Senior High School Students' Understanding Of Mathematical Proof

Empirical proof and logic proof are stressed in secondary school. Some research found that students'understanding of proof was not very well. There was difficulty when students were asked to give their own written proof.This study investigated 275 high school students in grade 10 to explore their understanding of proof in algebra and geometry, and to explore their ability to give proof. This study also investigated 9 mathematical teachers in high school to know their view on mathematical proof.From this study we can get the following conclusions:(1) Half of the students can accept the five roles of proof.(2) Most students can identify effective methods of proof, but they think that the form is an important factor to determine the validity of proof. Sometimes students can feel that there are some problems in the empirical proof, but they have to take this method for some reasons.(3) The students think that the prose proof in algebra can explain why the proposition is true better than other proofs, but much more students use formal proof when they are requested to write proof. The two-column proof can explain why the proposition is true than other methods in geometry and the students often use this kind of proof when they give a proof. Most students can gain a result from a general conclusion correctly, but they can't understand the relation between a proposition and its converse proposition well. For all correct proof methods, the student who thinks this method is more suitable to explain the proposition to others must believe that this proof is suitable to explain it to himself.(4) The students'ability to give written proof in geometry is not well too; most of them guess the answer and can't give a proof. None of them use empirical proof or prose proof. Only few students can give a right logical proof.(5) The boys'understanding of proof is better than the girls', the girls focus on the form of proof, while the boys focus on logic in proof. Except the wrong two-column proof in geometry, there appears to be no significant relation between gender and the understanding of proof.The results of this study provide mathematical teachers with further insight into how to improve students'ability of proof.