اثربخشی برنامه آموزشی مبتنی بر نظریه یادگیری زایشی بر استدلال ریاضی و عملکرد تحصیلی دانش‌آموزان دوره متوسطه اول

In today's era, the traditional learning that has surrounded our educational system for many years no longer meets the needs of students and teachers. From this point of view, learning theories can help meet the needs of students and teachers. Among these theories that are used to develop self-motivated, self-regulated, and self-controlled learners is the generative learning theory (GLT) introduced by Wittrock (1974). In recent decades, the attention of many education experts has been focused on the study of the factors affecting the learning of mathematics lessons. Extensive research has been done in this field, which shows that one of the main reasons for the problems of learning and progress in mathematics is that students often rely on repetition and habit and use inappropriate and inadequate methods and superficial reasoning for mathematical concepts. According to TIMSS (1999), learners in classes that emphasised reasoning and problem-solving methods had better results in learning different mathematical concepts than in other classes. Mathematical reasoning, which means thinking according to reason and proof, is the same as reaching solutions through mathematical concepts. Examining the results of TIMSS (2007, 2011) indicates that the average value of Iranian students' math scores in the fourth and eighth grades in the area of mathematical reasoning is significantly lower than the international average value. In educational systems, academic performance is the academic standing of students, which is the grade of different academic courses measured by standardised tests. According to Pham and Taylor (1999), academic performance consists of: self-efficacy, emotional impact, planning, lack of outcome control, and motivation.
This research is a semi-experimental type with a pre-test-post-test design with a control group. The statistical population of this research included eighth grade female students in Gilanegreb city (Kermanshah province) in the academic year 2022-2023. In order to eliminate the interfering effect, two classes from two different schools, which were taught by the same math teacher, were selected by the available sampling method and completely randomly divided into two groups, namely the experimental group (30 people) and the control group (30 people).

Before starting the training, both study groups were subjected to a pre-test, and they were asked to answer the desired questions in addition to cooperating. The experimental group was subjected to the intervention of an educational package based on generative learning theory. The teaching method used to teach this educational package was the cooperative teaching method, which tried to involve the learners in the learning process in a practical way so that learning could be done at a higher level. The experimental group was trained with the generative learning method during eight sessions lasting 40 minutes. During these sessions, the control group was not given any kind of training based on generative learning, but the usual teaching method was used for them. After the completion of the training course, a post-test was conducted between the experimental group and the control group, and then the collected raw data were analysed by covariance analysis and SPSS-26 software. Research tools included the Rezaei Mathematical Reasoning Questionnaire, Pham and Taylor's Academic Performance Questionnaire, and an educational program based on generative learning theory. The findings of the research were divided into two descriptive and inferential parts, and in the descriptive part, the average of mathematical reasoning in the experimental group increased in the post-test position compared to the pre-test. Also, the average variable of academic performance and its components (self-efficacy, planning, and motivation) increased in the post-test position compared to the pre-test, while the components of emotional effects and lack of control in the experimental group were reduced in the post-test situation compared to the pre-test. In examining the first hypothesis, after confirming the assumptions of the covariance analysis in the inferential part of the findings, the results of the univariate covariance analysis showed that the effect of the independent variable (training program based on generative learning theory) on the dependent variable of mathematical reasoning is significant in improving mathematical reasoning in the post-test stage. According to the effect size prepared from Cohen's D formula for the variable of mathematical reasoning (0.639), it is clear that the training program based on generative learning theory is able to determine a significant percentage of changes in mathematical reasoning. Multivariate covariance analysis was used to investigate the second hypothesis.

After ensuring the normality of the data distribution, the assumption of homogeneity of the data, and the homogeneity of the regression slope, the significant level of the Hotelling effect (F = 14.729, P = 0.000) confirms that there is a significant difference between the experimental and control groups in terms of post-test academic performance compared to pre-test control. The effect coefficient shows that the difference between the two groups is 0.450, related to the generative education program intervention. Also, the results of multivariate covariance analysis show that the education program based on generative learning theory is able to determine some of the changes in the components of academic performance. The effect size obtained from Cohen's D formula for the self-efficacy component was 0.208, the emotional impact component was 0.012, the planning component was 0.067, the lack of control component was 0.014, and the motivation component was 0.402; therefore, the training program based on the generative learning theory has had a moderate effect on the components of emotional impact and lack of control. The results of this research indicate the confirmation of the first hypothesis and the effect of the educational program based on generative learning theory on students' mathematical reasoning. Also, the obtained results show that the reproductive education program is able to determine a significant percentage of changes in mathematical reasoning. In addition, the examination of the results of the analysis of the second hypothesis showed that there is a significant difference between the experimental group and the control group in the number of academic performance components. The results of the examination of the means showed that the mean of the experimental group in the components of academic performance (self-efficacy, planning, and motivation) in the post-test position compared to the pre-test has increased, and the mean in the components of emotional effects and lack of control in the experimental group has decreased in the post-test position compared to the pre-test. Therefore, it can be said that an educational program based on generative learning theory has a significant effect on academic performance and its components.