ملوک حبیبی

The purpose of this research is to evaluate the level of algebraic thinking of 10th grade students based on the framework provided by Cairn, Kaput and Pantzi in four levels (a) generalization of calculations, (b) functional thinking, (c) modeling language and (d) proof.The statistical population of the research was 10th grade students of Technical and Vocational Colleges in Tehran and the statistical sample was 62 people (31 girls and 31 boys) who were studying in the academic year 1402-1401. The sample was selected purposefully. The research method is descriptive-survey. A researcher-made test was taken with confirmed validity and reliability, and the research results were analyzed using descriptive and inferential statistics.The results of this research indicated that in all four levels of algebraic thinking, students demonstrated poor performance. The overall average scores obtained by students were 35.5% in the generalization of computations, 36.5% in functional thinking, 14.9% in modeling, and 4% in algebraic proof. The results of the independent t-test confirmed that there is a significant difference in the levels of algebraic thinking between female and male students, with female students having higher levels of algebraic thinking.

The purpose of this study is the effect of the control factor from Schofield's perspective on the misunderstandings of ninth grade students in algebraic expressions in Komijan city. For Schonfield, control means how to select and use the appropriate resources and strategies to help solve the problem. This research is semi-experimental in terms of practical purpose and method of implementation. The statistical population of this study was 240 people, of which a sample of 50 people was randomly available in two classes of 25 people as a test and control group. The research instrument was a researcher-made test according to the table of misunderstandings and its validity was confirmed by CVR method and the reliability of the questions with Cronbach's alpha coefficient was acceptable 0.756. After the pre-test, 7 extracurricular sessions were performed for each group. To collect statistical data, a post-test with Cronbach's alpha of 0.784 was performed on the two groups and the data collected by t-test were analyzed with a significant level of p <0.05. The results showed that strengthening control skills According to Schonfield, it is effectivein reducing students' misunderstandings in solving problems related to algebraic expressions.

The purpose of this study is The effect of Control Factor from Schoenfeld’s Viewpoint on Students’ Errors Based on Hodes Nolting Model in the Topic of Function for 11th grade mathematics Field in Karaj County’s. This study is a semi-experimental one. The population of this study consists of all male students in 11th grade of Karaj, distrct 1 within the educational year of 1399-1400. Two 25-student classes were selected based on convenience sampling out of all above-mentioned population. To collect the data, two researcher-made tests were used for the two stages of pre-test and post-test, to evaluate the effect of applying Schoenfield control according to the students' Hodes Nolting error model.The term “control” is defined as major decisions with respect to selection and use of resources and approaches. Hodes Nolting errors consist of careless errors, conceptual errors, application errors, and procedural errors. For the reliability of the test, the Cronbach's alpha value for the pre-test was about 0.702 and the post-test was about 0.824, and for checking the validity of the test, the CVR coefficient was used and the value was 0.8, which is acceptable. The results showed that applying Schoenfeld’s control could significantly reduce students' errors in the subject of function according to Hods-Nolting model.

The purpose of this study was to evaluate the effect of multiple representational education on meaningful learning of the concepts of length, level, and volume measurement in elementary students. Multiple representation means introducing or demonstrating a concept in different situations and forms that can create a deep understanding in the learner's mind. The research method was semi-experimental with two experimental and control groups. Samples were selected by convenience sampling method and were divided into two equal groups of experimental and control. In the experimental group, the concepts were taught in a multiple-presentation manner and in the control group, in the traditional way. Finally, a post-test with conceptual questions was given to students in both groups. Validity of these tests was measured by CVR method and confirmed by 0.99. Cronbach's alpha reliability was 0.887 for pre-test and 0.727 for post-test. The results were analyzed by t-test for two independent groups using SPSS software. The findings of the study showed that teaching based on multiple representations had a significant effect on the meaningful learning of the measurement topic.

The purpose of this study was to investigate the effect of Polya's problem-solving model on reducing the Newton's error in the 10th year students of mathematics in combining problem-solving problems, Tehran province. This research has been donesemi-experimental. The statistical population of this study is 100 students of the 10th year of mathematics in Marlich and Serasiab areas of Malard County in Tehran during the academic year 97-96. Of these 30 students, the sample is available as sample. To collect the data, two researcher-made tests for the two pre-test and post-test phases each included six questions from six different types of questions, in order to investigate the effect of using the Polya problem solving model on student Newman's error reduction. The Cronbach's alpha value was obtained to verify the reliability of 0.73 and CVR to verify the validity of the questions used between 0.8 to 1 To analyze the data, frequency, percentage, mean, variance, and also U test for inferential analysis were used. The results of these tests showed that the use of Polye problem solving model could reduce the errors in the stages of perception and transformation significantly, but significant changes Processing and encoding steps were not observed

The objective of this research is to study students' understanding of the concept of integral in the framework of APOS theory. Finding a method and approach leading to conceptual understanding of integral is a challenge faced by most of mathematics teachers. APOS theory is one that is used to study learning mathematical concepts at universities. This is a qualitative study using survey method. This paper reports the analysis of students' answers to seven questions about integrals of functions. According to the findings most students have failed to get a conceptual understanding of integral. They solve integral problems only if they have access to a routine solution. According to APOS theory most students are in action and process levels and a few manage to get higher levels and form a schema of integral.so we can use APOS to growth student undrestanding ib intrgral concept,for this we must work on teacher educvation in math.

The main purpose of this research is to analyze the errors of the experimental fourth-grade students in solving word problems based on the Newman's error analysis model in Semirom city. The statistical population of this study included all the experimental fourth-grade students in Semirom in the academic year of 2016-2017, which were 160 people and among them, 120 people were selected through Cochran sampling and stratified random sampling method proportional to the volume. This research is applicative in terms of purpose, and is descriptive correlational, in terms of implementation. The data gathering tool was a standard and researcher-made test with 6 questions and a qualitative interview. The findings of this study showed that there is a positive and significant relationship between reading, understanding, converting, processing and encoding errors with students' performance. Correlation coefficient also showed a positive and significant relationship between conceptual and applicative structures, and there is a positive and non-significant relationship between conceptual and computational structures as well as, there is a negative and significant relationship between applicative and computational structures. The highest prevalence of student errors was in the first three phases of Newman's errors (non-mathematical literacy).

The Van Hiele is a learning model that offers different types of thinking which students experience, when faced with geometric shapes. It includes the stage of visual encounter with the geometric shape, to the formal perception of geometrical proof. Misunderstandings can cause confusion and failure of students to solve problems. Sometimes, because of the interrelated nature of mathematical concepts, misunderstandings cause problems in the future learning of students. The purpose of this study was to identify the misconceptions of 8th grade students in geometrical skills and its related subjects. It also intends to use Van Hiele's theory to improve geometrical skills of the students. The statistical population of this study included 8th grade male students, at junior high schools, in the first district of Sanandaj educational department in the academic year of 1395-96. The sample consisted of 318 students who were selected by random cluster sampling method. Regarding its purpose, this study was applied, and in terms of its implementation, it was descriptive and a kind of field study as well. The measuring scale of this study consisted of written tests. Cronbach alpha coefficient was 0/896. The result of this research showed that most students had many various errors in geometry and its related subjects. The mean score of students in the experimental group was lower than that of the control group in terms of the misconception. There was a significant difference between students’ performance at the control and experimental groups at Van Hiele's thinking level. This difference was in favor of the experimental group students. There was also significant difference at 0/05 level between students at both groups in geometrical skills and this difference was in favor of the experimental group, as well.