WHAT
ARE THE PRINCIPLES BEHIND CGI ?
prepared
by:
KOHOT 10
In the United States, schools all
over Wisconsin, children are learning Mathematics faster than their teachers
expected. They are more motivated and confident. The reason is: Cognitively
Guided Instruction or CGI.
This new approach in teaching Mathematics was developed after years of research by School of Education Professor Thomas Carpenter and Elizabeth Fennema and sponsored by the National Science Foundation. The program adopts an innovative approach to teaching Mathematics.
In short, CGI encourages teachers to take what their students know about Mathematics and then build on the foundation. It focuses on problem solving. As a result, children have a chance to solve interesting Mathematics problems rather than drilling them. Quote from Dyanne Van Den Heuvel (a teacher using CGI in teaching) “It teaches them to be problem solvers, not calculators.”
Carpenter’s research conducted over 15 years reveals how children think and how teachers learn to teach. The research clearly indicates that children do not come to school “empty-minded” instead with many skills. Unfortunately, the Mathematics curriculum does not build on the knowledge and in some cases even wipes it out. CGI helps teachers understand what knowledge children bring (have) and what problem solving skills they have in order to build on those. Instead of teachers telling the answers/one way to solve a problem, children discover methods that work for them. And the task of a teacher is to understand their thinking and know what are the appropriate next steps to help the students to learn Mathematics.
WHAT
ARE THE PRINCIPLES BEHIND CGI ?
1. Teachers must learn (understand) their students’ Mathematical thinking and the methods used by them in problem solving.
2. Teachers should be able to interpret how students solve problems. He would analyses students’ thinking by asking appropriate questions and listen to their response.
3. Teachers would plan/construct suitable teaching strategies based on their understanding of students’ Mathematical thinking and also their process of problem solving. Cooperative learning is strongly recommended in this sort of classroom teaching.
4. Teachers should organize their lesson plan so that there is always active students involvement. In this way, students can build up their mathematical knowledge with meaningful understanding.
5. Teacher using CGI must make sure the teaching of Mathematics emphasizes the relationship between concept, skills and the process of problem solving.
BASIC
SKILLS NEEDED BY TEACHER IN ADAPTING CGI IN CLASSROOM
TEACHING
1. Teachers must know their students’ mathematical mind, especially disorganized information embedded in it.
2. Teachers must focus on “problem-solving” in their classroom teaching.
3. Teachers must be able to interpret how their students think about certain Mathematical concept.
4. Teachers must be able to decide the follow-up learning activities, based on their understanding of students’ mathematical thinking at that juncture.
THE
ROLE OF TEACHER AND STUDENT IN CGI CLASSROOM TEACHING
1. Teacher and students work together to solve assignment.
2. Teacher questions students how they arrived at the answer or what strategy they used to solve the problem.
3. Teacher learns how (ways) students get the answers.
4. Teachers explain different ways of solving certain problem.
5. Students who failed to solve would learn the correct way to get the answer.
6. Students learn different ways to solve a particular problem through classroom discussion/ explanation given by their peers.
7. Student can choose the method used in problem solving that best suits him.
WHAT
HAPPENS ;IN A TYPICAL CGI CLASSROOM TEACHING
1. Students spend most of their time in problem solving.
2. At the initial stage, student is not shown/told how to solve the problem by the teacher.
3. Students try to solve problems using methods they are capable of. (may be more than one method).
4. Every students report/explain how to solve a particular problem to their peers / teacher.
5. The teacher and classmate listen and ask questions until they understand the solution proposed by a student
6. Teacher uses the information gathered from the students’ presentation and decide on how the following teaching process should be carry out in order to facilitate optimum learning taking place.
Until now, research findings in US clearly indicate that students taught under CGI program performed better than their peers who were taught by the traditional methods. And they are generally more enthusiastic about Mathematics. Says Van Den Heuvel, “I’m really excited about the program because it changes how you teach and how you facilitate children’s learning. I t has taught me about how children think and how I as a teacher can help them grow as learners. This is powerful information for me and teachers.”
To make CGI program a success, it required continued effort and support over the years. One type of support that seems especially important to almost all teachers was on going conversation and interaction with other teachers who are also CGI practitioners. Also encouraging was the support teachers reported gaining from interaction with their own students. The actual experience of seeing their students generate solutions to complex mathematical questions led many
of these teachers to a grounded understanding and belief in CGI. The positive effects of CGI invention seem to be most pervasive and long lasting in those teachers who construct for themselves more conceptual and flexible meanings for CGI rather than adopting meanings that were introduced in the original workshops. Carpenter and Fennema originally had set out not to “train” teachers to” implement” a program they had devised but rather to convince teachers to develop and use CGI knowledge in ways that best fit them, their students and their unique situations. However there are teachers who thought CGI as a set of new procedures for teaching mathematics but seemed able to incorporate these procedures onto their existing mathematical program and current teaching techniques.
Any way, there are some questions still unanswered: To what extent do factors common in many schools prevent teachers from adopting the CGI program, and to what extent is the teachers’ of these factors and reforms that are the real barrier? What teacher-student relationships and roles will allow teachers to learn from their students as well as students to learn from their teachers, and how are these connected to teachers’ and students’ idea about knowledge and learning? Finally, to what extent these issues apply to subject areas beyond mathematics, and how can teacher reform their teaching
as a whole.
As such, I sincerely hope that teachers in the Malaysian school system would start to learn about CGI and try to implement this new but innovative teaching approach in their classroom teaching. Hopefully it would be successful (although it may take a few years). This would help the Malaysian students in their learning process in Mathematics and at the same time help the teachers to be better educators in classroom learning. By that time, students would no longer find Mathematics a difficult and boring subject in school but enjoy learning Mathematics. And their progress and interest shown in Mathematics would be the greatest reward a teacher could ask for.
After all, this is what teachers are for! Isn’t it?
REFERENCE
www.news.wisc.edu/chancellor/pubserv/ward5.html