Critical Thinking and Middle School Mathematics

Critical thinking is an area of research which has profound implications for educators. Included in this research are the components of creative thinking as well as those of critical thinking and the dispositions needed to do both. Through critical and creative thinking research we are learning what thinking is and what characteristics good thinkers have. If the ultimate goal of educators is to produce a thinking citizenry, then educators need to avail themselves of this current research knowledge. To date, the experts in critical and creative thinking have addressed the curriculum areas of English Literature, Social Studies and Science, using many examples from each of how an educator might teach thinking skills while teaching these subjects. However, examples of how one might teach critical and creative thinking skills in the subject area of mathematics are decidedly absent. While there is research on mathematical problem solving and quantitative thinking in young children how critical and creative thinking can be taught at this level within the subject area of mathematics is unclear. What is needed, then, is an exploration of the specific critical and creative thinking skills used in a mathematics curriculum which is designed for good quantitative thinking. This paper presents an analysis of those thinking skills defined in current research as critical and/or creative which can be found in selected activities of a middle school mathematics curriculum. The curriculum selected was designed by its authors to develop good quantitative thinking in students. For the purposes of this analysis, that goal is assumed to be accomplished, that is, that the students are developing good quantitative thinking when using this program. Therefore, the analysis of thinking skills in this paper goes beyond the goal of the authors to show another level of thinking skills which can be used to enhance the material. After the analysis methods are given for classroom instruction, assessment of students and for the transfer of the critical and creative thinking skills to other areas of the middle school curriculum