I was going to blur out the student's name to protect his privacy, and then I realised he had (very considerately) already made his name unreadable. Unfortunately for me, he also made all of his working out illegible too.

In the section that says "instructions to candidates", it says:

"Make sure you know what you have to do before starting your answer."Does anyone else disagree completely with this advice?

When trying to solve a maths problem, you will very rarely know what you have to do before you start answering it. For example, take the last question of this paper:

When I look at this question, I don't know exactly what the steps are and what the proof looks like. I know it will involve some angle rules, but which ones and in which order, I don't know. It would be completely stupid to sit there looking at the question for fifteen minutes trying to work out exactly what I need to do before starting my answer. The sensible thing to do would be to write down something you do know. For example, you know that OQ and OR are both radii and hence equal in length. After that, you might be a bit stuck, so you start trying things. Eventually, you might realise that drawing in the line PO would be helpful. At this point, you still don't know how you're going to complete the proof. You give some angles some letters, so that you can write some relationships more easily. You could let PQO=x, and therefore QPO=x too. Let ORP = y, so OPR =y. Then you might decide to work out QOP and ROP, not because you know that it's going to help, but because you know how to do it so you may as well. QOP= 180-2x, ROP = 180-2y. Then you work out QOR, because, well, it's there. QOR = 360-(180-2x)-(180-2y) = 2x+2y. Then you realise that QPR= x+y which means that you have proved it. Then you do a happy dance and probably write your maths teacher a note like "circle theorems is bae" (yes one of my students actually wrote that).

At no point during this proof had you worked out what you needed to do to answer the question. You tried some stuff, and some stuff led to other stuff, and eventually the problem was solved. This is how maths problems should be solved. If you know exactly how to answer the question before you start answering it, it's probably not a very interesting question.

I'm wondering whether the creator of this exam question intended for the students to know what they have to do before answering it. That would mean they were expecting students to have memorised by heart proofs to all of the circle theorems. What a depressing thought that is. How is regurgitating a bunch of proofs a sign of good mathematical thinking?

My head of department has a speech he likes to give students on this topic. (Actually, he has lots of speeches he likes to give, as his (and my) students know all too well). He says that it's like untangling your earphones. Earphones, as we know, automatically tangle themselves as soon as you stop using them. And when you want to use them, you have to spend a good five minutes untangling them. When you do this, do you look at the ball of entwined wires in your hand and think, "right, first I'll move that bit under that bit, then I'll pull this end through there, then I'll twist that bit round..."? Of course you don't, that would be silly. Instead, you get stuck in trying to untangle them. You pull bits and you twist bits and you play around with it. And eventually, no matter how bad the tangling was, you always succeed in getting them straightened out. This is exactly how you should tackle a maths problem.

So my advice would be to ignore the advice on the front of the exam paper. Well, except the bit that says "read each question carefully". Oh and also the bit that says "You are reminded of the need for clear presentation in your answers" (which several of my students definitely ignored).

Emma x x x

I completely agree (and I'm going to ask for a copyright fee each time you quote me ��).

ReplyDeleteThe only defense for this statement would be if the instruction is intended to mean, "Make sure you understand what you are trying to find out."

I don't remember seeing this on previous papers, but perhaps I just haven't looked carefully enough (obviously not as easily bored as you, though how you can be bored when you've got 93 papers to mark is beyond me!).

And, by the way, I think you'll find it was your suggestion to have 31 in your class?

ReplyDeleteNot just this, under an arrangement of online Education is that understudies can without source much of a stretch get the chance to add to the program dialogs identified with their subject and offer companion audit.

ReplyDeleteTo comprehend and bolster the full advantages of higher education people in general and higher education pioneers need to take part in http://www.breitling2002.com/writing-college-essay/ basic and genuine discourses about the part of higher education in the public eye.

ReplyDeleteGive us a chance to legitimize our claim that the normal effects of education are missing is the life of many instructed individuals by analyzing an extremely delicate part of life of taught individuals, their accounts. cheap courses

ReplyDeleteHow to do the arrangements?? The most vital thing which is required to cross the edge of these exams is intensive learning. citations in apa style

ReplyDeleteWhat are the goals of education? TECHNOLOGY UNIVERSITY For what reason should guardians send their youngsters to class? Education is a standout amongst the most manhandled or, rather, misconstrued human encounters.

ReplyDeleteThe visitor is serious about solving her problem and is therefore willing to buy products that help her to achieve her mission,electrical installation

ReplyDelete17. I value the article post.Really thank you! Really Coolkv2 kalpakkam

ReplyDelete. Interesting post. I Have Been wondering about this issue, amity international school so thanks for posting. Pretty cool post.It 's really very nice and Useful post.Thanks

ReplyDeleteWell done! Nice post! This really helps me to find the answers to my question. top 10 boarding school in delhiHoping, that you will continue posting articles having lots of useful information. Thanks a lot!

ReplyDeleteEducational cost repayment isn't just for those kids that have recently been in state funded school.

ReplyDeleteRecall what number of these expositions they will peruse, you have to ensure yours stands apart from the group.

ReplyDeletepune365.com

Among the most effortless approaches to get your kid into early education is by utilizing explicitly made early learning books and DVDs.https://www.hngn.com/articles/229828/20200605/school-assignment-writing-how-to-improve-your-skills.htm

ReplyDeleteThis particular is usually apparently essential and moreover outstanding truth along with for sure fair-minded and moreover admittedly useful My business is looking to find in advance designed for this specific useful stuffs… cfa level 1 mock exam 2019 pdf

ReplyDelete