Problem solving and critical thinking in mathematics

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Machine translated pages not guaranteed for accuracy. Click Here for our professional translations. Too many facts, too little conceptualizing, too problem solving and critical thinking in mathematics memorizing, and too little thinking.

The question at issue in this paper is: What is the current state of critical thinking in higher education? Most college faculty at all levels lack a substantive concept of critical thinking. Most college faculty don’t realize that they lack a substantive concept of critical thinking, believe that they sufficiently understand it, and assume they are already teaching students it. These three facts, taken together, represent serious obstacles to essential, long-term institutional change, for only when administrative and faculty leaders grasp the nature, implications, and power of a robust concept of critical thinking — as well as gain insight into the negative implications of its absence — are they able to orchestrate effective professional development. This paper highlights the depth of the problem and its solution — a comprehensive, substantive concept of critical thinking fostered across the curriculum. As long as we rest content with a fuzzy concept of critical thinking or an overly narrow one, we will not be able to effectively teach for it. Consequently, students will continue to leave our colleges without the intellectual skills necessary for reasoning through complex issues.

Studies demonstrate that most college faculty lack a substantive concept of critical thinking. It does not inform their conception of the student’s role as learner. It does not affect how they conceptualize their own role as instructors. They do not link it to the essential thinking that defines the content they teach. Most faculty have these problems, yet with little awareness that they do. The majority of college faculty consider their teaching strategies just fine, no matter what the data reveal. Whatever problems exist in their instruction they see as the fault of students or beyond their control.

Research demonstrates that, contrary to popular faculty belief, critical thinking is not fostered in the typical college classroom. Numerous studies of college classrooms reveal that, rather than actively involving our students in learning, we lecture, even though lectures are not nearly as effective as other means for developing cognitive skills. In addition, students may be attending to lectures only about one-half of their time in class, and retention from lectures is low. Studies suggest our methods often fail to dislodge students’ misconceptions and ensure learning of complex, abstract concepts. Capacity for problem solving is limited by our use of inappropriately simple practice exercises. Classroom tests often set the standard for students’ learning. As with instruction, however, we tend to emphasize recall of memorized factual information rather than intellectual challenge.