جستجوی مقالات مرتبط با کلیدواژه "نظریه درک شکل های هندسی" در نشریات گروه "علوم تربیتی"

The research results show that students face many challenges and difficulties in learning geometry, and many of these difficulties appear in solving geometric problems, especially problems that require the use of geometrical figures. To improve students' performance in solving geometric problems, it is necessary to study related theories. One of the theories presented to describe students' understanding of geometrical figures is the theory of figural apprehension. In this theory, the correct use of geometrical figures in solving problems requires perceptual, sequential, discursive, and operative apprehensions, whose strengthening improves geometry learning and fosters mathematical creativity. The current study aims to investigate the tenth grade mathematics students’ apprehensions of geometrical figures and also to examine the problems of the geometry textbook of this grade to compare the students' apprehensions with the content presented to them. Also, some of the students’ common mistakes in response to geometry problems are pointed out. Research Questions: How able are the 10th grade male and female mathematics students to solve geometric problems corresponding to each type of apprehension and what mistakes do they make while solving geometric problems? 2- To what extent do the 10th grade students' apprehension of geometrical figures correspond to the problems of the geometry textbook of this grade?

According to the research questions, the research process consists of two phases. In the first phase, the students' apprehensions of geometrical figures and their mistakes were investigated by survey method. The statistical population was male and female 10th grade mathematics students in Pakdasht city, and 235 of them were selected by cluster random method as the sample. To collect the data for this phase of the research, a descriptive test including eight problems was used. For its validation, face and content qualitative validity were examined. To check the reliability of the research test, first, the students' responses were assigned to three parts: correct, incomplete, and incorrect or no response, then scored and Cronbach's alpha coefficient was calculated. Descriptive statistics were used to analyze the data. In the second phase of the research, the content analysis method was used to examine the 10th grade geometry textbook. The statistical population was all the problems of the 10th grade geometry textbook published in 2023. The sample and the population size were considered the same. To analyze the textbook, first, all the problems were classified based on the four apprehensions. Content analysis forms were used, whose qualitative face and content validity were confirmed by several mathematics and geometry experts. To check the reliability of the data collection instrument to analyze the content of the book, one of the chapters of the 10th grade geometry textbook (the third chapter) was randomly selected and its problems were coded by two coders who were familiar with the research subject. Then the Holsti reliability coefficient was calculated and the value was 0.76.

According to the frequency of the students' responses to the test, the highest number of incorrect or no responses were related to discursive and operative problems, and there was no significant difference between the performance of girls and boys. Regarding the students' mistakes, the results show that many students are unable to recognize geometrical figures, draw them correctly by drawing instruments, make logical reasoning to justify geometric claims and make appropriate changes to the geometrical figures to find the solution to the problems. The results of the content analysis of the 10th grade geometry textbook also revealed that more than half of the problems in this book require discursive and operative apprehensions.

In the process of teaching and learning geometry, it is necessary to focus on all four apprehensions introduced in the theory of figural apprehension. In the present study, the 10th grade students' apprehensions and the geometry textbook have been investigated based on the theory of figural apprehension. The results of the present study indicated that in response to discursive and operative problems, the percentage of incorrect and no responses is more than the perceptual and sequential problems. On the other hand, the results of the content analysis of the 10th grade geometry textbook showed that solving more than half of the problems in this book requires discursive and operative apprehensions. Therefore, students' apprehension and the content presented to them in the textbook do not match. Also, the results of this research revealed some of the students' mistakes in response to geometric problems. The reason for these mistakes seems to be misunderstanding the concepts and characteristics of geometrical figures, relying on mere intuition, considering special situations in the process of proving, and sometimes considering geometrical claims as obvious without any need to be proved, etc. If teachers and professors get familiar with this theory, they can learn about the causes of the students’ common mistakes in solving geometric problems and its link to the four apprehensions. Also, they can organize teaching steps regarding the students’ weak points. The results of such research can also help textbook authors and educational planners to reform educational policies.

The purpose of this study was to investigate 10th grade male and female students' apprehension of geometrical figures based on Duval’s theory, which was done through survey method. The statistical population is 10th grade boys and girls of Pakdasht city and the sample includes 235 students who were selected by cluster random sampling method. The tool is a test based on related research whose face and content validity were investigated by experts and its reliability was confirmed by Cronbach's alpha criterion. Descriptive statistics and inferential statistics including one sample t-test, correlation coefficient and multivariate analysis of variance (MANOVA) were used to analyze the data. According to Duval’s theory, learning geometry and applying geometrical figures requires four apprehensions, which are perceptual, sequential, operative and discursive. The results indicated that for issues that require discursive apprehension, students' average scores are lower than the average. In general, students' performance in solving problems related to discursive and operative apprehension is lower than their performance in solving problems that require perceptual and sequential apprehension. There is no significant difference between the performance of boys and girls. Also, the results of the Pearson correlation test indicated that there is a significant and positive correlation between every two dimensions of figural apprehensions. The results of the present study inform teachers about the strengths and weaknesses of students and as a result, will improve the methods of teaching geometry. It can also help authors and educational planners determine educational policies.