The aim of the research is to identify the effect of teaching according to thinking keys on the achievement and formal thinking for third-grade intermediate female students To achieve this aim, the following null hypotheses were formulated: 1- There is no statistically significant difference at the significance level (0.05) between the average scores of the experimental group students who will study according to the thinking keys strategies and the average of the control group students who will study in the usual way in the mathematics achievement test 2- There is no statistically significant difference at the significance level (0.05) between the average scores of the experimental group who will study according to the thinking keys strategy and the average scores of the control group students who will study in the usual way in the formal thinking test in mathematics. The research sample was intentionally selected from Al-Zohour High School for Girls, and the research sample consisted of (61) female students from the third intermediate grade female students, and two groups were selected, with (30) students for the experimental group, and (31) for the control group. To collect the research data , two tests were developed , one of which measured achievement and consisted of (31) items, and the other test measured the skills of formal thinking, as the test in its final form consisted of (40) items of the objective type multiple-choice.

thinking keys, achievement, formal thinking, middle school students.