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无论是培养学生的知识与能力,还是培养学生的核心素养,举例都是必经之路。在概念教学、原理教学以及问题解决中,需要合理应用正例、反例、特例和变式来提升学生的数学核心素养。利用正例,能帮助学生掌握数学原理,并能以原理为依据解决特定情境的具体问题。利用反例,能帮助学生从反方向加深对原理的理解和认识,将之与正例结合,学生对数学原理的理解会更全面。利用特例,会使数学概念的外延更清晰,可以帮助学生系统地理解数学概念。利用变式,能够进一步丰富非常态的教学材料,在开放问题的引领下,学生可以更加灵活地运用数学原理,使学生的数学素养得到提升。
Whether it is to develop students ’knowledge and ability, or train students’ core literacy, for example, all must pass through. In concept teaching, teaching of principle and problem solving, positive examples, counter-examples, special cases and variations are needed to improve students’ core literacy skills. Positive examples can help students master mathematical principles and can solve specific problems of specific contexts based on principles. Using counterexamples can help students to deepen the understanding and understanding of the principle from the opposite direction. When combined with positive examples, students’ understanding of mathematical principles will be more comprehensive. The use of exceptions makes the concept of maths more explicit and helps students to systematically understand mathematical concepts. The use of variants can further enrich the abnormal teaching materials. Under the guidance of the open question, students can use mathematical principles more flexibly to improve their mathematical literacy.