Integration of Critical Thinking Skills into Elementary School Teacher Education Courses in Mathematics.

Background Critical thinking receives increasing emphasis from educators looking to infuse analytical thinking skills into the curriculum. Many educators are tempted to equate critical thinking with higher order thinking skills within the last steps of Bloom's taxonomy: analysis, synthesis and evaluation. Ennis argues that this taxonomy is insufficient (Bloom et al., 1974; Ennis, 1981). He believes that neither provides enough guidance to teach and learn these skills. R. Paul (1985) concurs with Ennis that the taxonomy has served educators, agreeing that it is a useful "framework for the educational process" (Paul, 1985, 36), but argues that it is limited. One limitation is its hierarchical nature which dictates a uni-directional flow between strata. Bloom indicates that the taxonomy was intended "as a method of classifying the objectives, experiences, learning processes, evaluation questions and problems of education, [but] did not intend to provide a constraint on educational philosophy, teaching methods, or curriculum development. " (Paul, 1985, 39.) Attempts have been made to define critical thinking (Ennis, 1981; Paul, 1985; Lipman, 1988). Critical thinking is described as rational thinking reflected in actions and decisions (Ennis, 1981; Hitchcock, 1983). It is used to solve problems, choose between alternatives, and make judgments (Beyer, 1995). It shares affinities with creative thinking and decision-making (Innabi and El Sheikh, 2007). Lipman defines critical thinking as skilfful, responsible thinking facilitating goodjudgment because it 1) relies upon criteria [at hand], 2) is self-correcting, and 3) is sensitive to context. Good judgment, he says, is only possible through good reasoning skills, which assumes competent inquiry, concept-formation, and translation skills. Ennis (1985) defines critical thinking as "reflective and reasonable thinking that is focused on deciding what to believe or do" (45), paralleling Lipman's formulation. These definitions highlight proclivities as well as abilities. Ennis's list includes the following traits as fundamental to the art of critical thinking: precision, clarification, erudition, open-mindedness, seeking reasons and dealing with all parts of the problem. Critical thinking is not only a set of skills to be learned, but skills which need to be accompanied by sets of behaviors in order to make them effective such as: thinking critically in daily life, monitoring and thinking about one's own thought processes, and acting congruently with one's critical thinking (Sternberg, 1983; Paul, 1985; Norris, 1985). Once critical thinking skills and accompanying behaviors are defined, one can look at the importance of critical thinking in education. The emphasis in today's education is shifting from the acquisition of facts to the process of thinking. The contemporary goal is to have students think for themselves (Lipman, 1988). For many educators and philosophers, critical thinking is not a way to education but a prerequisite (Norris, 1985; McPeck, 1981; Siegel, 1980). One advantage cited is the creation of a community of inquiry, where each member monitors his/her thinking, as well as critiques other members' methods and procedures; thus, individuals not only self correct thinking processes, but contribute overall to group thinking skills (Lipman, 1988.) In such a community where questioning becomes a way of reflection, students are encouraged to question the validity of sources of information, including teachers (Siegel, 1980). Moreover, the teachers need to convey to students these skills, since research indicates that many high school and college students do not demonstrate strong critical thinking skills (Norris, 1985). Two virtues of critical thinking in education are greatly enhanced reading comprehension and the ability to communicate the in-depth perception gained from increased understanding (Lipman, 1988). Yet the benefits of critical thinking skills are not limited to the above. …