The geometric activities also occur scatteredly and disorderly during the process ofgeometric elements and geometric quantities teaching, the teachers have not really applied effectively
Trang 1HANOI UNIVERSITY OF EDUCATION
DEVELOPMENT OF GEOMETRIC THINKING FOR UPPER KINDERGARTEN AND PRIMARY SCHOOL
CHILDREN THROUGH GEOMETRIC ACTIVITIES
Major: Theory and methods of teaching Mathematics Code: 62 14 01 11
Trang 2HA NOI – 2013
Trang 31.ASS.Prof, Dr Nguyen Anh Tuan
2.ASS.Prof, Dr Vu Quoc Chung
Judge 1: ASS.Prof, Dr Tran Kieu
Judge 2: ASS.Prof, Dr Vu Duong Thuy
Judge 3: Dr Nguyen Van Thuan
Thesis will be defended in front of Council at University Hanoi University of Education, date:……….
Trang 5A.Articles have been published
1 Nguyen Manh Tuan (2009), Van hiele’s viewpoint on forming geometric symbols in kindergatern children and pupils of early
primary school, Journal of Education No 224, pp.35-38.
2 Nguyen Manh Tuan (2010), Spatial imagination and development of spatial imagination for students in early years of primary
level with educational software Journal of Education No 248, pp.5-7.
3 Nguyen Manh Tuan (2011), Developing Spatial Imagination in Children Aged 5-6 years by Formatting Shape
Representations Proceedings 13, Global COE Program "Science of Human Development for Restructuring the Gap - Widening
Society", Ochanomizu University, pp.153-156
4 Nguyen Manh Tuan (2011), Training geometric thinking for children aged 5-6 and early primary (grade 1, 2, 3) through
teaching the relative position of things, Journal of Science National University of Education, No 6, pp.96-103.
5 Nguyen Manh Tuan (2011), Studying the impact of spatial sense and spatial imagination in upper kindergatern children,
Journal of Education No 266, pp.9-11
6 Nguyen Anh Tuan - Nguyen Manh Tuan (2011), Drilling geometry thinking for kindergatern and primary school children
(Grade 1, 2, 3), Journal of Science Education, Institute of Education Sciences, Vietnam, No 72, pp.35-40.
7 Nguyen Manh Tuan (2012), Orientation for forming methodological knowledge for upper kindergatern children and lower
primary students through several geometric activities Journal of Education No 289, pp.36-39.
B.Scientific Research subjects
1 Nguyen Manh Tuan (2011), The process and a number of methods to form geometric symbols from upper kindergarten to the
early primary school children (grades 1, 2, 3), the topic of school.
Trang 81 The reasons for this topic
The development of thinking, creative ability and practical skills education is a requirement in our education today
Education development strategy for 2011-2020 (Decision No 711/QD-TTg) stated: " Fundamental and comprehensive innovation
of education in the direction of standardization, modernization, socialization, democratize, international integration, focus on improving the quality, especially the quality of moral education, lifestyle, thinking, creative ability, practical skills to not only meet the requirements of socio-economic development but also focus on satisfying the needs of development for each learner, the person who has aptitude can develop their talent "
Innovation project of textbook content emphasized on development of capacity and thinking for children, in which theyhave plenty of opportunity to solve the problem and show how to solve the problem with other people; require them to apply theknowledge to solve the situations which set out in practical life for individuals and communities Doing that also meanscontributing to "load reduction" for learners
Developing for children's thinking through the teacher established and organized activities that is regarded as the guidingideology throughout the innovation of teaching methods According to A.N.Leonchev, the discovery of the common structurebetween the two types of inside activity and outside activity is one of the most important discovery of modern psychologicalscience: " Inside activity and outside activity have the same structure, Inside activity comes from outside activity, is formed fromoutside activity.Thinking as inside activity is formed through the human’s process of working
Geometry teaching is a favorable condition for development of thinking for learners - especially the quality of flexible ,independence and creativity thinking , develops spatial imagination and intellectual activities such as comparison, analysis,synthesis, generalization, At the primary level, the formation of geometric elements and geometric quantities also helps
Trang 9children with fundamental knowledge of mathematics, helps children be aware of the world around them and learn mathematics
in the future in higher levels In which, the method of using the geometric activities plays an important role in teaching geometricelements and geometric quantities and develops thinking for learners Through geometric activities, the children can learn in theactivities and by the activities, can self-doing, self-deciding, can experience practical life leading to contribute to promotepositiveness, independence, creativeness, increase interest in the Math class that keep children innocent and happy in early schoolage
However, organizing geometric activities at school has some limitations Although the content of kindergarten and primary
education program now focus on more geometric activities, but teachers do not really evaluate the level of thinking andawareness of children in geometric activities The geometric activities also occur scatteredly and disorderly during the process ofgeometric elements and geometric quantities teaching, the teachers have not really applied effectively in the Review class orextracurricular activities, especially the 2 sessions - class / one day in elementary school, the teachers usually recommend ordeduct from reference books, primary school children mainly take time to do homework in class, the teachers focus on teachingknowledge more than training and developing thinking for children, organize less activities for children The reason is thatteachers do not pay proper attention to the role of geometric activities for the development of thinking, the establishment andorganization of geometric activities which required time-consuming, the teachers are difficult and confused in evaluatingchildren, do not control children
Before the children enter elementary school, children have certain awareness and understanding through activities whichhelp chidren be familiar with Math in kindergarten, five-year-old universal project of the Ministry of Education and Training hasbeen implemented with the goal of completing the whole country in 2015 and also raised new questions about the "connection"the content of program of making familiar with Math for children at upper kindergarten and curriculum in mathematics for
Trang 10elementary children school So researching on teaching Math in general, geometric elements and geometric quantities teaching inparticular from children at kindergarten (5 years) to children at primary school is necessary, the teacher must not teach before theprogram , "primarized education" children at kindergarten, at the same time avoid children’s psychology to be"boring" whenentering the first grade.
For these reasons, the chosen topic is: " Development of geometric thinking for upper kindergatern and primary school children through
geometric activities”
2 The research purposes
Development of geometric thinking for upper kindergarten children and at primary school children through the selection,construction, orgnization some geometric activities
3 The objects of research
The process of formation of the geometric elements and geometric quantities for upper kindergarten children and atprimary school children
4 Scientific hypothesis
Because the activity plays an important role in the development of children's thinking, so if we can evaluate the children’slevel of geometric thinking and design, organize suitable geometric activities in teaching of geometric elements and geometricquantities, children’s geometric thinking will be better developed, teaching of geometric elements and geometric quantities willachieve higher efficiency
5 The research tasks
Research the basic of theory
Trang 11The topic studied about basic theoretical of geometric thinking and characteristics of development geometrica thinking inupper kindergarten children and at primary school children;concepts related geometric thinking; levels of geometric thinking.
Investigate the level of geometric thinking capacity in upper kindergarten children and at primary school children5.3.Estabish some methods to develop geometric thinking capacity of upper kindergarten children and at primary school children
- Assess the level of geometric thinking capacity through some geometric activities
- Develop and organize some geometric activities to establish the way to solve the problem;
- Increase applying mathematics in practice;
- Apply situation theory and make situations to develop geometric thinking for children
Pedagogical experiment: Pedagogical experiments test the validity of scientific theories and the feasibility of themethods which are proposed and studied by the topic
6 The scope of the research
Study of the development of geometric thinking for upper kindergarten children and at primary school children through
some geometrical activities in schools.
7 Research Methodology
- Academic research methods: study the psychological characteristics of upper kindergarten children and at primaryschool children; study the development of thinking in general and geometric thinking in particular in the process ofteaching of geometric elements and geometric quantities for children in the country and over the world;
- Method of summarizing educational experiences;
- Methods of observation: Observe and record the activities of teachers and children in kindergarten and primary school tolearn manual operation, organize for kids in the class making acquainted with geometric symbols;
Trang 12- Methods of statistic: Using statistical methods to handle statistics to measure the level of geometric thinkingcapacity in children to confirm the validity of scientific theories and the feasibility of the method which is raised in thetopic.
8 Issues defended in thesis
- The concept of geometric thinking in upper kindergarten children and at primary school children, the performance ofgeometric thinking capacity in children through some geometric activities
- Assess the geometric thinking capacity in upper kindergarten children and at primary school children in some geometricactivities
- Develop geometric thinking through the estalishment and organization some geometric activities in upper kindergarten
children and at primary school children
9 The structure of the thesis
Besides the Introduction, Conclusion, References and Appendix, the thesis consists of three chapters:
Chapter 1: Fundamentals of theory and practice
Chapter 2: A number of methods to develop geometric thinking in upper kindergarten children and at primary school children
Chapter 3: Pedagogical experiment
Trang 13CHAPER 1 : FUNDAMENTAL OF THEORY AND PRACTICE 1.1 History of research
1.1.1 The research in Viet Nam
In general, these researches focus on methods of establishing and organizing thinking activities to develop thinkingthrough geometric elements and geometric quantities teaching in upper kindergarten children and at primary school children,however the geometric activities is built mainly based on the teaching content in each class,the research of geometric activitythroughout the classes from kindergarten and at primary school has not really been interested and focused
1.1.2 The research in the world
Dutch mathematics educators Van Hiele gave level of geometric thinking from low to high, from that he made theevaluation tests for children and teaching methods which is applicable to each level are widely used in design of teachingprogram content (in kindergarten children, primary school children and high school) in many countries in the world
Geometric thinking requires a combination of spatial concepts and symbols, between logical thinking and spatialperception Clements said that even when the children know a triangle has three sides and three angles, they called the "▲" is atriangle but they can not accept the "▼" is a triangle because it "spin down under "- in other words, the visual icon element can"obscure " thinking logic element and language Here the teacher plays an important role in establishing between the space thesymbol and cognitive concept
According to Hoffer (1981), the geometric thinking is the capacity which teachers need to form in children in the teaching
of geometry, he gave five groups of necessary skills of geometry thinking
i) The capacity of visual - images: Identify, observe the characteristics of geometry, reading a map, identify the differentpositions;
Trang 14ii) The capacity of language: Use correct terminology and accuracy language in describing the object and spatialrelationships;
iii) The capacity of making shape: Create icons of two-dimensional or three-dimensional, drawing similar figures, drawingsymmetric figures;
iv) The capacity of logical thinking: Classification, recognition criteria to classify, create and test hypotheses andinference; demonstration;
v) The capacity of applying: Apply knowledge learned in practice, solving practical problems by geometry
The research in the country and over the world have shown the existence of geometric thinking, the factors that affect thecapacity of the geometric thinking, the level of geometric thinking in children, have studied the role of the geometric activity forthe formation and development of geometric thinking However, the evaluation of the geometric thinking in geometric activityhas not been interested In the same content of teaching or the same geometric activity ,the children show different ways to solveproblem, how to think, how to solve the problem, the different difficulties and "obstacles", therefore it is necessary to have initialresearch of evaluation geometric thinking capacity in geometric activities On the other hand, the construction and organization ofgeometric activities to promote geometric thinking and the differentiate between children has not really been focused, yet notbeen diverse, not been rich, not shown the way of development from this level to the next higher level
1.2 Geometric thinking
1.2.1 The concept of geometric thinking
Our concept: "Geometric thinking is the process including: 1) the perception of space; 2) the implementation of intellectual activities such as comparison, analysis, synthesis, generalization, abstractionsymbolized, inference, provement; 3) show how to solve the problem and 4) apply in practice "
Trang 15In which: Doing intellectual activities by children is the most important and it can be decided that children have geometric thinking or not
From conception above, The characterics of geometric thinking can be described :
1) The intellectual activities of geometric thinking is based on the perception of space
In work of thinking by eyes ,Arnheim argues that "the most important intellectual activities deriveddirectly from our perception of the world, and the view is considered premium sensory system whichcovered and formed our cognitive processes "Spatial perception itself is not thinking but is necessary tocarry out the geometric thinking, it will be difficult to solve geometric Mathematics without drawingobservation or at least thinking about drawing Spacial perception is included in the perception of spatialobjects and spatial relations and movement combination between the senses (mostly the combinationbetween hand and eye ) In teaching the first age at school , the early basis visual is more significant because the child's thinking
is mainly visual thinking
2) Geometric thinking has a close relationship with space imagination
- Geometric thinking is the condittion for children to carry out space imagination
For example : “How many cubes are there in the picture ?” This exercise requires children to use space imagination in
solving problems.However, that imagination is only formed in the process of observation, puzzle, analyze, compare cubes inpractice
For example: The exercise for grade 1 in China: "Can you guess that how many door arethere in the picture, how many flowerpots are there in the picture (look for the most reasonableanswer)?"(Picture 1.7)
Picture 1.7 Picture 1.6
Trang 16This problem requires the children to have space imagination.To do this, the children must have training activities ofobservation and analysis - synthesis objects in space there is the analysis of what they "see" and what they "know but do not see
"(geometric thinking activities)
With a problem that can not be solved by geometric thinking, spatial imagination can help predict results, as “solving”method for the situation.Moreover it creates a destination for thingking towards, or in other words, it orients for geometricthinking.Thus the difficulties of geometric thinking is a premise for spatial imagination, and spatial imagination becomes thedestination for geometric thinking to develop
3) Language is a part of geometric thinking
4) The children can apply in practice which is a base to access geometric thinking
The ability to apply in practice is an important criteria for determining children’s geometric thingking capicity , they began
to approach with specific objects and relations, practice intellectual activities and return the application with the specific objectsaround them.Through the teaching of geometric elements and geometric quantities, not only to teach children about things ofobjects or spatial relations, but also to require what the children will do in practice
On the base of the study of the characteristics of thinking upper kindergarten and elementary children (Section 1.2.4), the
study of level of geometric thinking according to Van Hiele (Section 1.2.3), can be understood: "Geometric thinking at this age is
the process including: 1) the perception of space; 2) Carry out intellectual activities such as comparison, analysis, synthesis, 3) show the way to solve the problem, and 4) apply in practice "
1.2.2 The role of geometric thinking
1.2.3 The level of geometric thinking according to Van Hiele
Trang 171.2.4 The characteristics of geometric thinking in upper kindergarten and elementary children
1.2.5 The capacity of geometric thinking in children
1.3.Develop the capacity of geometric thinking for children through geometric activities.
is necessary.Thus the teachers found the way to develop geometric thinking and geometric activity in children and appropriateteaching methods Creating the way to solve problems during geometry activities, setting knowledge-tectonic situations, innovatethe assessment to contribute to reduce programs in textbooks
1.3.2.Performance of geometric thinking capacity of big kindergarten and elementary children during geometric activities
In the process of geometric activities for children, there can be proposal of evaluation of geometric thinking through thefollowing performance:
1) The capacity to perform intellectual activities (comparison, analysis, synthesis) is reflected on:
- Means which children used in activity: Which means and materials do children choose? How to use them ?
- Which difficuities, "obstacles" do children have in the process working?
- The result of activity : How is the level of completeness of activities?
2) The capacity of the language: