This article is based on research on pre-service teachers＇ perspectives on their mathematics knowledge of proof in geometry. The study was framed using tile mathematical knowledge for teaching framework. This qualita...This article is based on research on pre-service teachers＇ perspectives on their mathematics knowledge of proof in geometry. The study was framed using tile mathematical knowledge for teaching framework. This qualitative study employed the use of a task-based worksheet, focus group sessions and semi-structured individual interviews. The task-based worksheet was completed by 180 pre-service mathematics teachers （second, third and fourth year mathematics education students）. Pre-service mathematics teachers are student teachers who have not yet completed their training to become teachers. After the analysis of the task-based worksheet, 20 participants were invited to participate in focus group sessions and individual interviews. The findings of the study reveal that the participants possess peripheral mathematics knowledge of proof in geometry. The study aims at assisting pre-service teachers and interested educationists to explore innovative methods of acquiring and imparting mathematics knowledge of proof in geometry. The study proposes possible changes in curriculum at school and university level.展开更多
The purpose of our paper is to show, on the example of Tbilisi, how places become sacred and the sights of pilgrimage; what are the modern and traditional forms of pilgrimage in Georgia. The study showed that the grav...The purpose of our paper is to show, on the example of Tbilisi, how places become sacred and the sights of pilgrimage; what are the modern and traditional forms of pilgrimage in Georgia. The study showed that the graves of the prominent people for their pure life and miraculous deeds, who lived during the Soviet and post-Soviet periods until now are the places of veneration. These people before official canonization became saints for people and as I call them, they became “folk Saints”, as the forms of their veneration are the same as canonized ones. After post-Soviet revival of religiousness in the late 1970es, one form of pilgrimage became especially popular in the Orthodox Church of Georgia. On the memorial days of Saints or just after Sunday liturgy priest and congregation visit graves of these Saints or prominent churches dedicated to them, where they pray and have small services. The study showed that this form was not traditional Georgian form of pilgrimage, but Russian one. I also argue that there might have been five forms of traditional pilgrimage in Georgia. The study was based on historical sources, published scientific works and the personal field ethnographic materials.展开更多
The basic problem in teaching mechanics of materials is that some subjects discussed in the reference books are not easy to understand for most of the students. Using experience of many years teaching mechanics of mat...The basic problem in teaching mechanics of materials is that some subjects discussed in the reference books are not easy to understand for most of the students. Using experience of many years teaching mechanics of materials, we have been continuously trying to find easier methods to help the students get a better understanding of fundamental concepts. This effort and investigation has led to innovative and simple approaches to prove the equations much easier than the existing ones and also to clarify complicated concept. In this paper, we are offering our innovative proof for elastic flexure formulas as well as an interesting model for the moment sign convention in the cross section of a beam. In this method, considering a portion of a beam under pure bending and obtaining the stress distribution in the cross section and applying the balance of the considered portion, we prove the Elastic Flexure Formulas much easier than the existing methods. Emphasizing on deeper understanding, some notes and a new model are offered during this proof.展开更多
文摘This article is based on research on pre-service teachers＇ perspectives on their mathematics knowledge of proof in geometry. The study was framed using tile mathematical knowledge for teaching framework. This qualitative study employed the use of a task-based worksheet, focus group sessions and semi-structured individual interviews. The task-based worksheet was completed by 180 pre-service mathematics teachers （second, third and fourth year mathematics education students）. Pre-service mathematics teachers are student teachers who have not yet completed their training to become teachers. After the analysis of the task-based worksheet, 20 participants were invited to participate in focus group sessions and individual interviews. The findings of the study reveal that the participants possess peripheral mathematics knowledge of proof in geometry. The study aims at assisting pre-service teachers and interested educationists to explore innovative methods of acquiring and imparting mathematics knowledge of proof in geometry. The study proposes possible changes in curriculum at school and university level.
文摘The purpose of our paper is to show, on the example of Tbilisi, how places become sacred and the sights of pilgrimage; what are the modern and traditional forms of pilgrimage in Georgia. The study showed that the graves of the prominent people for their pure life and miraculous deeds, who lived during the Soviet and post-Soviet periods until now are the places of veneration. These people before official canonization became saints for people and as I call them, they became “folk Saints”, as the forms of their veneration are the same as canonized ones. After post-Soviet revival of religiousness in the late 1970es, one form of pilgrimage became especially popular in the Orthodox Church of Georgia. On the memorial days of Saints or just after Sunday liturgy priest and congregation visit graves of these Saints or prominent churches dedicated to them, where they pray and have small services. The study showed that this form was not traditional Georgian form of pilgrimage, but Russian one. I also argue that there might have been five forms of traditional pilgrimage in Georgia. The study was based on historical sources, published scientific works and the personal field ethnographic materials.
文摘The basic problem in teaching mechanics of materials is that some subjects discussed in the reference books are not easy to understand for most of the students. Using experience of many years teaching mechanics of materials, we have been continuously trying to find easier methods to help the students get a better understanding of fundamental concepts. This effort and investigation has led to innovative and simple approaches to prove the equations much easier than the existing ones and also to clarify complicated concept. In this paper, we are offering our innovative proof for elastic flexure formulas as well as an interesting model for the moment sign convention in the cross section of a beam. In this method, considering a portion of a beam under pure bending and obtaining the stress distribution in the cross section and applying the balance of the considered portion, we prove the Elastic Flexure Formulas much easier than the existing methods. Emphasizing on deeper understanding, some notes and a new model are offered during this proof.
