Hoa Anh Tuong 2010, Lesson study- Theoretical basis và applying in mathematics teaching, Proceedings of the scientific conference of master students and PhD students in 2010, Ho Chi Minh
Trang 1UNIVERSITY OF PEDAGOGY HO CHI MINH CITY
-HOA ANH TUONG
Specialization: Theory and Methods of Teaching
and Learning Mathematics Scientific Code: 62.14.01.11
SUMMARY OF DOCTORAL THESIS ON EDUCATIONAL SCIENCE
HO CHI MINH CITY– 2014
Trang 2UNIVERSITY OF PEDAGOGY HO CHI MINH CITY
Supervisor : Assoc Prof Dr Tran Vui
Reviewer 1: Prof Dr Dao Tam
Vinh University
Reviewer 2: Assoc Prof Dr Nguyen Phu Loc
Can Tho University Reviewer 3: Dr Le Thai Bao Thien Trung
University of pedagogy Ho Chi Minh city
The Thesis Evaluation University Committee:UNIVERSITY OF PEDAGOGY HO CHI MINH CITY
Thesis can be found at:
- General Science Library of Ho Chi Minh City
- Library of University of Pedagogy Ho Chi Minh City
Trang 3RELATED TO CONTENT OF THESIS
1 Hoa Anh Tuong (2009), Lesson study-a view in researching mathematical
education, Journal of Science and Education, Hue University’s College of Education, ISSN 1859-1612, No 04/2009, pp 105-112
2 Hoa Anh Tuong (2009), Research to make opportunity for students to
communicate mathematics, Journal of Education, Ministry of education and training, ISSN 0866-7476, No 222 (period 2-9/2009), pp 50-52
3 Hoa Anh Tuong (2010), Mathematical creativity in teaching exercises, Journal
of Saigon University, ISSN 1859-3208, No 04 (9/2010), pp 54-60
4 Hoa Anh Tuong (2010), Using lesson study in the lesson “Area of a Polygon”,
Journal of Science, Ho Chi Minh city University of Education, ISSN
1859-3100, No 24 (12/2010), pp 133-140
5 Hoa Anh Tuong (2011), Thalès theorem-A research to improve the quality of
teaching and learning, Journal of Science, Ho Chi Minh city University of Education, ISSN 1859-3100, No 27 (4/2011), pp 54-61.
6 Hoa Anh Tuong (2011), Approach a problem by solving different ways,
Teaching and learning today, Journal of Vietnam central learning promotion association, ISSN 1859-2694, No 9 (2011), pp 59-60
7 Hoa Anh Tuong (2011), To look at the problem in different ways, Journal of Science, Saigon University, ISSN 1859-3208, No 07 (9/2011), pp 105-111
8 Hoa Anh Tuong (2011), Using the external visual representations in
mathematics for teaching students grade 6, Journal of Science, Vinh University, ISSN 1859-2228, Vol 40, No.1A (2011), pp 56-65.
9 Hoa Anh Tuong (2011), Using “Open–ended problem” stimulus student to
communicate mathematics, Journal of Science, Ho Chi Minh city University of Education, ISSN 1859-3100, No 31 (10/2011), pp 121-124.
Trang 4study geometry actively, Journal of Science, Vinh University, ISSN
1859-2228, Vol 41, No 1A (2012), pp 85-91
11 Hoa Anh Tuong (2013), Focus on innovative teaching method-a view of
practical researcher, Journal of Science, Saigon University, ISSN 1859-3208,
No 14 (6/2013), pp 81-87
12 Hoa Anh Tuong (2010), Theoretical basis of constructivism theory in
mathematics teaching, Proceedings of the scientific conference of master
students and PhD students in 2010, Ho Chi Minh city University of Education,
pp 92-102
13 Hoa Anh Tuong (2010), Lesson study- Theoretical basis và applying in
mathematics teaching, Proceedings of the scientific conference of master
students and PhD students in 2010, Ho Chi Minh city University of Education,
pp 103-116
14 Hoa Anh Tuong (2012), The Use Of Visual Representation In Reasoning And
Expanding Mathematics Problem: Lesson Study On The Area Polygon,
Proccedings of the 5th International Conference on Educational Research(ICER) 2012, Challenging Education for Future Change, September 8-9, 2012,Khon Kaen University, Thailand, pp 417-424
15 Hoa Anh Tuong (2013), Applying "open - ended task" to help secondary
students to communicate mathematics, Proccedings of the 6th International
Conference on Educational Research (ICER) 2013, ASEAN Education in the
21st century, February 23-24, 2013, Mahasarakham University, Cambodia, pp.394-405
16 Hoa Anh Tuong (2013), Solution to decrease distance between training teachers of education mathematics and teaching mathematics of new teachers
in vietnamese secondary school, International Conference on Mathematical
Research, Education and Application, December 21st-23rd, 2013, UEL, HCMC 2013, pp.105 (abstract)
VNU-17 Hoa Anh Tuong (2014), Apply model of lesson study in teaching mathematics,
Proceedings of the scientific conference on the teaching of natural sciences in
2014, An Giang province, pp 127-134
Trang 51 Definition of terms
Mathematical communication is a way of sharing ideas and clarifying
understanding Through communication, ideas become the objects ofreflection, refinement, discussion, and amendment The communicationprocess also helps to build meaning, permanence ideas and makes thempublic (Lim, 2008)
Mathematical communication competence: including the disclosure is
our own political opinions about the mathematics problems, understandpeople's ideas when they present the matter, express their own ideas crisplyand clearly, use mathematical language, conventions and symbols (PhamGia Đuc và Pham Đuc Quang, 2002; Mónica Miyagui, 2007)
Open-ended problems are often thought of as tasks for which more than
a single correct solution is possible (Erkki, 1997) Foong (2002) describesthe open-ended problems as “ill-structured” because they comprise missingdatas or assumptions with no fixed procedures that guarantee a correctsolution
Lesson study is a professional development form in which research on
teaching and learning in classroom is carried out systematically andcollaboratively by a group of teachers in order to improve their teachingpractices (James W.Stigler & nnk, 2009; Nguyen Thi Duyen, 2013) Agroup of teachers collaboratively designs the lesson plan, implements andobserves the lesson in the classroom, discusses and reflects on the lessonwhich is taught, revises the lesson plan, and teaches the new version of theedited lesson plan
A study lesson is a lesson that the lesson study group chooses to explore
in the lesson study process
Trang 6 Chang (2008) stated “The first goal of mathematical communication is
to understand the mathematical language” Emori (2008) stated “All themathematical experiences are done through communication Mathematicalcommunication is needed to develop mathematical thinking becausethinking development is explained by the manner's language and ways ofcommunication”
Lesson study helps teachers continuously innovate teaching andimprove learning for students In lesson study, teachers play a central role
in deciding what is new in teaching and learning and directly implementinnovation in the real classroom Through lesson study, teachers doaccumulate real experience, and improve lesson study
In this study, we tried to design lesson plan discussed colleagues bythe process of lesson study in order to provide the opportunities for students
to show, debate, deduce, and present the proof Since then, they need tocommunicate and evoke mathematical ideas in the process of constructingnew knowledge
We choose the research topic: "Using lesson study to developmathematical communication competence for secondary school students."
3 Purpose of the study
How to organize classroom to promote and develop students’mathematical communication competencies
To research and design a number of lesson contents in mathematicsgrade 8 to promote students to communicate mathematics
To look at the scale levels of mathematical communicationcompetence are used in evaluating students through some of study lessonsbeen studied experimentally
4 Research Questions
The first research question: How to use basic way of communicatingmathematics effectively (mathematical representation, interpretation,argumentation, and presenting the proof) in mathematics classroom?
The second research question: How to organize mathematics classroomthat can promote and develop students’ mathematical communicationcompetencies?
The third research question: Which lesson contents in mathematicsgrade 8 and how to design lesson plans create opportunities for students topromote mathematical communication process?
Trang 7The fourth research question: How to evaluate the development ofcommunicative competence of students through studied lessons?
To give the scale levels of mathematical communication competence
6 The significance of the study
The thesis will be meaningful for education by:
Surveying the basic way of communicating mathematics which isexpressed by Vietnamese students in the classroom
Proposing forms of teaching methods to develop mathematicalcommunication competence of students according to their mathematicalability; thereby, forming confidence for Vietnamese students in sharing,discussing with peers and teachers
Designing some lesson plans in mathematics grade 8 has manyopportunities to promote students to communicate
Proposing the scale levels of mathematical communication competence
7 The layout of the thesis
The thesis included 6 chapters except for the introduction and conclusion
remark Chapter 1 Mathematical communication in classrooms Chapter
2 Lesson study and open-ended problems Chapter 3 Methods Chapter
4 Developing mathematical communication competence through lesson
study Chapter 6 Conclusion and recommendation Chapter 5 The
results of the research questions
8 Summary of introduction
Chapter 1 Mathematical communication in classrooms
1.1 Origin of mathematical communication
“Mathematical communication is a kind of communication Greek origin of
the word communication is related with community… Mathematical
communication is the communication in mathematics” (Isoda, 2008)
Trang 81.2 Communication in mathematics classrooms
Communication in mathematics classrooms is the interaction betweenstudents-teacher-students, through verbal communication and usingeveryday language
1.3 Other studies in mathematical communication
We present some mathematical communication practices in some countries
In thesis, we choose the meaning of communicate mathematical is the waystudents express their mathematical perspectives (Brenner, 1994).Mathematical communication has three distinct aspects: Communication
about mathematics, communication in mathematics, communication with
mathematics
1.4 The role of mathematical communication in classrooms
Emori (2008), “Mathematical communication is a key idea which isimportant not only for the improvement to learn mathematics but also forthe development of necessary skills in the development of sustainablesociety knowledge”
1.5 The scale levels of mathematical communication competence
1.5.1 The six proficiency levels in mathematics
In six proficiency levels in mathematics, from the third level,
it has proficiencies: Representation, interpretation, argumentation andreasoning
1.5.2 The basic way of communicating mathematics
In this research, I choose the basic ways of communicating mathematics:Representation, interpretation, argumentation, presenting the proof becausethese basic ways are related to communicating mathematics
1.5.3 Standard about communicating mathematics
1.5.3.1 Four forms of communication in Mathematics classroom
Oral communication; listerning; speaking communication; and writing
1.5.3.2 Standard about mathematical communication
Organize and consolidate their mathematical thinking throughcommunication Communicate their mathematical thinking coherently andclearly to peers, teachers, and others Analyze and evaluate themathematical thinking and strategies of others Use the language ofmathematics to express mathematical ideas precisely (NCTM, 2007)
1.5.4 The scale levels of mathematical communication competence
Trang 91.5.4.1 The scale levels of mathematical communication competence
Level zero No communication
Level 1 Expressing initial idea
- Students describe and present methods or algorithms to solve the givenproblem (not to mention the method is right or wrong)
- Students know how to use the mathematical concepts, terminologies,symbols and conventions formally
- Students can argue which appropriate mathematical concepts,terminologies, symbols and conventions they should use
Level 4 Proving
- Students use mathematical concepts, mathematical logic to prove thegiven results
- Students use mathematical language to present mathematical results
1.5.4.2 Example of mathematical communication
We illustrated a lesson on October 3, 2010 in class 6A3 (51 students) ofSaigon Practical High school
Friday, August 26th 2011 was Vi’s birthday
a) After 7 days was of her mother’s birthday What should be the day anddate of her mother's birthday? Why?
b) What should be the day after 52 days from the birthday of Vi? Why?
c) November 20th 2011 was Vi father’s birthday What should be the day?Why?
Student showed the basic way of communicating mathematics asfollows:
Representation: Students could use calendar to find the date in a week
from 26/8 to 2/9; Monday schedule of every month from 17/10 to 21/11 to
Trang 10find a solution They knew 7 days respectively 1week, 30 days or 31 daysrespectively 1 month.
Interpretation: Students tried to find a solution Depending on their
abilities, they had different ideas The easiest way was writtern a specificschedule in a week If you change the assumptions of the problem, such assentences b) changes 52 to 520 and change the sentence c) November 20,
2011 to December 27, 2014; this way will be not suitable Student shouldunderstand which solutions could still be used when the requirements havechanged It means that students are aware of the rationality of expression
Argumentation: Students know how to use the law of 7 day cycle, the
day will repeat From there, students know how to find remainder in thedivision by 7 to find the day In addition, students remembered how manydays have in August and September, then to perform operations unlesssuitable to find how many days have in the month Students recognized theproblems may have link to each other
Presenting the proof: Students themselves understood how to solve the
problem by listening to peers who demonstrated the problem
Evaluate the scale levels of mathematical communication competence:
Expressing initial idea: Students described a way to solve the problem
by writing the calendar in the week from 26/8 to 2/9, Monday schedule inthe month from 17/10 to 21/11 They applied the algorithm based on theremainder in the division by 7 They used reasonable mathematicaloperations: addition, subtraction, division
Explaining: Students recognized the validity of each solution Students
realized algorithm to find the remainder in the division by 7 morereasonable than other solution
Argumenting: Students expressed logical reasoning, solution of each
problem clearly
Proving: Students used algorithms to find the remainder in division 7,
the language of mathematics, logical reasoning in the presenting the proof
Trang 11“Lesson Study” (jugyou-kenkyu) in Japanese thus came to be knownaround the world as a unique Japanese method of lesson improvementdesigned to facilitate the development of high quality lessons.
2.1.2 Other researchs in Lesson Study
“Japanese Lesson Study in Mathematics: its impact, diversity and potential for educational improvement” (Isoda, 2005).
Thailand implements lesson study: To investigate changes in teachers’pedagogy and their professional development when they are using the open-approach teaching method To clarify how teachers recognize their learningexperiences in the classroom where open-approach teaching method hasbeen implemented
Fernandez also investigated how teachers took advantage of learningopportunities that were created by lesson study
In Vietnam: Tran Vui (2006a, 2006b, 2007), wrote a number of articles
about the effectiveness of applying the model lesson study in practice
teaching mathematics in elementary school and secondary school NguyenDuan and Vu Thi Son (2010) wrote a paper on approaching lesson study todevelop professional capacity of teachers Nguyen Thi Duyen (2013) has anumber of articles on applied lesson study in the practice of teachingmathematics in high schools
2.1.3 Process of lesson study
There are many different variations of lesson study process, however alesson study process generally involves a group of teachers collaborativelydesigning the lesson plan, implementing and observing the lesson in theclassroom, discussing and reflecting on the lesson which is taught, revisingthe lesson plan, and teaching the new version of the edited lesson plan(James W.Stigler & nnk, 2009)
2.1.4 The factor of implementing process of lesson study
To be successful implementation of lesson study process has many factorssuch as teachers, students, schools, programs, textbooks
2.1.5 Example of implementing process of lesson study
From the orientation of textbook to prove theorem sum of 4 angles of a
quadrilateral and the formula to find sum of angles of the polygon n
vertices (textbook mathematics grade 8, volume 1, page 65 and page 115).Through discussions with teachers about students' difficulties in proving
Trang 12theorem and solving the problem, we adjust and improve lessons plan tohelp students find other ways to prove theorem “sum of 4 angles of a
quadrilateral” and set formula to find “sum of angles of the polygon with n edges” by n.
2.2 Open-ended problems
2.2.1 Origin of open-ended problems
The Open-Ended Problem Solving is based on the research conducted byShimada S., which is called “The Open-Ended Approach” The Open-Ended Approach provides students with “experience in finding newsomething in the process” (Shimada 1997)
2.2.2 The role of open-ended problems
2.2.3 Example of study lesson using open-ended problems
Applying the “open-ended problems” in teaching is a question which istypical teaching situations but the purpose of the question is open-endedsuch as: there are many different solutions, there are many results, orientateinvolved issues
Example 2.1 To find the kind of quadrilateral.
Give a triangle ABC (AB < AC) with M, N and P respectively are midpoints of segments AB, AC và BC; AH is altitude Prove that quadrilateral MNPH is an isosceles trapezoid?
The requirements of the problem “To prove the quadrilateral MNPH is
an isosceles trapezoid”, is a closed-ended problem, we adjust the problem
as follows: Give a triangle ABC (AB < AC) with M, N and P respectively are midpoints of segments AB, AC và BC; AH is the altitude What is the kind of quadrilateral MNPH? Why?
The requirements of the problem “What is the kind of quadrilateral
MNPH? Why?” is an open-ended problem because students actively find
out many different results according to the ability to apply knowledge
In particularly, students argue, explain: why quadrilateral MNPH is a
trapezoid or an isosceles trapezoid Students should have figure readingskills, then thinking and applying the hypothesis of the problem to find outthe ways to solve the problem So the teacher evaluates student’s ability toapply
In addition, teachers create opportunities for students to convertproblems to similar contents through open-ended problem, such as: Find the
Trang 13pair of equal segments in quadrilateral MNPH? Find the pair of equal angles in quadrilateral MNPH? Find the pair of equal segments and angles
in two triangles MNH và MNP? Explain? Then, students try to find as many
solutions as possible This stimulates student to learn actively and applyassumptions to solve given problem
In addition, teachers give students another open-ended problem “What
properties are there in quadrilateral MNPH?” Students have skills in
reading figure and create a number of conclusions:
The edge: opposite sides are parallel, adjacent sides are equal The diagonal: diagonals are equal Angles: 2 angles adjacent based side are
equal, 2 angles adjacent side are complement and 2 opposite angles arecomplement Symmetry: There is one axis of symmetry which is the line
passed two midpoints of the two based sides and center of symmetrydoesn’t have
When the students listed the
characteristics above, they have mastered
how to prove the quadrilateral become a
trapezoid or an isosceles trapezoid and the
properties of an isosceles trapezoid, and
know whether the axis of symmetry and
center of symmetry of the isosceles
trapezoid exist? Students practice to prove
two equal triangles
Figure 2.4 Quadrilateral MNPH
2.3 Summary chapter 2
Chapter 3 METHODS 3.1 Research Design
Research process was conducted according to the following steps:
- Survey the learning environment through the investigation process
- Look the available research results in using open-ended problems,mathematical representations
- Research on the integration to the basic way of communicatingmathematics for students
P
N M
H A
Trang 14- Make the lesson plans through experiment to determine the strengths
of the lesson plan designed to develop mathematical communicationcompetence for students
3.2 Research Subjects
The research object of the thesis include: How does the basic way ofcommunicating mathematics apply? How can classroom be organized tocreate demands and opportunities to express mathematical communicationand skills design lesson plans in mathematics grade 8 that can makestudents express mathematical communication? Or how can students’mathematical communication competence be evaluated?
3.3 Research scopes
- Research the lesson plans using open-ended problems to developmathematical communication competence for students
- Students participate in the experimental lessons: 166 students
- References: mainly in the references listed in the references section
- Survey contents: student’s thinking about learning mathematics, ways
to learn mathematics, what happens regularly in the mathematicsclassrooms
3.4 Methods of data collection
- Gather information from the research topic presented in textbooks aswell as the perfection of teachers teaching on that subject
- Gather information from surveying students
- Collect data from observing students and assess showing basic ways ofcommunicating mathematics in the experimental lessons
3.5 Methods of data analysis
From the collected data mentioned in section 3.4, we:
- Analyze and propose adjusting through the lesson plans
- Conduct statistical data to assess the students' perspection Since then,design study lessons
- Evaluate the effectiveness of lesson plans and adjust to promotestudents’ mathematical communication competence
3.6 Research tool by the process of lesson study
3.7 The study of mathematics contents
3.7.1 Objectives and requirements of teaching mathematics in secondary school