The effectiveness of a suggested training Program based on Reciprocal Teaching in developing Critical thinking and the ability to Problem Solving for Mathematics Teachers at the Preparatory stage.

The aim of the current research is to build a suggested training program based on the reciprocal teaching for preparatory school mathematical teachers, and measuring its effectiveness in developing their ability to a critical thinking in mathematics , and mathematical problem solving. It is aimed at determining the relation between teaches’ ability in a mathematical critical thinking and a mathematical problem solving as well.so the researcher has built the suggested training program and a mathematical critical thinking test and a mathematical problem solving test. The researcher selected random sample consisting of 69 preparatory school mathematical teachers (36 experimental, 33 control). Tests were applied on the experimental and control groups (pre-test), then the suggested training program was taught to the experimental group. After completing the training process, tests were applied on the two groups (post-test). Statistical analysis of the data has revealed a number of results:

The performance of the experimental group in mathematical critical thinking and a mathematical problem solving is better than the control group in the post-test.
The performance of the experimental group in mathematical critical thinking and a mathematical problem solving is better in the post-test than in the pre-test.
The effectiveness of the suggested training program in developing the preparatory school mathematical teachers in Know the assumptions, interpretation, induction, error handling and critical thinking as a whole.
The suggested training program wasn’t effective in developing the preparatory school mathematical teachers in evaluation of arguments and reasoning
The suggested training program wasn’t effective in developing the ability of the preparatory school mathematical teachers in mathematical problem solving.
There is a positive and statistically significant correlation between the ability of the preparatory school mathematical teachers in mathematical problem solving and every skill of the critical thinking; knowledge of assumptions, interpretation, induction, evaluation of arguments, reasoning, error handling and critical thinking as a whole.

The research recommended the necessity of preparing a critical thinking and problem solving course for students of the mathematical department in the university of education, and using it in teaching mathematics in pre-university education and reorganizing the mathematics curriculum content for grades K-12 to include critical thinking and problem solving.