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 and Utith 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 of culture 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. Ulep from 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’ by Cheng 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)’ by Prof. 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’ By Akihiko 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 from Vietnam
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.
