Circle Geometry: What will the NSW HSC Markers Accept?

"The angle between a chord and tangent at the point of contact is equal to the angle in the alternate segment"

There has been a lot of discussion between staff at my school as to whether you must state the entire reason, or whether a shortened version would be accepted. After having a look at last years Extension 1 Mathematics HSC Exam and Suggested Solutions (as provided by the BOS), they have as their reason "angle in alternate segment". I assume that also "alternate segment theorem" would be accepted.

I am pleased that this is accepted - after all, what is it that we are testing? Whether students can memorise specific wording of a definition, or whether they understand and can apply that information?

If it can be easily understood what a student has done and that they understand the concepts being examined, they should (and in this case will) be awarded the appropriate marks.

How to Videos on using a Casio fx9860g AU to do Financial Mathematics and Algebraic Modelling in General Mathematics

Casio Education have videos which clearly explain how to use their graphics calculator for the most popular applications in the General Mathematics course in NSW. There is are 2 PDFs that go with each video that can be printed and distributed to students.

While students need to be proficient at performing calculations without the graphics calculator function (as these are increasingly being included in HSC examinations), they should be familiar with using their graphics calculator to quickly perform the calculation.

When using a graphics calculator, the focus changes for mere computation to understanding of the question and problem solving. Students do not have to be concerned with the automated process of calculation getting in the way of them understanding and learning.

Topics include:

Financial Mathematics

• Compound Interest


• Present Value


• Future Value (no video, just PDF at time of post)

Algebraic Modelling

• Developing a model


• Using a model


• Refining a model


• Verifying a model

There are many more class activites and dowloads that can be found here. 

Mathematics Professional Development in Sydney and Overseas in Term 3 2011

 

Here are some PD sessions you may not want to miss. Remember all the PD for the year can be found on http://www.maths.net.au/ais/pd

Conferences:

MANSW Annual Conference
Date: 16 September 2011 to 19 September 2011 Location: Wollongong Novotel More Details: http://mansw.nsw.edu.au/pd/conference.htm

The 16th Asian Technology Conference in Mathematics
Date: 19 September 2011 to 24 September 2011 Location: Bolu, Turkey More Details: http://atcm.mathandtech.org/

NZAMT: NZ Maths Association Annual Conference: Mathematical Journeys 2011
Date: 19 July 2011 to 23 July 2011 Location: Dunedin, New Zealand More Details: http://www.akblimited.co.nz/NZAMT/

Canberra Maths Association Annual Conference
Date: 19 August 2011 to 21 August 2011 Location: ACU, Canberra More Details: http://www.pa.ash.org.au/canberramaths/4ProfDev.htm

11th International Conference of the Mathematics Education into the 21st Century Project
Date: 10 September 2011 to 17 September 2011 Location: Grahamstown, South Africa More Details: mailto:alan@rogerson.pol.pl
 

Other Professional Development

TTA: Engaging Computer Tasks for Years 9 and 10 Maths (Course 1)(ECT00)
Date: 18 July 2011 Location: Online More Details: http://www.tta.edu.au/courses/listbykla/klaId/8/page/1/state/NSW

TTA: GeoGebra: A Dynamic Approach to Yr 9-10 Trigonometry
Date: 18 July 2011 Location: Online More Details: http://www.tta.edu.au/courses/listbykla/klaId/8/page/1/state/NSW

TTA: Dynamic Geometry and Algebra with GeoGebra
Date: 18 July 2011 Location: Online More Details: http://www.tta.edu.au/courses/listbykla/klaId/8/page/1/state/NSW

TTA: Coordinate Geometry - a conceptual approach with GeoGebra
Date: 18 July 2011 Location: Online More Details: http://www.tta.edu.au/courses/listbykla/klaId/8/page/1/state/NSW

TTA: Dealing with Data in Years 7 to 10
Date: 18 July 2011 Location: Online More Details: http://www.tta.edu.au/courses/listbykla/klaId/8/page/1/state/NSW

Applied Mathematics Preliminary Course (Year 11) (MANSW)
Date: 25 July 2011 - 4:30 pm to 6:30 pm Location: Auburn Girls High School & Video Conferencing More Details: http://mansw.nsw.edu.au/pd/secondary.htm

Visual Mathematics ...I See IT, I Get IT (AIS)
Date: 4 August 2011 - 9:00 am to 3:00 pm Location: AIS Conference Centre More Details: http://www2.aisnsw.edu.au/CoursesEvents/Pages/CourseDetail.aspx?cid=4647dbbf-fbe6-df11-af9d-005056b841f8

Applied Mathematics HSC Course (Year 12) (MANSW)
Date: 15 August 2011 - 4:30 pm to 6:30 pm Location: Auburn Girls High School & Video Conferencing More Details: http://mansw.nsw.edu.au/pd/secondary.htm

Head Teacher Network, Arncliffe (MANSW)
Date: 23 August 2011 - 4:30 pm to 6:30 pm Location: Teluba Professional Services Centre, Cnr Segenhoe & Avenal Streets, Arncliffe 2205 More Details: http://mansw.nsw.edu.au/pd/secondary.htm

HODs of Mathematics 'Issues' Day (AIS)
Date: 25 August 2011 - 9:00 am to 3:00 pm Location: The Scots College More Details: http://www2.aisnsw.edu.au/CoursesEvents/Pages/CourseDetail.aspx?cid=e6508e25-1bee-df11-af9d-005056b841f8

TTA: Supporting Struggling Students in Yr 7-8 Mathematics
Date: 30 August 2011 - 9:30 am to 3:30 pm Location: Sydney CBD More Details: http://www.tta.edu.au/courses/listbykla/klaId/8/page/1/state/NSW

From Fractions To Algebra (AIS)
Date: 8 September 2011 - 9:00 am to 3:00 pm Location: AIS Conference Centre More Details: http://www2.aisnsw.edu.au/CoursesEvents/Pages/CourseDetail.aspx?cid=68e999f8-a4e7-df11-af9d-005056b841f8

TTA: Dynamic Geometry and Algebra with GeoGebra
Date: 12 September 2011 Location: Online More Details: http://www.tta.edu.au/courses/listbykla/klaId/8/page/1/state/NSW

TTA: GeoGebra: A Dynamic Approach to Yr 9-10 Trigonometry
Date: 12 September 2011 Location: Online More Details: http://www.tta.edu.au/courses/listbykla/klaId/8/page/1/state/NSW

TTA: Engaging Computer Tasks for Years 9 and 10 Maths (Course 1)(ECT00)
Date: 12 September 2011 Location: Online More Details: http://www.tta.edu.au/courses/listbykla/klaId/8/page/1/state/NSW

TTA: Dealing with Data in Years 7 to 10
Date: 12 September 2011 Location: Online More Details: http://www.tta.edu.au/courses/listbykla/klaId/8/page/1/state/NSW

TTA: Coordinate Geometry - a conceptual approach with GeoGebra
Date: 12 September 2011 Location: Online More Details: http://www.tta.edu.au/courses/listbykla/klaId/8/page/1/state/NSW

Mathematical Induction: What will the NSW HSC Markers accept for a conclusion?

One of my students asked me this question last year. Here is my research and response. 

2008 Ext 1 Mathematical Induction Question


From the marker comments (produced by the Board of Studies) they seem to suggest that there was:

• 1 mark for  step,
  


• 1 mark for 'the inductive step' (assuming true for )
  


• 1 mark for proving true for
  

In addition, from 2009, the BOS has started to provide "sample answers"


The marking guideline clearly gives one mark for proving true for n = 1 (this is actually part (i) of the question). For part (ii), one mark is given for the 'inductive step' --- i.e. assuming true for n = k and one mark for proving true for n = k+1. It looks like NO marks are allocated to the conclusion.

At MANSW's Markers Reports and advice days in the past it has been said that a conclusion as brief as "Hence proved by Mathematical Induction" would be sufficient.


However, there is no harm in taking the 5-10 seconds to write a conclusion.


In 2010, Q7(a) was a reasonable typical divisibility induction question. The marker's notes affirm one mark for proving n = 1, The inductive step and proving n = k + 1 are both important steps. The conclusion was not mentioned in the notes, except to say that there is no point writing out the structure of an induction proof (conclusion) without any attempt at a proof. The conclusion given is very similar to the previous year: "result is true for all integers n > 1 by induction."

Use an iPad (+ Griffin Stylus) & SplashtopRemote to create your own IWB instead of using a Tablet PC

I currently use a TabletPC and love its functionality. I can setup lessons in Microsoft OneNote, with links to all the resources I will be using for the lesson (including Geogebra applets). I love being able to using my table PC to write on the screen and have it automatically updated to the screen. Unfortunately I face losing my TabletPC and have been looking into other alternatives.

1. Epson BrightLink Projectors.
We have recently had these interactive projectors installed. Unlike a typical IWB, they project onto a normal whiteboard and you use a special pen to interact with the connected computer. I have found this quite freeing, being able to stand in front of the class, and point to exactly what I want. However, when it comes to digitally writing, the quality is not good enough and I retreat to my TabletPC to do any written work. The BrightLink is great for working with Geogebra!

 



2. iPad and Stylus with SplashTop Remote
I love Splashtop Remote as it allows me to control my computer from my iPhone (and and iPad, when I get my hands on one). This Griffin stylus is quite nice and it works (unlike the 50c one that I got on ebay). It is great with being interactive, but the quality of digital writing is not great - It's also difficult to get the exact point to put it on the ipad so when writing a 5, the top sometimes isn't joined to the rest of it. So, this solution is very similar to using the brightlink, with the added flexibility to walk around the room.



3. Wacom Tablet. I have seen these tablets used by Douglas Butler (TSM,Oundle) and have been very impressed with the precision he has with them. These are quite expensive, but look like the best solution for digital writing, if I do not have a TabletPC in the future.

I will write a post later about why a TabletPC is an essential tool for Mathematics Teachers.