TVET
A. Poorang; N. Asghary; A. Shahvarani Semnani
Abstract
and is a potent means for developing algebraic thinking which necessitates students’ understanding of the functional relationship between measure spaces. The ability to recognize and identify the structural similarity and multiple comparisons in the proportional reasoning process is the base of ...
Read More
and is a potent means for developing algebraic thinking which necessitates students’ understanding of the functional relationship between measure spaces. The ability to recognize and identify the structural similarity and multiple comparisons in the proportional reasoning process is the base of algebra and advanced mathematics. The concept of proportion and the necessities of developing proportional thinking are cognitively complex and its teaching demands concept-oriented approaches. Studing the quality of teachers' perceptions draws the perspective of the method and development of conceptual structures among the students. The present study focused on determining the extent of recognizing non-proportional situations and also the kind of selected strategies to solve proportional verbal issues in the teaching activity. Considering the importance of the context of this problem, the study focused on four semantic types of the problems in this field. Considering the pedagogical thinking of teachers in solving proportional problems provides the discussion on the obstacles of using the proportional reasoning among different semantic types. Methods: The study was done by descriptive survey method. The statistical population included 180 teachers of primary schools and mathematics teachers of the first level of the secondary schools, and prospective teachers who participated in the study voluntarily. The research instrument was a researecher-developed test containing 17 problems comprised of 3 non-proportional situations of additive problem types and 14 direct proportional problems, presented in the missing-value type which were either researcher-devised or selected from reliable research sources. The content validity of the test was confirmed by professors in the field of mathematics and testing and psychometrics. The collected data were analyzed using inferential and descriptive statistics. Findings: The results of the first study revealed that the primary school teachers and the prospective teachers were faced with some difficulties in recognizing non-proportional statements. It seems that the superficial characteristics of verbal problem including having a structure similar to the proportional problems of the type of missing value and also the multiplicative nature of numerical structure are involved in determining the situation as a proportional structure. In studying the the strategies of solving the proportional problems in the teaching activity, the responses of the participants were analyzed using the descrtiptive method based on 9 types of problem-solving strategies. The results of the analyses showed that all of the first levele of the secondary school teachers and the prospective teachers of both of these levels, at least in one of their first two priorities in teaching these problems, applied algorithmic proportional strategies or algebraic equation formulation while being slightly influenced by semantic types. Teachers of the primary schools had little desire to use the algorithmic proportional strategies. On the contrary, as compared to other teachers, they had a higher preference for using functional and numerical proportional reasoning. However, they did not prefer to use proportional functional reasoning in their activities. On the other hand, the first two priorities of the primary school teachers were not included in any semantic types, utilization of more complex proportional reasonings, and scale factor. Conclusion: The results emphasize the necessity of the development of pedagogical content knowledge in this field in order to develop the application of the strategies of functional proportional reasoning and appropriate representations by teachers which are aimed at providing more desirable conditions for students’ proportional reasoning development. Unexpected behaviors of prospective teachers in this study emphasize creating higher sensitivity to the consequences of delaying the emergence of students’ relative thinking in the instructional plans of teacher training courses.
Modern Educational Approaches
N. Yaftian; M. R. Ansari
Abstract
Background and Objectives: Understanding mathematical concepts is impossible without emphasizing reasoning and takes on instrumental and procedural aspects, and can be more easily recreated if mathematics is learned as a reasoned science instead of a set of procedures. On the other hand, the goal of ...
Read More
Background and Objectives: Understanding mathematical concepts is impossible without emphasizing reasoning and takes on instrumental and procedural aspects, and can be more easily recreated if mathematics is learned as a reasoned science instead of a set of procedures. On the other hand, the goal of any educational system is to prepare students for social life; So that they can perform their daily duties well as a citizen. In this regard, they must be able to convince themselves and others with the reasoning they present. However, students face widespread difficulties in understanding reasoning and proof in mathematics as well as in assessing their correctness. Therefore, it is important for students to evaluate the correctness and validity of mathematical reasoning and to use these reasoning to convince themselves and others and deserves further attention and research. The purpose of this research was to study the ability of 11th grade students to evaluate mathematical reasoning to identify the strengths and weaknesses of students.. Methods:The present study was conducted by survey method.The statistical population consisted of the 11th grade students in Zanjan and the sample includes 393 boy and girl students selected by random cluster sampling from the gifted, exemplary public, Shahed and public schools and the sample was selected to include all levels of students.. The research instrument is a researcher-made test consisting of 3 problems in familiar, completely familiar and unfamiliar situations. Students were provided with some responses for each of these three situations to determine which responses can be selected to convince themselves, which ones can be chosen to convince friends, and finally which ones can be selected to get the best score. Descriptive and inferential statistics (Chi-square test) were used for data analysis. Findings: The findings indicated that students were not capable of evaluating mathematical reasoning and in more than 60% of cases they were particularly interested in using formal methods. Selecting the responses to persuade themselves and friends in more unfamiliar situations indicated that students paid less attentionto to accepted criteria for accepting a logical reasoning. Students' performance to get the best score from the teacher indicated that their attention to correct and incorrectsymbolic responses has increased, the form of presentation seems to be more important to them,. Although they are not able to distinguish formal proof content from the false one, they have ea better understanding for distinguishing invalid reasoning in the familiar situations. The results showed that in some cases gender influenced students' performance. Conclusion: It can be said that the current teaching method in mathematics has not had significant results in the area of reasoning and proof. Therefore, it is necessary to review the teaching methods and the content of the textbooks. The results of this research can be used by education policy makers and textbook authors to pay special attention to the situation of reasoning in mathematics textbooks by being aware of students' views on mathematical reasoning, and perhaps by changing the way textbooks are written, a fundamental step to solve difficulties. Also, by being aware of students' performance in the field of reasoning and proof, math teachers can identify the strengths and weaknesses of their students in the process of math proofs and identify their misconceptions in this field.
Educational Technology - Public education
E. Reyhani; F. Fathollahi; F. Kolahdouz
Abstract
Reasoning and proof in mathematics education are important at all educational levels, from school to university. Understanding mathematics without emphasis on reasoning and proving is almost impossible. The purpose of this study was to investigate the university students’ conception of mathematical ...
Read More
Reasoning and proof in mathematics education are important at all educational levels, from school to university. Understanding mathematics without emphasis on reasoning and proving is almost impossible. The purpose of this study was to investigate the university students’ conception of mathematical proof. For this, a survey method was used. The participants of this study were 170 students collected from four universities; Shahid Rajaee Teacher Training, Shahid Beheshti, Science and Technology and Amirkabir University of Technology as available samples. The data collecting Instrument was a questionnaire based on the modified version of Roy and et.al (2010). In this questionnaire a theorem with its proving was presented and then the students were asked to answer the questions about the process of making the mathematical proof. A model was used to evaluate the students’ answers to questions based on Ramos and et.al (2011). It is consists of both global and local aspects. This model investigates seven different levels of understanding of the process of making mathematical proof. The findings of the study showed that most of the students had a local comprehension of the proof. In fact, they understood the relations between the concepts and statements in the proof. But a small percentage of them had a more holistic comprehension of the proof. It seems several factors, including the lack of attention to the assumptions of the theorem, their inability to provide logical reasoning and rational organization of statements of the proof, and most importantly, the lack of students’ knowledge may be insufficient in this inability.
