Examiners day (1 Viewer)

[buchanan]

Do you want to know how the 2006 4 Unit exams were marked?

Go to the Mason Theatre at Macquarie University tomorrow at 8:45am. The marking teams will give presentations.

Note however that these presentations will also include the marking of the 2006 SC as well as the 2006 General Maths, 2 Unit and 3 Unit exams.

 

[buchanan]

Who went? I did.

Examiners comments:

SC: http://www.mansw.nsw.edu.au/pd/ppt/MANSW-Examiners-Day-2007.ppt

HSC:

G: http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2006exams/pdf_doc/general_maths_notes_06.pdf

2u: http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2006exams/pdf_doc/maths_notes_06.pdf

3u: http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2006exams/pdf_doc/maths_ext1_notes_06.pdf

4u: http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2006exams/pdf_doc/maths_ext2_notes_06.pdf

Note that the presenter for Q6 in the 2 unit (Greg Powers) has contradicted the supervisor of marking and the chief examiner. He said in no uncertain terms that the abbreviation alt. for alternate was not accepted whereas the supervisor of marking and the chief examiner said it was accepted:

Clarification about abbreviations and Geometrical Reasons

At the HSC and SC 2006: Feedback and Advice Day held at Macquarie University on Saturday 24th February some teachers may have been given the impression that common abbreviations for geometrical terms (such as 'alt' for 'alternate') were not accepted by HSC markers in 2006.

Carol Taylor, the Director of Assessment and Reporting, at the Office of the Board of Studies has provided the following clarification for the information of all MANSW members:

"The Supervisor of Marking and the Chief Examiner for the 2006 HSC examinations in Mathematics, Mathematics Extension 1 and Mathematics Extension 2 have advised me that commonly accepted abbreviations in geometrical proofs were accepted by markers, provided that the abbreviation left the marker in no doubt that the student knew the relevant theorem or property. This is consistent with past practice in these examinations."

We hope this further information clarifies the situation for all MANSW members.

http://www.mansw.nsw.edu.au/pd/hsc-and-sc-2006-feedback-and-advice.htm

 

[blakwidow]

thanks buchanan. These will come in handy especially for maths induction for the final statement.

Each book has a different conclusion

 

[buchanan]

That was another controversy that came up because the MANSW solutions for 3 unit had the mantra Since the result is true for n=1, the result is true for n=1+1=2 and n=2+1=3, and so on. Therefore, the result is true for all positive integer values of n. It was put there by Scott Lankshear, Head of Mathematics at SCEGGS Darlinghurst.

When this came to my attention, I discussed it prior to Catherine Whalan's 3 unit presentation with Ian Woodhouse, Rod Yager (the chief examiner) and Scott Lankshear himself. Ian and Rod agreed with me (and Scott disagreed) that it should be more like the one given in MANSW's 4 unit solution: Hence by the principle of mathemtical induction, the result is true for all n > 1

So during Catherine's presentation, I interrupted her when she came to the 3 unit induction and recited MANSW's mantra and asked her if MANSW wants students to do it that way. She said that a mark wouldn't be given for it and then Rod also interrupted and said that the 4 unit conclusion is the correct one. Ian repeated this comment when he did the 4 unit presentation.

BTW, <a href="http://www.angelfire.com/ab7/fourunit/mansw2006sol-ext2.pdf">here</a> are the 2006 HSC solutions for Ext.2.

 

[~shinigami~]

That was another controversy that came up because the MANSW solutions for 3 unit had the mantra Since the result is true for n=1, the result is true for n=1+1=2 and n=2+1=3, and so on. Therefore, the result is true for all positive integer values of n. It was put there by Scott Lankshear, Head of Mathematics at SCEGGS Darlinghurst.

When this came to my attention, I discussed it prior to Catherine Whalan's 3 unit presentation with Ian Woodhouse, Rod Yager (the chief examiner) and Scott Lankshear himself. Ian and Rod agreed with me (and Scott disagreed) that it should be more like the one given in MANSW's 4 unit solution: Hence by the principle of mathemtical induction, the result is true for all n > 1

So during Catherine's presentation, I interrupted her when she came to the 3 unit induction and recited MANSW's mantra and asked her if MANSW wants students to do it that way. She said that a mark wouldn't be given for it and then Rod also interrupted and said that the 4 unit conclusion is the correct one. Ian repeated this comment when he did the 4 unit presentation.

BTW, <a href="http://www.angelfire.com/ab7/fourunit/mansw2006sol-ext2.pdf">here</a> are the 2006 HSC solutions for Ext.2.

Sorry, I'm still a little confused. Which one are we supposed to use?

 

[SoulSearcher]

Something similar to this one:

Hence by the principle of mathemtical induction, the result is true for all n > 1

 

[buchanan]

Yeah. That's according to Ian Woodhouse (head maths teacher at James Ruse) and Rod Yager (chief examiner).

Scott Lankshear (head maths teacher at SCEGGS Darlinghurst) disagrees. He wants students to do it the wrong way.

Scott's not alone in this. Rod told me that 75% of teachers are training students to do it the wrong way.

 

[AMorris]

Are they really going to deduct marks off us just because we don't include the correct 'mantra' at the end. That's basically ridiculous. As long as your proof is obviously induction and you've stated the word induction somewhere it's quite obvious what the student is doing.

 

[blakwidow]

u get one mark for writing

when n = 1 ... statement true

and another mark for the conclusion.

 

[Trebla]

Most mathematical induction questions are 3 marks. The first mark goes to proving the statement is true for the opening term (or minimum possible value of n), the next goes to the statement of assumption and the final mark goes to the proof that the statement is true for the following term. No marks are allocated for the conclusion in induction in the HSC, though the same can't be said for individual school assessment papers.

 

[Mill]

u get one mark for writing

when n = 1 ... statement true

and another mark for the conclusion.

This poster:

(i) did not read the thread;
(ii) did not follow the links provided;
(iii) doesn't know what they are talking about;
(iv) all of the above.

 

[buchanan]

I would like to comment on the induction part of the question.

It has come to my attention that many teachers are training their students to write some form of the following mantra at the end of induction problems.

The statement is true for n=0 and hence is true for n=1. The statement is true for n=1 and hence is true for n=2. The statement is true for n=2 and hence is true for n=3 and so on. Hence the statement is true for all integers n≥0 (by induction).

In many cases the words 'by induction' are omitted.

It needs to be pointed out that

(a) No marks are awarded for this mantra in the marking guidelines for the HSC.

(b) Much time is wasted writing it

(c) Most importantly, the above mantra, especially if the word induction is left out, is at best misleading.

There is a logical (and subtle) difficulty in trying to argue that because the statement is true for any (finite) integer n, it follows that it is true for all non-negative integers n. The axiom of induction is needed to fix this difficulty.

It would be better both mathematically, and for the students themselves, if they ended induction proofs with the simple statement

Hence the statement is true for all n≥0 by induction.

I might add that students who persist in writing this mantra actually LOSE marks in our discrete Mathematics courses at University, so teachers are not doing their students any service, either in the short term (HSC marks) or in the long term. I (and others) have been complaining about this for a long time but without success.

Furthermore, the official BOS position is in the 4 unit examiners comments for 2005:

The setting out of the induction warrants comment. A very large number of candidates who successfully completed the question (and many who attempted it) ended the induction proof with some version of the following:

"The statement is true for n = 0 and hence is true for n = 1. The statement is true for n=1 and hence is true for n=2. The statement is true for n=2 and hence is true for n=3 and so on. Hence the statement is true for all integers n≥0 (by induction)."

In a large number of cases the words "by induction" were omitted. Much time is wasted writing such a lengthy final statement and it would be better if candidates ended induction proofs with a simple statement like:

"Hence the statement is true for all n≥0 by induction."

(page 9 of http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2005exams/pdf_doc/maths_ext_2_er_05.pdf )