tag:blogger.com,1999:blog-7245208048685880741.post5897017601384085382..comments2017-02-10T11:18:37.932-05:00Comments on Rational Expressions: Maybe It's OK To Prove Obvious ThingsMichael Pershannoreply@blogger.comBlogger2125tag:blogger.com,1999:blog-7245208048685880741.post-72472455728701015102015-01-17T19:23:43.404-05:002015-01-17T19:23:43.404-05:00I quote you : "Our job, partially, is to ma...I quote you : "Our job, partially, is to make sure that students have reasons to give in their arguments."<br />This should be done with all sorts of things, not just proofs. An account of an algebraic argument, say for solving a pair of simultaneous equations, should really have a connecting description stating or explaining the reasons for at least some of the steps. Howard Phillipshttp://howardat58.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-7245208048685880741.post-3225350133363178912015-01-16T20:30:29.724-05:002015-01-16T20:30:29.724-05:00Well, when I read question 4.1 I was a bit puzzled...Well, when I read question 4.1 I was a bit puzzled. My brain said "What does it mean to say that two integers are congruent?" . Then I thought "They mean congruent mod m to each other". They should have written it, as otherwise the statement is rubbish. Do I get full marks for this?<br /><br />The other problem is more general. How far back are they expected to go ? Euclid 's definition of parallel, indirectly put, is that if two lines cross a third line and the sum of the adjacent angles (correct term ??) is not equal to two right angles then the first two lines will meet, so in the example they are using two things about the lines in the picture which are not axioms.Howard Phillipshttp://howardat58.wordpress.comnoreply@blogger.com