjab State. The sample was selected using Multistage Stratified Random Sampling Technique.

Six Piagetian Tasks Adapted from Inhelder and Piaget, Science Achievement Test (Test-retest reliability coefficient= 0.86) were developed by researcher for data collection 

The research was Descriptive Survey in nature.

The data were analyzed by Mean, SD, Skewness & Kurtosis, t-test, Correlation, Multiple Regression Equation and Factor Analysis.

The findings of the study were: (1) While more than fifty percent (62%) high students reach formal operational level in attaining the concept of proportionality. In the remaining two abilities, the picture is at variance. Only 15% and 16% of the subjects attain concepts of propositional logic and combinatorial analysis respectively at formal level. (2) The concept of personality at formal level is attained by greater number of high school boys than girls. On the other hand high school girls out perform boys in the development of concept of propositional logic at formal level. No significant sex differences are found as for as attainment of the ability of combinatorial analysis at formal level is concerned. (3) The development attainment at all the three formal operational abilities under study, namely, proportionality, propositional logic and combinational analysis is higher among urban students than rural. (4) The three cognitive abilities, namely, proportionality, propositional logic and combinational analysis are significantly and positively related with achievement in science there by implying that in their formal stage operational abilities are quite similar, if not identical, to abilities required for achievement in science at the high school level. (5a) Formal operational abilities, namely, proportionality, propositional logic and combinational analysis are significantly predictors of the subject- wise achievement in physics, biology, chemistry, and also of total science achievement. (5b) The predictive efficiency of three abilities for achievement in science is not significantly different from each other except in the case of proportionality and combinational analysis for prediction of achievement in physics in which case the differences are significant and in favour of proportionality. (6a) The conjoint predictability of three variables proportionality, propositional logic and combinational analysis is higher as compared to their singular contribution or the contribution of any two of the three variables taken together at a time for the prediction of subject-wise achievement in physics, biology, chemistry and total science achievement. (6b) The conjoint effect of three predictor variables is maximum for the criterion measure of total science achievement and minimum for the measure of achievement in physics. (7) In factor analysis, original factor I shows the predominance of an underlying element of cognition.