Effectiveness of Cooperative Learning with Advisor Group Strategy in 7th Grade Mathematics Classroom

This study aims to determine the Effectiveness of the Cooperative Learning Model with Group Advisory Strategy in Mathematics Learning of the Grade VII SMP. This research is pre-experiment with techniques sampling is cluster random sampling. Data collection was carried out using observation sheets of implementation of learning, test results of learning (pretest and posttest), observation sheets of student activities, and student questionnaire responses. The data analysis technique used is descriptive and inferential statistical analysis. The results of descriptive statistical analysis showed: (1) The average score of learning outcomes after learning reaches 80.04 with standard deviation of 8.79, (2) the posttest results show that classical completeness is achieved 91% (3) The average percentage of student activity is 89% (4) the average percentage of students who gave positive response 89%. The results of inferential statistical analysis showed : (1) The average value of students taught using cooperative learning models with the Advisor Group Strategy is greater than completeness, which is 70, and (2) The proportion of classical completeness of learning outcomes after the application of the cooperative learning model with Group Advisors Strategy achieve classical completeness. From the results of this research it can be concluded that cooperative learning models with the Group Advisory Strategy are effectively used in students of grade VII.

Necessary and sufficient conditions for pairwise majority decisions on path-connected domains

In this paper, we consider choice functions that are unanimous, anonymous, symmetric, and group strategy-proof and consider domains that are single-peaked on some tree. We prove the following three results in this setting. First, there exists a unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. Second, a choice function is unanimous, anonymous, symmetric, and group strategy-proof on a single-peaked domain on a tree if and only if it is the pairwise majority rule (also known as the tree-median rule) and the number of agents is odd. Third, there exists a unanimous, anonymous, symmetric, and strategy-proof choice function on a strongly path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. As a corollary of these results, we obtain that there exists no unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if the number of agents is even.