Research On Junior Students’ Conceptions Of Algebra Proof

In middle school mathematics, geometry develops students’reasoning and proof, and algebra is one of the important content. Since proof can promote understanding, we need immerse proof into all middle school mathematics, including algebra. Algebra and geometry can promote students’learning algebra, as well as proof. How do junior three students recognize the role algebraic proof can play after they have learned algebraic proof?This paper investigates students’ conceptions of algebraic proof from three perspectives:1. How do students recognize the role of proof;2. How do students choose the process of proof;3. How do students establish the process of proof.The participants were48junior three middle school students. Through the questionnaire and the interview, the study investigated the participants’conceptions of algebraic proof. The results are:1. Most students have realized that proof can be used as a tool to verify propositions.50percent of the students have realized that proof can enhance their mathematical understandings and their logical thinking abilities. A minority of students thinks that proof can build up connections between different disciplines and also learn new knowledge.2. There are no obvious differences between the type of proof that can adapt to the level of students’thinking and help them getting a high score. The standard of which the students use to choose as the way of proof is their understanding with the process, rather than the format of the proof. Students prefer to choose the way more explainable and convincing.3. Students’ ability to build up a proof is in the medium level, and the most regular type of the proof is algebraic proof. Those who has lower base offer examples to justify. The main reason that they could not use algebraic proof is that they could not use knowledge to build models and express numbers with letters.Based the results, we make four suggestions:1. Creating rich opportunities to learn and experience proof; 2. Putting emphasis on students’spontaneous knowledge of example, and helping students to recognize that the experienced proof is not the true mathematical proof;3. Encouraging students to recognize both the generality of proof and the generality of expressing numbers with letters;4. Putting emphasis on students’recognizing the type of proof with characters.