فصلنامه مطالعات برنامه درسی
پیاپی 24 (بهار 1391)

The preliminary experiences of children in learning mathematics are very important. Research shows، the formation of these experiences highly depends on the mathematics curriculum that they are exposed to، and it would determine their progress in future. Considering this، in last decades، cognitive researchers have done several studies on teaching mathematics to young children and they introduced cognitive approach as a defendable approach in mathematics curriculum design and teaching. Considering the role and the importance of this approach in mathematics education، current study was conducted using the meta-analysis of written documents and research findings in cognitive science and mathematics education. In this regard، the required infrastructures for implementing thisapproach in mathematics education at the elementary level have been explained. Finally، based on these findings، the structure of developing mathematics content and teaching methods for the elementary school that suits this approach was introduced.

Combinatorics has not had a real place in mathematics curriculum of many educational systems and this situation is still a case in those systems. However، by the major reform of the secondary education in Iran that started in 1992، combinatorics became one of the mathematics subjects of high school. In specific، one of the four chapters of “discrete mathematics” textbook is devoted to combinatorics. Further، this topic has been used as a mean to identify students'' special talents in creative mathematical problem solving and sifting them through for IMO and other mathematics contest given that students could choose different strategies to solve similar combinatorial problems and counting per se. The chief reason is that combinatorial problems do not need much prior subject matter knowledge as opposed to many other mathematical subjects such as analysis and differential equations. Because of the new direction in mathematics curriculum and the importance of combinatorial thinking in school mathematics، the present study aimed to shed more lights into the nature of combinatorial thinking using metaanalysis as the research methodology.

In this survey، using a trend study، a comparison between the Iranian students’ performance and other countries of the region was done regarding cognitive and content domains، gender، and the degree in which، the performance is closed to the international benchmarks. The results show that the average of Iranian students’ performance in all the cognitive and content domains is different from what was expected. In fact، the ranking of Iranian students has decreased as the number of participating countries in TIMSS studies has increased. As well، the results of investigating the input benchmarks and educational processes show that the amount of these benchmarks in Iran is either lower or close to the average marks of aforementioned countries. Since the performance as an output is influenced by input and educational process، therefore to improve the mathematics performance of Iranian students، it is necessary to pay attention to the improvement of both input benchmarks and educational process.

The use of technology in mathematics classes has caused great debates about the ways in which، the integration of different generations of technology with formal school mathematics curriculum could yield any fruitful result. Among these technologies، “CAS” and “DMS” have attracted many educators’ attention to use them in calculus classes. This issue is especially important in Iran since the educational system has officially announced that one of its main missions for the near future is the enhancement of technology in Iranian schools. Therefore، a study was designed to examine the possibility of such integration using the “optimization” chapter of the calculus textbook of the 11th year high school in physics- mathematics branch of the theoretical strand. Because of the new direction in mathematics curriculum and the importance of combinatorial thinking in school mathematics، the present study aimed to shed more lights into the nature of combinatorial thinking using metaanalysis as the research methodology.

The central theme of this paper is two folded; one is the important issue of “Reasoning Quotient” meaning children’s ability to make geometric argument and defend it; and second is “curriculum” as children''s learning from external sources that they could be refer to. They both acting as internal and external frame of reference for children and influence their performance. To test this claim، a study was conducted to investigate the pre-school children’s beliefs about geometry as well as learning more about the ways in which، they defend their beliefs. The findings showed that children used reasoning to defend their experimental beliefs and defend their theoretical beliefs by refereeing to familiar adults. The study revealed that “reasoning quotient” as natural human capacity is used by children and as their exposure to the formal curriculum increase، the latter decrease rather severely.

In the third edition of the National Curriculum in Iran، there are some emphasis on the role of mathematical modeling and application. In this line; the authors of the new Calculus Textbook (Hesaban) for Grade11، application and modeling approach has introduced as a major goal for the change. To examine the achievement degree of this goal، a content analysis study was conducted to analyze all problems of this new calculus textbook in terms of application and modeling، using a theoretical framework with five categories namely; context- free problems (or mathematical context problems)، injudicious problems، context-separable problems، standard applications and modeling problems. Results of content analysis revealed that none of the problems were classified as “injudicious” and “modeling” problems، 89% of problems categorized as “without context”. As well، 8% of problems identified as “standard application” and lastly، 3% of problems belonged to “context-separable” category. In conclusion، the present research shows that the role of modeling in the new Calculus is rather superficial and almost all socalled “applied problems” of this textbook are in fact، “standard application”. At the end، the study gives a few recommendations to the mathematics curriculum designers and textbook authors to the ways in which، the “modeling and application” approach.

The purpose of this was to investigate Grade 10 students’ conception of mathematical reasoning and proof and a survey methodology was used. 338 grade 10male and female students from two central towns of Iran were selected randomly and participated in the study. The data collecting instrument was based on a modified version of Harel & Sowder''s model (1998، 2007) and a questionnaire designed accordingly adapting Healy & Hoyles’ questionnaire (2000). Both descriptive and inferential statistics were used to analyzing the data. Findings of the study showed that most of the students’ conception of reasoning and proof were incomplete. In addition، students had difficulties with making mathematical proof but they did better in selecting credible reasoning. According to Harel & Sowder''s model، most of the students had «external conviction proof scheme» and «empirical proof scheme.”

In this study، mathematics teachers'' beliefs about mathematics and mathematical problem solving were investigated. For this purpose، 26 high school mathematics teachers voluntarily participated in the study. For the data collection، a questionnaire was administered and the data were analyzed using cluster analysis method. The results showed that the teachers are grouped into three clusters according to their responses to Beliefs survey instrument. As well، the findings of the study showed that whereas many of the teachers appeared to hold beliefs consistent with Problem-solving and student-centered views،significant numbers of them were uncertain as to the appropriateness of their beliefs in implementing their beliefs in their teaching. In addition، female teachers were used more student-centered teaching approaches than their male colleagues. In conclusion، teaching experiences is not sufficient for teachers to acquire beliefs consistent with a constructivist perspective.