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Mathematics Instruction with Computer Instantiated Manipulatives (CIM)
Research Proposal
Akihiko Takahashi
Introduction
The new ambitious instruction has not been widely implemented in mathematics classrooms in the United State because it is not easy for teachers to change their teaching (Hiebert, 1999). Many schools and teachers face various difficulties in changing their lessons and have sought a solution to this situation. One of the ways to a solution is an appropriate use of new technology in order to help teachers to shift their teaching toward reform mathematics.
The reform movement on teaching and learning mathematics has been underway for a decade. The National Research Council advocated A Report to the Nation on the Future of Mathematics Education (1989), and the National Council of Teachers of Mathematics proposed the Curriculum and Evaluation Standards for School Mathematics as a broad framework to guide reform in school mathematics (1989). One of the major aspects of current reform movements is changing from traditional classrooms that focus on teacher’s lecture to student-centered classrooms that focus on students’ engagement in mathematical activities. This is because, proponents argue, mathematical classrooms should focus more on developing students’ mathematical thinking. However, American mathematics classrooms have not really changed, because most teachers do not have enough opportunities to learn new methods of teaching (Hiebert, 1999). American teachers have fewer opportunities to have systematic training after graduation from college compared to Asian teachers. Moreover, American teachers tend to be isolated in their classrooms, so that it is hard for them to find the opportunities to discuss their classroom lessons and teaching technique with their colleagues. One of the causes of these phenomena is that American teachers have less nonteaching time at their schools compared to Asian teachers (Stevenson and Stigler, 1992).
A lack of nonteaching time at school makes it difficult for teachers to use techniques of reform mathematics. Although the reform documents suggest using manipulatives and other tools in order to involve students mathematics learning actively (NCTM, 1989: NCTM, 1999), using manipulatives and other tools in mathematics classroom requires teachers to have extra time for preparation. For example, teachers have to make sure that enough manipulatives and other tools are available for all in order to have hands-on activities in mathematics lessons. Also, sometimes teachers have to do preliminary experiments to make sure that manipulatives and other tools work effectively. It is too hard for teachers to prepare for hands-on activities using manipulatives and other tools without enough nonteaching time at school. How can teachers shift their lessons from traditional worksheet-based paper-and-pencil mathematics to student-centered activities-based mathematics?
The latest technology makes it possible to have interactive web sites on the Internet without any special software. In other words, it may be possible to provide students with hands-on activities by Computer Instantiated Manipulatives (CIM) using interactive web pages without using concrete manipulatives and other tools. Moreover, Computer Instantiated Manipulatives (CIM) allow teachers to provide students with hands-on activities with less time for preparation. Teachers do not have to prepare concrete manipulatives and tools because the Internet can provide enough manipulatives and other tools for each student. If the Internet can be used as an alternative way to provide students with hands-on activities, students could have more hands-on activities in mathematics lessons.
This research project is designed to learn whether the Computer Instantiated Manipulatives (CIM) provided by the Internet can be used as an alternative to hands-on activities using concrete manipulatives in open-ended problem solving.
Open-ended problem solving often involves students in hands-on activities by using manipulatives especially in geometry for elementary grades. However, using manipulatives in younger grades is much more difficult because more time is needed to prepare materials for younger students and teachers have to expend much time and effort to organize students’ activities. Teachers have to spend extra time even for one period of mathematics lesson to get students prepared with the hands-on activity.
Considering this circumstance, open-ended problem solving, especially for elementary grades, needs a new approach that could surmount the difficulties of hands-on activities.
Does an open-ended problem-solving lesson using the Computer Instantiated Manipulatives (CIM) provide students with learning opportunity that is equivalent to one using concrete manipulatives?
Design
I will develop a pretest, posttest, and two sets of instructions, one for the experimental groups and the other for the control groups. Tow sets of instructions involve series of identical open-ended problem solving activities but are based on different type of manipulatives. One instruction is based on cybernetics Pattern Blocks provided by Internet and the other is based on physical Pattern Blocks. Then, I will compare the students’ activities that are based on cybernetics Pattern Blocks provided by Internet and the students’ activities that are based on physical Pattern Blocks (control group) in series of identical open-ended problem solving lessons. The subject of this research is an existing fourth-grade class at a public school in Champaign-Urbana, and the design of this study is quasi-experimental.
Procedures
Twenty fourth-grade children will be divided into two groups. The way of dividing children into two groups is carried out in the following procedure in order to divide participants into two same quality groups: first, every two children are matched according to their scores on the pretest, then, one member of each pair is assigned randomly to one group and other member is assigned to the other group.
Each group will be assigned to one of the following instructions: cybernetics Pattern Blocks instruction and physical Pattern Blocks instruction. One group uses cybernetics Pattern Blocks provided by Internet and the other uses physical Pattern Blocks. Although these two instructions are designed to use different types of manipulatives, the instructions are based on identical open-ended problem solving activities.
Pretest and assignment to treatments
The pretest consists of 20-items covering basic concepts of geometry based on van Hiele’s model of children’s geometric thinking. Students are matched according to their score on the pretest with each student’s total test score. Pairs were formed by taking adjacently ranked total scores. One member of each pair is assigned at random to the control group. The other member is assigned to the experimental group.
Students’ pretest performances are also analyzed and compared with their posttest performance as the dependent variable.
Posttest
The posttest contains two parts: one part consists of the same items as the pretest and the other part consists of the items that cover the contents of the instruction. Following the posttest, four students are interviewed: two students scoring highest on the posttest from each group, two students scoring lowest on the posttest from each group. All interviews are videotaped and transcribed.
Instructions
Instruction is composed of teacher-centered and student-centered open-ended problem solving activities, and it followed highly detailed lesson plan that includes what to demonstrate, what to say, and what to ask. Therefore, the instructor(s) should understand the basic concept of open-ended problem solving lessons before the instruction. All the instruction is videotaped.
Posttest results are analyzed in two parts. The first part of the analysis examines changes in students’ accuracy from pretest to posttest by the using total score of items that are common in pretest and posttest as the dependent variable. The second part of the analysis examines students’ responses to questions dealing with content that are introduced in the instruction. These analyses are done from two perspectives: performance and method of the items that cover the contents of the instruction as the dependent variable. Analysis of performance focuses on the correctness of students’ answers. Analysis of method focuses on whether and in what ways students’ use of methods are influenced by instruction. Moreover, subsets of students are interviewed in order to assess students’ understanding of the content that is introduced during the instruction.
The process of instructions is analyzed qualitatively. Because open-ended problems bring various different solution methods and answers based on each student’s idea, a large amount of instructional time is spent having students discuss their solution methods and answers. Therefore, students’ comments and written work during the discussion and activities are examined in order to determine what influenced students solution method on the posttest items.
Based on the above analyses, I would investigate whether the use of the Computer Instantiated Manipulatives (CIM) provides students with learning opportunities that are equivalent to one using concrete manipulatives in the instruction based on the series of open-ended problem-solving.
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