{"id":671,"date":"2006-10-05T11:37:47","date_gmt":"2006-10-05T11:37:47","guid":{"rendered":"http:\/\/scienceblogs.com\/principles\/2006\/10\/05\/wrong-answers-are-infinite-in\/"},"modified":"2006-10-05T11:37:47","modified_gmt":"2006-10-05T11:37:47","slug":"wrong-answers-are-infinite-in","status":"publish","type":"post","link":"http:\/\/chadorzel.com\/principles\/2006\/10\/05\/wrong-answers-are-infinite-in\/","title":{"rendered":"Wrong Answers are Infinite in Number"},"content":{"rendered":"

Last week, Mike Dunford was struggling with some teaching issues<\/a>, relating to what level of effort he should expect from his students. His original decision drew some harsh criticism, both in his comments and from Sandra Porter<\/a>, leading Mike to reconsider matters<\/a>.<\/p>\n

I meant to comment at the time, but I gave an exam last Thursday, which kept me kind of busy, and then there was the SAT Challenge to get ready.The issues Mike raises present some tough questions: on the one hand, you want students to learn to learn for themselves, and that occasionally runs counter to their immediate impulses, which are often to avoid work at all costs. As the Dean Dad puts it<\/a>:<\/p>\n

\n

Unlike almost any other industry, in higher ed we have a substantial number of customers who are happier if the product is shoddy, or not delivered at all.<\/p>\n<\/blockquote>\n

At the same time, you need to avoid situations where progress can be completely derailed by really basic misunderstandings. This is particularly important when the entire problem could be avoided by providing a trivial amount of extra information. Students have an amazing gift for slipping through the tiniest gaps in the statement of an assignment, and taking off in wholly novel directions. They can go wrong in ways that just never occur to faculty who know the full context of the problems being studied.<\/p>\n

Example below the fold:<\/a>
\n<\/p>\n

For the exam I gave last wek, I needed a problem dealing with one-dimensional motion under constant acceleration. I opted to use the example of somebody throwing a ball up into the air. I set it up so the thrower was standing on a balcony, and asked students to find the time taken for the ball to go up and fall back down to ground level, and what the speed was when it hit.<\/p>\n

As the final part of the question, to sort out those who really have the concepts nailed from those who can just manipulate equations, I asked what would happen if a second person threw a ball downward at the same speed that the first ball was thrown up. Which ball would be moving faster when it hit the ground?<\/p>\n

Now, this is a classic problem in physics classes. The answer is that both are moving at the same speed, because the ball thrown upward returns to its starting point moving with the same speed, in the opposite direction. The two balls accelerate identically from that point on, and hit the ground with the same speed.<\/p>\n

It’s a classic question, and immediately obvious to any faculty member what it’s getting at, so it didn’t even occur to me that I had forgotten to specify that the second person was standing on the same balcony as the first. The question just wouldn’t make any sense otherwise, so it’s an obvious assumption, to me.<\/p>\n

Sure enough, though, I had a couple of students who picked up on that missing bit of information, and arrived at a different answer. I had to give them credit for it, too, because while their confusion might not seem sensible to me, because I know the background of the question, it was ultimately my fault– I failed to give them all the information they needed.<\/p>\n

(Most of them got it. They’re pretty sharp.)<\/p>\n

Correctly anticipating the wrong answers is one of the things I find hardest about trying to make up quiz and exam questions. The problem I have is similar to what Mike describes– I try so hard to avoid “babying” them, that I end up under-specifying problems. And that inevitably leads to trouble.<\/p>\n","protected":false},"excerpt":{"rendered":"

Last week, Mike Dunford was struggling with some teaching issues, relating to what level of effort he should expect from his students. His original decision drew some harsh criticism, both in his comments and from Sandra Porter, leading Mike to reconsider matters. I meant to comment at the time, but I gave an exam last… Continue reading Wrong Answers are Infinite in Number<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"1","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,13,7],"tags":[],"class_list":["post-671","post","type-post","status-publish","format-standard","hentry","category-academia","category-education","category-physics","entry"],"_links":{"self":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/671","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/comments?post=671"}],"version-history":[{"count":0,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/671\/revisions"}],"wp:attachment":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/media?parent=671"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/categories?post=671"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/tags?post=671"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}