By Dian Permatasari
On 2 – 5 November 2011, there are APEC - Ubon Ratchathani
International Symposium 2011 with the theme Innovation on Problem Solving -
Based Mathematics Textbooks and E-Textbooks.
The symposium aimed to study the cooperation of learning
innovations in Mathematics in different cultures among APEC members and to
promote cooperation among APEC members in Mathematics learning and teaching
innovation development which are used in different cultures. Researchers from
16 countries participated in the symposium and were provided with opportunities
to share ideas and exchange experiences. The special participant is Mr.
Marsigit from Indonesia. This is Mr. Marsigit’s experience when he is in Thailand.
The activities of Mr. Marsigit in the APEC – Ubon
Ratchathani International Symposium 2011 are
1. Mr. Marsigit is as the
member of invited speaker. Invited speaker is the person that famous and have a
network in education area.
2. Mr. Marsigit has been
presenting their paper as specialist instructor. There are 15 person in here,
and they have one ours to present their paper.
3. As the observer and
commentator at the open class activity, Mr. Marsigit get the first room. In the
first room, there are 5 observers and commentator, and one teacher, that is,
Cheng Chun Chor Litwin, Marsigit, Madihah Khalid, Catherine Lewis, and teacher.
They observe the 1st grade about how the 1st grade can calculate
the number of dragonfly.
The teacher given the picture of dragonfly that must be
calculate in front of the class and also give one picture of it in each
students. Next, the student must be calculated the dragonfly and collected it
to the teacher. After it, the teacher will be chosen the student to present
their answer.
The teacher changes the method to calculate the dragonfly,
that is, use the cube to calculate the dragonfly. With this method, Mr.
Marsigit thinks that it makes the students feel more difficult to calculate the
dragonfly.
4. Mr. Marsigit is a
commentator of invited speaker’s presentation. They are Prof.Maitree Inprasitha from
Rusia that tells about probability theory in 7 – 9 grade andUtith Inprasit from
Thailand that tells about Learning Mathematics Model.
This some comment from Mr. Marsigit for some participant :
· Expected
mathematical activities
In Mr. Marsigit’s opinion : The over plus of the human
thinking is because they have expectation. Example, Mr. Marsigit always comes
at 9 am. One time, because he has an agreement, at 9.10 am, he is not come yet.
So, we have an expectation that Mr. Marsigit is not come. Expectation can make
one person close to another person. And every one certain have an expectation.
· Finding
outeasier or more elegant approach
Mr. Marsigit has an opinion that the word ‘elegant’ doesn’t
match with it. if it is translated in Indonesia, it become ‘menyelesaikan soal
matematika dengan berwibawa’. This is one aspect of psychological, we must find
the word that correct for the sentence.
Mr. Marsigit has and opinion that people can think because
they have the sophisticated computer, that is, the human brain. This thing
differentiates the human and the other creature. Example, a cat has an
experience ever to go to Thailand, but it can’t thing.
Therefore, we need psychology as a basic of mathematics
model or design development.
In the following, we will review some papers of
mathematics educationist from different context ofculture in relation to the
aspects of Innovation on Problem Solving - Based Mathematics Textbooks and
E-Textbooks.
1. Isoda Masami from
Japan
In principle, mathematical activities carried out as problem
solving. That is, they are a sequence starting with ‘Generating wonder and
question, formulating problem by formalizing them understanding the problems,
planning, implementing, and reflecting on solution processes.
In his presentation, he writes “More Important end of a
problem solving must be start for next challenge.”
2. ‘Problem Solving
Approach in Teaching Learning of Mathematics in Vocational Senior High School’
by Marsigit and R. Rosnawati from Indonesia.
This paper tell that textbook or book is important thing to
increase the teaching and learning processes and problem solving skills. The
ideal textbooks are containing problem solving approach and it can produced by
the teacher self.
To develop textbook for junior mathematics, the
teachers need clear picture the procedures: problem solving activities,
reasoning and proof, mathematical communication, mathematical connections,
mathematical representation, the role of technology, content arrangement and
skills development, content appropriate and relevant, wide range of student
interests and abilities, and materials easy to follow and understand.
The problem solving based mathematics textbook in the
Vocational Senior High School can be developed based on the criteria outlined
by Polya and Pasmep that are: (1) Trial and Error, (2) Making diagram, (3)
Trying the simple problem, (4) Making Table, (5) Finding the pattern, (6)
Breaking down the goal, (7) Considering the possibilities, (8) Thinking
Logically , (9) Reversing the Order, and (10) Identifying the impossibility.
3. ‘Transforming A
Mathematics Textbook Practical Work Activity Into A Problem-Solving Task
Through Lesson Study’ by Soledad A. Ulepfrom Philipina
Mr. Ulep Paper’s tell about lesson study. So in high school
mathematics with the author as facilitator transformed a mathematics textbook
to introduce about the polynomial function. The author facilitated discussions
with the teacher so they can develop their mathematical thinking to learn about
it and solve its problem. The students make boxes with an open top and they
must discover that each cut that they made was actually the side of a square
whose length would later become the height of the box. They would realize that
the quantities length, width, and volume of the box changed as the height of
the box changed and they could represent these functional using equations. In
the end, Mr. Ulep recommends that it would be good for text books to use
problem that would be an opportunities for students to think instead of
activities where they are just asked to follow a set of procedures.
4. ‘The Development of
Hands-on and E-Activities for Learning Mathematical Models’ by Supot
Seebut, Sasitorn Pusjuso, Sakda Noinang, and Utith Inprasit from Thailand
The ultimate goal of mathematics learning is to make the
students confidently in real world condition. Mathematical modeling is a
form of real-world problem solving by translating the problem into mathematics
form to find the solution because all mathematics concept have roots in real
world.
1. The process of
mathematical modeling consists of four main stages:
2. Observing a
phenomenon, delineating the problem situation inherent in the phenomenon, and
discerning the important factors (variables/parameters) that affect the problem
3. Conjecturing the
relationships among factors and interpreting them mathematically to obtain a
model for the phenomenon
4. Applying appropriate
mathematical analysis to the model
5. Obtaining results and
reinterpreting them in the context of the phenomenon under study and drawing
conclusions (Frank Swetz & J.S. Hartzler. (1991).
This process could be repeated until mathematical model is
appropriate to make prediction and conclusion about observed real world
situations.
There are some examples of hand-on mathematical modeling
like Wildlife Population Survey, Facility Location, and Car Parking. A
mathematical Model activity is developed in E-Activities. E-Activities were
developed to support learning mathematical models online. The conclusion of the
paper is Hands-on activities help them to understand about mathematical model’s
concept
5. ‘The Use of Dynamic
External Representation in Reasoning and Investigating Mathematics Problems:
Lesson Study on the Cross Section in Solid Geometry’ by Tran Vui from
Thailand
Tran Vui tells us that in Vietnam, the use of dynamic
external representations in communicating, learning, and teaching is
increasing. The purpose of it is to share the examples that it can invite the
students to visualize the school mathematics. The learners are able to
interpret and give a representation about their opinion, investigation,
reasoning, and communicating it with other. In Vietnam curriculum of high
school, it tries to decrease the training basic skills and procedures and
increase the hands-on activities to develop the mathematical thinking of the
students. Thus, they can implement it when they want to solve the problem. In
mathematics test, we must pay attention in the procedures, rule, and techniques
when answer the question. In this paper, Mr. Tran Vui provides 5 questions that
have different difficulty. The result is about 65% of students who can solve
the difficult problems with clear procedures in mathematics. Vietnamese
mathematics teachers believe that classroom activities are of outmost
importance for students learning mathematics. In particular, the use of dynamic
external representations encourage students to incorporate many different types
of representations into their sense-making, the students will become more
capable of solving mathematical problems and understanding underlying concepts.
6. ‘Using fractions
learning to enhance mathematical thinking’ byCheng Chun Chor Litwin from Hong
Kong
Mr. Litwin’s paper tells about lesson study for fraction
learning. This paper is based on teachings of fraction additions and fractions
with problem solving in two classes in a Hong Kong school, to investigate the
design of a lesson in promoting mathematical thinking. Fraction is one of
important topic primary mathematics. Using daily example is one method to make
the students interest to learn mathematics. There are two types of questions
used in this study for enhancing mathematical thinking with fractions. The
first type of questions is investigation on fraction additions with positive
integral value and their sums add to 1. The second type of questions is
solving problem based on equivalence fractions or using algebraic equation. This
paper suggests that fractions learning should also include the investigation of
fractions so that students could investigate with the concepts of fractions.
7. ‘Adventuring Through
Big Problems as Means of Innovations in Mathematics Education’ by Fou-Lai
Lin With Hui-Yu Hsu, Kai-Lin Yang, Jian-Cheng Chen, and Kyeong-Hwa Lee from
Taiwan
Three Big Problem
1. Problem One =
the challenge of integrating student perspective into teaching practices
2. Problem Two = the
group between theories / research practices
3. Problem Three = the
lack of learning theories in the teacher and educator
The five innovations derived from the study
a. Innovation One:
The need of principles for guiding teachers in designing conjecturing task
sequences
b. Innovation Two: The
need of design tools—the five types of conjecturing
c. Innovation
Three: The use of three entries as the primitive materials to initiate the
designs
d. Innovation Four: N+
strategy as means to scaffold teachers’ profession growth
e. Innovation Five:
incorporating students’ perspectives into the designs
Mr. Fou-Lai Lin suggests the five innovations that
can be some answers to the three existing problems: the difficulty in
integrating students’ perspectives into teaching practices; the gap between
theories/research and practices; and the lack of learning theories for
educators and teachers.
8. ‘Stochastic Line In
Russian Junior School (7 - 9 grades)’ byProf. Ivan Vysotskiy Moscow
Institute for Open Education
This paper tell us about statistics and probability theory
in junior high school and topics. In 2003, Russian Science and Education
Ministry had agreement that probability theory and statistics into the regular
school course. The paper is dedicated to main features of statistics and
probability theory in junior school and topics having been included into
educational course.
a. Descriptive
statistics.
b. Main probabilistic
concept in 8 – 9 grades.
c. Random
experiments and random events.
d. Combinatory and its
place in school stochastic course.
e. Random values
and distributions.
9. ‘Building Japanese-‐Style
Structured Problem-‐Solving Outside Japan: What Supports are Needed?’ By Catherine
C. Lewis
Mrs. Catherine C. Lewis paper focuses in mondai
kaiketsu gakushu – literally, learning through problem-‐solving, style of
mathematics insruction that has fascinated U.S. as well as researchers for
decades. US researcher called it SPS or Style Structured Problem-Solving. In
this method, student work carefully with their problem that they choose before
and tell their new mathematical understanding that developed in the problem.
a. I would like to
explore four major supports for SPS:
b. Mathematical Tasks
Suited to SPS
c. Knowledge of
Student
d. Thinking
Teaching Strategies
e. Motivation
Gained From Personal Experience of Problem-‐Solving
10. ‘Innovation in Problem Solving Based on
Mathematics Textbooks and E-textbooks’ By Madihah Khalid from Brunei
Darussalam
This paper tells that the teachers in Brunei Darussalam use
recommended textbook or book that supplied by Ministry Education to teach their
students. Beside it, some of the teachers try to search the material of study
from internet and change or adapt it according to the level of the students in
the classroom. This paper would examine the design of a lesson in the topic of
“comparing fractions” at year 4 level. The lesson can be considered a success
if the students were active, participative and looked interested. They still
need to increase the communicating, reasoning, or mathematical thinking skill.
11. ‘A tablet-based application for supporting
effective lesson study’ ByAkihiko Takahashi, Thomas McDougal
This paper tells about a tablet. Tablet is a tool to help
the teacher to collect useful data and use it as the basis of a productive
post-lesson discussion. Lesson Study Alliance and Project IMPULS are developing
an application for iPad, the LessonNote, to help practitioners of lesson study
improve the quality of their post-lesson discussions by improving the quality
of observational data collected during the lesson. the important capabilities
of it is
1. The timestamp
information creates possibilities for statistical analysis of the lesson
2. It should be possible
to share observation data.
3. Experienced lesson
study practitioners will often use copies of a seating chart to capture
“snapshots” of student progress during a lesson, across the entire class.
4. The timeline view
needs to enable zooming out to provide a good overview of how time was used
during the lesson.
At the end of this paper, the written have a plan to
continue developing LessonNote to add these and other capabilities.
12. ‘Improving Lessons on Mathematical Thinking
through Lesson Study ~ 3 Case Studies’ By Peggy Foo from Marshall
Cavendish Institute
This paper tells us about the mathematical thinking with the
3 Big Ideas and 4 Critical Question. The main purpose of this study is to
investigate the different types of professional knowledge teachers acquired
through Lesson Study with respect to promoting mathematical thinking in their
own classrooms. The Three Big Ideas is :
a. Focus on Student
Learning
b. Focus on Collaborative
Culture
c. Focus on
Data-Driven Outcomes
There are 4 critical area, that is :
1. What is it we expect
students to learn?
2. How will we know when
they have learned it?
3. How will we respond
when they don't learn?
4. How will we respond
when they already know it?
Peggy Foo has an opinion that Mathematics textbooks
since there is evidence that the four factors have already appeared in the
Singapore’s Primary Mathematics textbooks but perhaps more can be done to
improve the quantity and quality of open-ended tasks and good questions in
textbooks for different levels (including preschool and secondary levels).
13. ‘Design dynamic mathematics models in
E-textbooks to improve students’ abductive inferences’ By Nguyen Dang
Minh Phuc fromVietnam
This paper tells about the dynamic model models based on the
content of mathematics textbooks of high school in Vietnam to develop students’
abductive inferences. Abductive inference searching for the best explanation to
previous conclusions. The e-textbook like a textbook that conduct
investigations on models, suggest abductive inferences to explain the observed
results.
In this paper, the written try to design dynamic mathematics
models, create mathematics e-textbooks to help students improve their abductive
inference. E-textbook with dynamic mathematics models teachers can use
following levels below:
a. Use models right
away for activity.
b. Add, remove or edit
objects before using.
c. Create a
complete lesson plan
d. Create new models.
Throughout the entire contents of the school mathematics
program, dynamic mathematics models are designed to serve many different
purposes. Some models are introduced in this paper aim to improve students’
abductive inference, a type of inference that giving the best explanation for
the observed events, discovered results
In above is 13 papers that had been presenting in APEC- Ubon
Ratchathani International Symposium 2011. All of the participant give an Innovation
on Problem Solving - Based Mathematics Textbooks and E-Textbooks. Some of it
agree that textbooks and E-Textbooks is needed to help the student and the
teacher in teaching and learning processes and also increase the problem
solving skill.
