Abstract
To enhance students’ problem solving potential, an important skill for 21st century, teachers should concern what kinds of authentic-mathematics experiences that students can get through problem solving (Cai, Mamona-Downs, & Weber, 2005). In addition, mathematics classroom approach has changed radically from a drill-and-practice approach to more insight-based problem oriented approach (Van Oers, 2002). According to a problem solving mathematics classroom, in which an open approach is used as a teaching approach, students are required to adapt what they have learned to solve problem situations (Inprasitha, 2010). These problem situations are designed based on students’ experiences. Regarding these points, a purpose of this study was to investigate key universal activities, which are based on Bishop (1988) who presented the key universal activities as foundations for students’ mathematical learning. Case study was employed in this study. Video and audio tape recording, and field note taking were used as methods for collecting data of a targeted group including six of grade 1 students in 2010 academic year of a school participating the Project for Professional Development of Mathematics Teachers through Lesson Study and Open Approach. Data were analyzed by using descriptive statistic and analytic description. The results showed that there were various key universal activities in each problem situation occurring in problem solving mathematics classroom. These key universal activities have been enhancing the students to solve the problems efficiently.
Highlights
In the 21st century, there are more increasing of a complexity of problems that one could encounter, both in a country and in the world
In socio-cultural points of view, as Bishop (1988) has realized that mathematics is a cultural phenomena, a mathematical enculturation process is a process in which concepts, meanings, processes and values are shaped according to certain manner, and emphasizing on social context where there is an interaction between those who participate in this process
Observe the research lesson (Do) were composed of 2 theoretical frameworks; 1) Open Approach as a Teaching Approach (Inprasitha, 2010) used to analyze phases of the classroom that emphasize on problem solving, and 2) Key Universal Activities (Bishop, 1988) used to analyzed activities occurred in each phase of the classroom whether these activities composed of the key universal activities which are the foundations for students’ mathematical learning
Summary
In the 21st century, there are more increasing of a complexity of problems that one could encounter, both in a country and in the world. Classrooms must be changed from “traditional classroom” that devotes most of instructional time to teacher’s recitation and practices, to “reform classroom” that provides wider task demand to inquire students’ effective problem-solving strategies and communication practices (Forman, 1996) According to this point, what is critical is not whether the teachers should use problem solving as an approach to teach mathematics, but rather what kinds of authentic experiences concerning mathematics that students can get through problem solving (Cai, Mamona-Downs, & Weber, 2005). These activities promote the transformation from technique, or a way of doing, to meaning, or a way of doing
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