We Should Teach More Logical Reasoning in First-Year Mathematics Courses
摘要
How much explicit logical reasoning instruction should be included in first-year mathematics courses, particularly those for non-math majors? We argue that all first-year students in mathematics courses should receive explicit instruction in logical reasoning. Engaging with precise logical statements is a fundamental skill in mathematics, especially at the university level. Given that we regularly justify mathematical results in our teaching, it is essential that students understand the reasoning behind these justifications. Since many students typically receive minimal instruction in logical reasoning during secondary education, it becomes the responsibility of university instructors to bridge this gap. Research indicates that conditional reasoning, especially with “if–then” statements, is not intuitive for most students, but those students who emphasize exact reasoning perform better on mathematical tasks than those who emphasize applications. Furthermore, the UNESCO report “THE FUTURES WE BUILD: Abilities and competencies for the future of education and work” identifies critical thinking, effective communication, and complex problem-solving as key competencies for the future, all of which are underpinned by strong logical reasoning skills. In this viewpoint, we make the case for the inclusion of explicit logical reasoning instruction in first-year mathematics courses. We will provide examples of classroom situations where logical reasoning skills are crucial, review research on how these skills contribute to student success both within and beyond mathematics courses, and suggest strategies for integrating logical reasoning into the curriculum. Finally, we will address the challenges of implementing this instruction in first-year mathematics courses.