Teachable Agents in Mathematics Education

To investigate whether argument mapping, with a use of RationaleTM software, cultivates students’ critical thinking skills, an experimental research was designed and implemented in Cyprus’ primary schools. Thirty 6 th grade primary classes participated in the research for a period of nine months. Three groups of ten classes each were formed, of which two were the experimental groups and the third was the control group. The first experimental group worked in groups of three, with one computer for each group, on reasoning activities using RationaleTM software. The second experimental group worked on the same reasoning activities in the same way but using pencil and paper instead of any software. Students in the control group worked on reasoning activities using their Greek language textbooks, without any specific intervention in their learning process. A pre-test and a post-test were submitted to all students participated in the research in order to assess their reasoning and critical thinking skills. The comparison of pre-test and post-test means scores reveals that there is a statistically significant difference in, due to the performance of the students of the first and the second experimental group where the teaching intervention took place. The study findings are indicating that carefully designed argument mapping activities supported by argument visualization software, combined with systematic, conscious and organized quality practice within a cooperative and constructivist learning environment by educators specially trained in the theory and practice of critical thinking may promote the cultivation of students’ critical thinking skills. Extended summary Reasoning is a central component of critical thinking (Butchart, Forster, Gold, Bigelow, Korb & Oppy, 2009; Εnnis, 1987; Fisher & Scriven, 1997; Kuhn, 1991; Moore & Parker, 2007; van Gelder, 2001) and an important social dexterity for the future active citizens of democratic societies since it is involved in all beliefs of individuals, in their judgments, in their conclusions and in the way they face their everyday problems (Kline, 1998; Kuhn, 1992). Many studies have shown that students are able to develop reasoning but often face difficulties associated with how they construct, organize and present their arguments (Andriessen, 2006; Bell, 2004; Erduran, Simon & Osborne, 2004; Felton & Kuhn, 2001; Jimeinez, Rodriguez & Duschl, 2000; Kuhn, 1989, 1991, 1992; Kuhn & Udel, 2003; Sandoval, 2003; Suthers, 2003). The typical format for the presentation of reasoning is prose (e.g. arguments found in newspapers, books or internet resources). Extracting the structure of the relationships in a reasoning as typically presented in prose, however, is very difficult (van Gelder, 2002). Van Gelder (2002) suggests argument maps as a way to develop and present arguments because they are more readable and comprehensible than prose. An argument map is a visual representation of an argument that immediately identifies claims, reasons and objections. Argument maps require less interpretation since all relationships are made completely explicit using simple visual conventions. They can be understood more easily via colours, shapes, arrows position in space, and other visual clues and they are well suited to the non-sequential structure of most arguments (van Gelder, 2003). Relevant research shows that the ability to construct argument diagrams improves students’ critical thinking skills (Harrell 2004, 2005; Twardy 2004; van Gelder, 2001, 2003). Despite their effectiveness, argument maps has never really been used as a practical tool for real reasoning or deliberation (van Gelder, 2002; Twardy, 2004). The main reason, among others, is that their creation with manual technologies (pen and paper or white boards) is both difficult and time consuming (van Gelder, 2002). Using software specifically designed to support argument mapping such as RationaleTM (van Gelder, 2007), which helps students to create, organize and manage argument maps, one can now assemble argument maps easily and rapidly. This may overcome the limitations of manual technologies and help students to confront most of the difficulties faced when attempting to develop and support logical arguments (Bell, 2004; Clark & Sampson, 2006, 2008; Evagorou & Osborne, 2008; Twardy, 2004; Sandoval, 2003; Suthers, 2003; van Gelder, 2001, 2002, 2003). This particular software was chosen for this study because it is user friendly and as thus appropriate to be used by primary school students. To investigate whether argument mapping, with a use of RationaleTM software, cultivates students’ critical thinking skills, an experimental research was designed and implemented in seventeen Cyprus’ primary schools. Thirty 6 grade primary classes (N=481) participated in the research for a period of nine months. Three groups of ten classes each were formed, of which two were the experimental groups and the third was the control group. Critical Thinking Test (CTT) was submitted to all students participated in the research in order to assess their critical thinking skills before and after the instructional intervention. Test was designed, developed and validated by the researcher for the purposes of this study and based on the core critical thinking skills according to the American Philosophical Association (1990). After the pre-test all teachers of the two experimental groups (20 teachers) received fifteen hours training in non-school time by the researcher for the implementation of the instructional intervention. Upon the completion of their training teachers were asked to implement the instructional intervention in their classrooms and work on reasoning activities. The first experimental group worked in groups of three, with each group using one computer, on reasoning activities (argument jigsaw, wrong argument map structure, construction of argument map, argument chess and debate) using RationaleTM software. The second experimental group worked on the same reasoning activities in the same way but using pencil and paper, instead of any software. All applied activities used by the first and the second experimental group were developed by the researcher and the teachers during their training for the purposes of this research. Students in the control group worked on reasoning activities using their Greek language textbooks, without any specific intervention in their learning process. The data analysis revealed that the pre-test mean score of all students participated in the research was 8.56 whereas the mean score of the post-test was increased up to 10.14. The difference between the mean scores was statistically significant (t=-9.634, p=.000 for p<.05). This increase of the mean score was mainly due to the performance of the students of the first experimental group and the second experimental group where the instructional intervention for the cultivation of critical thinking skills took place. This conclusion is based on the evidence found by the comparison of pre-test and post-test means scores in both experimental groups. A statistically significant difference was found in the first experimental group mean scores (t = -13.181, p = .000 for p <.05) and in the second experimental group mean scores (t= -4.378, p = .000 for p<.05), with an increase of the mean scores for both groups. The findings of the study contribute to existing knowledge on critical thinking by examining the effects of argument mapping on the cultivation of primary students’ critical thinking skills. The findings offer additional evidence in the line of work showing that carefully designed argument mapping activities using argument visualization software, combined with systematic, conscious and organized quality practice in a cooperative and constructivist learning environment by trained educators in critical thinking theory and practice may promote the cultivation of students’ critical thinking skills. Scaffolding students’ critical thinking skills using argument maps and argument visualization software might be a promising path in developing thinking citizens who will appreciate the value of intellectual discourse and will be competent to engage in it effectively.