This research examined the conditions that arc necessary for lower secondary school students to use the discovery function (DF) of proof that enables us to make new products (propositions, proofs, conceptions, and assumptions etc.) with proofs. In conclusions, three kinds of conditions are necessary:(a) the condition of an original proof, (b) the conditions of a problem to make products with the original proof, and (c) the conditions of a student's activity to use the DF of original proof. In Section 3, to prepare a theoretical framework, the following two questions were considered:(a) "What is the DF of proof?," (b) "Why should we take the DF seriously?,". Then, the following three viewpoints were specified to discuss how lower secondary school students use the DF: an original proof, a problem to make products with the original proof, activity to use the DF of original proofs. In Section 4, the design of an experiment that observed the activity of two groups of lower secondary school students to use the DF was described. Based on the products, the conditions to use the DF and the need for referencing such conditions on students' activities were discussed in Section 5.
抄録全体を表示