There exists a complex debate within the mathematics community regarding how mathematics should be taught in our schools. Representatives from school districts, individual schools, universities, and the private sector are organizing open forums, focus groups, and discussions regarding the efficacy of mathematics education. The traditional viewpoint supports procedural approaches, which may include memorization, drill, and practice of rules and definitions as the optimum way to teach and learn mathematics. On the other hand, nontraditional approaches, such as the constructivist point of view, suggest that students should utilize their innate abilities to formulate their own algorithms in order to gain ownership of the specified mathematical topic.
Mathematics educators have argued these and similar concerns for many years. In addition, these debates have been spurred by the results of the Third International Math and Science Study (TIMSS), where American 8th graders were average and 12th graders’ scores were deficient when compared with similar age groups in other countries.
The National Council of Teachers of Mathematics (NCTM) has continually supported the idea that mathematics should be conceptually taught (i.e., teachers should teach mathematics for understanding and should make mathematics more functionally relevant to the student’s life). However, even NCTM has encountered resistance from educators who support more traditional approaches.
The NCTM Standards 2000 document presents a vision that includes a framework of ideas that may contribute to the future landscape of mathematics education in the next several decades. However, whether the NCTM Standards are embraced or not, professional discussion and debate must continue. Curriculum committees, local school boards, professional forums, working groups, and parent-teacher teams must have ongoing dialogue and develop the habit of reflective practice.
The methodologies for teaching and learning secondary school mathematics are an ever-changing process based on scientific advances and societal needs. Therefore, developing the habit of reflection can provide insight and guidance, and help facilitate positive systemic change in mathematics education and the mathematics classroom.
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