الملخص الإنجليزي
This study aimed to reveal the effectiveness a proposed enrichment program based on problem posing and problem-solving in the development of the ability of the mathematical problem-solving, the ability of the mathematical problem-posing and the ability of the mathematical reasoning and sense making among students of high achievement in light of their mathematical ability. To achieve the study aim, an enrichment training program was designed to focus on a set of mathematical ideas and skills in mathematics using problem-posing and problem-solving strategies to pose and solve non-routine mathematical problems, for students of high achievement to develop their mathematical problem-solving, problem-posing and reasoning and sense making abilities.
The researcher also designed three tests to measure the mathematical problem-posing, problem-solving, and reasoning and sense making. In addition, the Test of Mathematical Abilities (TOMA-3) was used to measure the students mathematical abilities before the experiment. The sample of the study consisted of 63 grade ten high achievers students, who were selected randomly from South Batinah governorate. The students were divided into control and experimental groups. For testing the study hypothesis data was analyzed by Analysis of Covariance (ANCOVA). The finding showed that: - There is a statistically significant difference at the level of significance (a= 0.05) between the mean scores of students in the experimental group and the mean scores of students in the control group in the post problemsolving test in favor of the experimental group. - There is no statistically significant difference at the level of significance(a= 0.05) between the mean scores of students in the experimental group and the mean scores of students in the control group in the problem-solving test due to the interaction between the group (control-experimental) and the mathematical ability (low-high). - There is a statistically significant difference at the level of significance (a=0.05) between the mean scores of students in the experimental group and the mean scores of students in the control group in the post problemposing test in favor of the experimental group.
- There is no statistically significant difference at the level of significance(a= 0.05) between the mean scores of students in the experimental group and the mean scores of students in the control group in the problem-posing test due to the interaction between the group (control- experimental) and the mathematical ability (low-high). - There is a statistically significant difference at the level of significance (a= 0.05) between the mean scores of students in the experimental group and the mean scores of students in the control group in the post reasoning and sense making test in favor of the experimental group. - There is a statistically significant difference at the level of significance (a= 0.05) between the mean scores of students in the experimental group and the mean scores of students in the control group in the post reasoning and sense making test due to the interaction between the group (control-experimental) and the mathematical ability (low-high) in favor of the experimental group. - Eta square was calculated (n = 0.272 for problem solving), (n = 0.244 for problem posing) and (n = 0.156 for reasoning and sense making)
In light of the study findings, the study recommends to enhance the abilities of mathematical problem-solving problem-posing and reasoning and sense making of students of high achievement by including the contents of the proposed program as part of the mathematics curricula.
