Since I was a member of the mathematics department of the school, I worked closely with the professors at the mathematics department of the university to implement new teaching materials and instructional techniques and to develop new curricula for elementary school mathematics.
At the time when I became an elementary school teacher, it was the thick of the reform movement from traditional teacher-centered instruction to problem solving based student-centered instruction in Japan, and I was deeply involved in the movement. By referring various American books such as How to solve it and Induction and analogy in mathematics by G. Polya, and Teaching problem solving by R. Charles and F. Lester, I worked with my colleagues and developed elementary mathematics lessons based on the idea of problem solving. This experience helped me to develop an understanding of children’s thinking in mathematics and understanding important teacher’s role to provide children with learning opportunities in mathematics lessons.
Moreover, I had a chance to take a part in the research project conducted by Prof. Sawada and Prof. Hashimoto to develop lesson plans and materials of open-ended problem solving. Open-ended problem solving has been widely accepted as one of the most advanced lesson styles by Japanese school mathematics. I, as a member of the research project team, made many experimental lessons with the ideas based on open-ended problem solving. The research project team started to developed open-ended problems for whole-class lessons in higher grades, and then, we moved to develop those for younger grades. Because I was an elementary school teacher, I was involved in developing problems for open-ended problem solving mainly for 1st through 4th grade. Although younger students were interested in open-ended problems, I have noticed that most of the younger students were generally not able to understand well in a case in which a teacher gave a story problem that was represented by only written sentences. On the other hand, when a teacher gave a problem with concrete manipulatives and other tools, most of the younger students were able to understand open-ended problems very well.
In general, Japanese elementary mathematics traditionally focuses on story problems that have been effective to the results as TIMSS shows, however, it is also the fact that there are difficulties for some younger children to understand story problems. Considering this circumstance, I tried to use problems by manipulative modes that provide a concrete way to help children to understand mathematical situations. As a result, I learned that with manipulatives, children tend to understand more easily problems which they might not be able to understand well only with linguistic modes. Then, I tried to use Cuisenaire Rods referring to the West German textbook and converted German style instruction to Japanese style whole-class instruction. I developed a series of lessons based on using Cuisenaire Rods for 1st grade and taught first grade students based on this lesson plan. I videotaped all the lessons and analyzed students’ activities qualitatively. The results of analysis interested Japanese researchers and my project was funded by government grant to continue the project.
Because I was teaching at Japanese School in Chicago from 1991 to 1994, I had a chance to know that the United States takes more advantages in lessons with manipulatives. During this period, I had many opportunities to observe American classrooms and to discuss with American teachers and educators about mathematics lessons using manipulatives. After I came back to Japan in 1994, I started to introduce manipulatives to Japanese mathematics lessons. I received much positive feedback and I wrote three books about Pattern Blocks activities for Japanese style problem solving lessons.
Despite the fact that Japanese elementary mathematics instruction has focused on story problems for long time, the hands-on activities have been getting more attention in Japan lately. However, using manipulatives and other tools in mathematics classrooms requires teachers to have extra time for preparation. For example, teachers have to make sure whether enough manipulatives and other tools are available for all in order to have hands-on activity in mathematics lesson. Also, sometimes teachers have to do preliminary experiment to make sure if manipulatives and other tools work effectively. How can teachers shift their lessons from traditional instruction to activities-based instruction?
By taking courses at UIUC, I have learn that the latest technology makes it possible to have interactive web site on the Internet without any special software. It may become possible to provide students with hands-on activity using interactive web page without using concrete manipulatives and other tools. It might make teachers to provide students with hands-on activities with less time for preparation. Although I do not believe that all the concrete manipulative based activities can be replaced by interactive web pages, I believe that the Internet might be able to be used as an alternative way to provide students with hands-on activities and some concrete activities can be replaced by using the Internet. Moreover, some Internet based activities might bring more benefits to students to understanding mathematics than concrete manipulative based activities. If this assumption is true, students could deeply understand mathematics by the help of using the Internet in addition to using concrete manipulatives and other tools in mathematics lessons.
Based on this assumption, I am currently studying a use of technology in mathematics instruction as a media to provide hands-on activities. A part of my study, I have completed the research project entitled “AN INVESTIGATION OF COMPUTER INSTANTIATED PROBLEM SOLVING (CIPS)”. The purpose of this research project was to learn whether the CIM provided by the Internet can be used as an alternative to hands-on activities using concrete manipulatives in open-ended problem-solving. From the obtained results, it appears that the Computer Instantiated Problem-Solving (CIPS) may provide students with learning opportunities equivalent to those occurring with concrete manipulatives . In conclusion, CIPS may contribute to mathematical reform in teaching and learning.
I had presentations of CIPS and open-ended problem solving at international conference, national conferences, and teacher preparation courses at UIUC. These offered excellent opportunities for me to have various reactions and invariable suggestions, and they helped me to make a further plan of my research project. There are two most important issues that I should consider for my further study. First, the CIPS of this research project applied only to small group activities and the experimenter did not play the role of a teacher. The experimenter did not teach students any mathematical concepts like teachers do; he just helped children to organize their group activities. Since open-ended problem-solving has been developed as an instructional strategy for classroom instruction through students’ collaborative work, the CIPS is expected to be applied in a classroom lesson, including teacher’s instruction, and to be examined in a classroom situation. Second, although the CIPS activity is intended to establish the opportunity for students in transition from level 1 to level 2 in order to learn basic concepts to understand congruence based on van Hiele’s theory, the students’ activities have not been evaluated from a perspective of mathematical content. In order to help students to develop a basic concept of congruence, a series of lessons including the CIPS of this research project would be needed. Without going through a series of lessons, it is very difficult to evaluate students’ development of a basic concept.
Concerning the above two issues, the further research project is expected to focus more on the application of CIPS in a classroom situation. The curriculum unit would consist of well-balanced activities including ones using concrete manipulatives and ones using Computer Instantiated Manipulatives (CIM). This kind of research may enable educators to better understand how to introduce this technology into their classrooms.
Another issue that I have learned from the conferences is the importance of having a wider theoretical background behind the current trend of mathematics education. I have learned from international studies such as SIMSS, TIMSS, and TIMSS-R that several differences and similarities in mathematics teaching and learning among the countries. For example, these studies explore that mathematics lessons in the United States and Japan have different aspects, and many teachers and educators have discussed the differences at the conferences. However, I do not think that finding differences is the final goal of these studies. The further goal should be seeking a better way to provide students with learning opportunities. In order to find a better way, we need to have a wider theoretical background to analyze those differences. I can see the same thing on various discussions in the United States called Math War. If some people have wider theoretical back ground, their discussion would be more constructive.
I would like to help teachers to improve their instruction by using my teaching experience in Japan and theoretical background that I have built up by taking various courses at UIUC.
Through my teaching experience, I have noticed that teachers need strong support to provide students with good instructions. This support should include not only in teaching materials such as textbooks, worksheets, manipulatives and other instructional tools but also in providing professional development opportunities such as various courses, workshops, lesson studies, and consultations. It is because providing teachers with teaching materials does not guarantee to improve their mathematics instruction. Teachers need to have an opportunity to understand how can they use these materials to improve their instruction.
In order to support teachers, experienced professionals are necessary in mathematics education. Therefore I would like to be a professional mathematics educator to help teachers to improve mathematics lessons, because I believe this provides students with learning opportunities that helps students deeper their understanding of mathematics.