Australian Curriculum Update

The latest draft can now be accessed at: http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10

The general idea is that all the ministers have agreed on the content, yet they say there is some work yet to complete before it can be implemented. Queensland will implement it in some schools from next year.

Here are some recent reports in newspapers on the update:

• http://www.abc.net.au/news/stories/2010/12/08/3088340.htm


• http://www.smh.com.au/national/must-do-better-national-curriculum-not-ready-for-classrooms-20101208-18pg9.html


• http://www.abc.net.au/news/stories/2010/12/08/3088301.htm

What if the largest states had the biggest populations?

After reading one of Simon Job's posts on mathsclass.net, I started to think about population density. Using the following data from wikipedia:

State	Area (km2)	Population
Western Australia	2529875	6967200
Queensland	1730648	5297600
Northern Territory	1349129	4279400
South Australia	983482	2163200
New South Wales	800642	1601800
Victoria	227416	500001
Tasmania	68401	344200
Australian Capital Territory	2358	219900

 

Consider the following question:

1. What is the population density of each of the states?


2. What is the population density of the entire country?


3. Why is the population density in each state different?


4. If people were to be redistributed, so that the population density across Australia was consistent, how many people would live in each state?

How many people would live in Tasmania?

Application to Teaching This activity and these questions relate very nicely to ratios in Stage 4 Mathematics.

Solving Real Problems or “Pseudocontexts”

Daniel Meyer has blogged a lot recently about "pseudocontexts" - that is: imposing mathematics on a situation that doesn't warrant it. A beautiful example is superimpsing a triangle on a picture of a dog, to find angles, etc.


Whilst it is very important that we include "Real world" contexts for our students, it is important that these are genuine and situations in the real world where mathematics is genuinely present.

Implications for Teaching:

Consider getting students to formulate the problem to be solved. To accomplish this, I suggest:


1. Giving too much info


Find the area:





2. Not giving enough information


Find the area (by taking appropriate measurements)





3. Give a hook for a real problem and let students work out the rest.


You currently live in Sydney and you need to plan a holiday in Brisbane. By considering transport, accommodation, time and the relevant costs of these, develop a recommendation for a one week holiday.


Students can include an estimate of petrol consumption, flight costs, distance travelled, if you drive you will have to stay somewhere on the way and many more factors.

Homework Grades using Google Docs

I currently grade my students homework using the following scale:

Grade	Description	Typical
1	Excellent	Completed with all working and marked
2	Good	Completed with working, but not marked
3	Satisfactory	Completed, without working
4	Cause for Concern	Approximately 50% complete
5	Intervention Required	Not attempted

 

I have tried a number of different methods to record these grades on a daily basis:

• On paper, with a class roll


• On my laptop, walking around the room


• On my iPhone, using a database app – HanDBase, StoreIt, Tap Forms

I have had great difficulty with these for a variety of reasons. This year, I started to call students out to my desk at the front of the room, so I could record it on my laptop. This worked quite well, but I am keen to be moving around the room. Google Docs has just released a new mobile version for creating and editing documents and I think that the spreadsheets fit the bill!



It's easiest to set up the file on the desktop version. I haven't set it up the way that I normally do, so that it's quick to record grades. Google Spreadsheets are set up for iPhone (and other mobiles) so that it is very easy to add a row. So, I have a column for each student (in my old excel markbook, I had a row for each student). It's easy to have a worksheet for HW grades and another one for marks. The other great benefit is that it's all backed up instantly and automatically all the time!

Constructions of Flags

Constructions can be a very skill based topic, with little application to the real world. Flag designs are incredibly complex and accurate and allow for some great creativity. The following picture is taken from The Style Manual that I referred to in an earlier post.



Here is a list of other links from a colleague that may be of benefit.

• Union jack measurements


• Greek flag


• Turkish flag


• South Africa


• Many flag constructions


• Scandinavian


• German flag


• Swedish


• Kenya


• Japan


• Guyanese flag

2010 Mathematics (2 Unit) HSC Solutions

Here are my solutions to the 2 unit Mathematics HSC. I like Question 10 as an interesting component B question to get the students thinking.

[slideshare id=7498804&doc=2010mathematicshscsolutions-110403060010-phpapp01&type=d&w=600]

2010 School Certificate Mathematics Exam Solutions

Below are my solutions to the School Certificate Paper. If you find any errors, please note them in the comments section below.

[slideshare id=7498801&doc=2010mathematicsschoolcertificatesolutions-110403060001-phpapp02&type=d]

Australian Curriculum: Update

A few points have been communicated out of NSW BOS/AIS/TAFE/CEC recently:

• NSW will ensure a maintenance of clarity of teaching and learning expectations


• Allow the Curriculum to be presented in stages, rather than years.


• They will address Life Skills


• Ensure that quality outcomes can be achieved within the current indicative time frames


• If endorsed in December, then writing of Syllabus documents will commence in January 2011


• Currently not being considered for implementation at this stage: Achievement Standards and General Capabilities

Link to PDF of letter

2010 General Mathematics HSC Solutions

Here are my solutions to the 2010 General Mathematics HSC Exam. If you have any corrections, please put them in the comments section below.

[slideshare id=7498802&doc=2010generalmathematicshscsolutions-110403060007-phpapp01&type=d]

Why do we teach Maths in a linear manner?

Just saw this amazing Prezi presentation. I'm interested in what can be done in Prezi for Maths. Have you seen anything good? Got any ideas?

Math is not linear on Prezi

What is the only word for units that is capitalised?

Newtons is the most common answer. Unfortunately, this is wrong and it should be written as newtons. The Austrlian Government has created a Style Manual: for authors, editors and printers. It outlines what the current practice is in terms of writing. There are lots of boring things, about how to use a full stop or colon. However, there is a whole chapter dedicated to numbers! I've read through this and noted the important characteristics for Mathematics Teachers. For example, the raised dash for negative is no longer used - rather, the "en dash" that we use for subtraction, is used for negative numbers. The document below includes 2 pages of goodness.

By the way - the answer to the question is Celsius.
Click to download
[scribd id=41127635 key=key-1om5eb20ltxhizpcx31m mode=list]

Screencasting

I've been thinking about how to change what I set my students for homework and communicate with them using multimedia. I've decided that screencasting will help fill this void after reader a post on another blog. Below are a few websites that offer screencasting.

Screenr
ScreenToaster
ScreenCast-o-matic
Jing
ScreenCastle
ScreenJelly

I've decided that ScreenToaser is the best of these for the following reasons:

• Web-based


• Ability to upload directly to youtube


• Ability to download as mov or swf


• Unlimited time of recording


• Supports webcam, audio and subtitles

You do need to register, but that's okay - it is an excellent product. Below is a video that I created for my Year 7 Class. I decided to add some homework (not much) to the end of the video - an easy way for me to make sure that the boys have watched it. It is only my first attempt, so I'll see what my students think.

Australian Curriculum update

ACARA have just released an update to the Australian Curriculum: Barry McGaw says that they have dealt with all the problems with the draft Maths Curriculum, including some comment on calculator use (but very limited). All going well this will be presented to the Minister on 11 November, which will be approved, in my opinion. It most likely won't be released the public through the Internet until December, given some earlier public comments.

Writing Maths in Microsoft Word 2007

Microsoft Word 2007 had a lot of enhancements on the previous version of Word (when you get used to it). I found that my worksheets and tests jsut didn't look right! I've worked out why. The 'Normal' style has changed. To change it back, you can follow these instructions (or just watch the video below).

1. Right click on 'Normal' in the Styles group on the Home tab. Select "Modify..."
2. Change the font to Times New Roman, 12pt.
3. Decrease Paragraph Spacing (currently 10pt After)
4. Single Space the document
5. Select "New documents on this template" and OK

Gender Differences in Mathematics

Preckel, F., Goetz, T., Pekrun, R., Kleine, M. (2008) ”Gender Differences in Gifted and Average-Ability Students: Comparing Girls’ and Boys’ Achievement, Self-Concept, Interest, and Motivation in Mathematics”, Gifted Child Quarterly, 52(2), 146-159

For gifted students, boys seem to have a more positive self-concept, interest and motivation, compared with girls. This gender difference is not evident amongst average-ability students.

Performance is different among males and females based on the content. For example, Males score better on Problem Solving tasks, whereas females score better on Mental Arithmetic.

There is an over-representation of males in higher levels of mathematical ability.

There is a correlation between ability group and self-concept, moreso for boys than girls. Boys estimate their mathematical ability higher than their female counterparts. I believe that this can have significant motivational impacts on students.

One of the implications of this paper is a preference for single-sex schooling. At one co-educational private school in Sydney, Maths classes have indeed been split up based on sex, which could be to the benefit of the students academically, whilst still providing social opportunities to interact with members of the opposite sex.

Equations in Word 2007

I have discovered a few problems with the In-Built 'Equation' editor:

1. You can't write a short or long division algorithm (is that the right word?) e.g.
   
2. To 'align at =' is a pain and does not always work as expected
   
3. If you write text and equations in the same line, it formats using Latex (looks horrible), try typing Evaluate and it turns out like:
   
4. Since it it NOT Times New Roman, the font in every equation looks considerably different from the text around it. 
   

My Solutions (how not to use it): Use MathType (unless you do option 2, which is way cheaper and almost as good!) Record a macro to put a button in the quick-access toolbar, to use "Microsoft Equation 3.0" with one click

1. Go to 'View' Tab
   
2. Macros (far right) > Record Macro
   
3. Click 'button' <select the new macro in the left hand column and add it to the right hand column, you can also customize to change the name and icon> Click OK
   
4. Go to 'Insert' Tab > Object > "Microsoft Equation 3.0" > OK
   
5. Click back on your word document (do not close the equation editor window) View tab > Macros > Stop Recording. Now close the equation editor window and you should have a nice little icon on the quick access toolbar.
   

 All that being said, it is nice to have "Microsoft Math" Add-in, and also the Microsoft Worksheet Generator. UPDATE: I've experienced some problems printing these new equations in Word 2007 - they don't print!! This link helps with the problem: http://support.microsoft.com/kb/960985/en-us

ACEL Response to NAPLAN

Here is the link to the article posted by ACEL, in response to NAPLAN.

ACEL Response to NAPLAN.pdf

A very interesting response to NAPLAN by ACEL. I have had a few thoughts whilst reading through this article, so thought I would share them with you.

I agree with much of what was expressed here, especially noting that there is a long delay in providing feedback and results to students and schools. It has been the case that by the time the results have come out, that the students understanding, application and ability can have changed quite significantly.

I think one of the most important issues with the MySchool website is the reporting of Year 7 results. A student’s numeracy and literacy in Year 7 at the time of sitting NAPLAN, is primarily based on their education prior to entering Year 7 and is therefore more of a reflection on the particular primary school a student attended, rather than the secondary school that it is linked with on the MySchool website.

There was a suggestion in the report that “value-added” should be reported instead of (or in addition to) raw marks. Given that I am already aware of some schools focusing on the Year 9 NAPLAN and not the Year 7 NAPLAN, this could pose some problems. If the desire is to get the best value-added scores, then a school is definitely encouraged to neglect Year 7 NAPLAN preparation, and focus on basic literacy and numeracy skills (possibly to the determent of the wider curriculum) in preparation for the Year 9 assessment.

Despite this, I believe that the notion of “value-added”, if it could be fairly and accurately calculated, is a worthwhile one. The big question is – how to calculate it.

Geogebra

I have recently abandoned The Geometers' Sketchpad, in favour of the free, regularly updated and feature rich GeoGebra. I had always found GSP clumsy in the way that you had to do things (maybe I was just getting used to it). GeoGebra seems more intuitive. The cartesion plane does not seem as though it is an after thought either, with good capabilities. I have started to create a number of GeoGebra applets. Here are the first three:

• Area of a triangle (proof)


• Area of a circle, by using inscribed polygons


• Angle sum of a triangle

Feel free to download them and use under the creative commons (AT-NC-SA) license.

Sharing: The Moral Imperative

The K12 online conference has just started and it is on iTunes U this year! This is great for watching and listening via my iPhone. I watched the video below, which gave a good background to sharing with other teachers. I am a teacher - which by its very meaning, means that I teach! So, why do I often keep my ideas and musings to myself?

This is the third time that I have commenced this blog at http://www.maths.net.au/. I originally got the domain back in 2007 and now find an urge to launch and maintain this blog. Please join me for some ramblings and musings - I hope that some of what I put here will be of benefit to you.

Reflections on ACER Research Conference

I had the fortunate opportunity to attend the ACER conference "Teaching Mathematics? make it count" over the last few days. There were many excellent papers presented, that will all be posted http://research.acer.edu.au/research_conference/RC2010/ in due course. Here are a few reflections:

1. Speaking in and about Mathematics Classrooms Internationally (David Clarke, University of Melbourne)

Research supports my classroom experience of students from a Korean cultural and ethnic heritage. Sometimes we have had students join our school in Year 10 or 11 from Korea who do not seem to engage in the classroom and contribute almost nothing to classroom discussions.

 

One interesting graph showed the number of public utterances (teacher/student) in classrooms from a variety of countries. It showed that there were almost no public utterances from students in Korea, compared with approximately 200 student public utterances from classrooms in Melbourne. So the question is raised of how to modify teaching to assist these students to engage and think through the material rather than simply take the teachers word as gospel.

 

Implications:

• We need to use modified teaching strategies for Korean students.


• Firstly, it is a good idea to address this directly, explicitly and confidentially: "I know you have some very good ideas and it would be good for you to share those ideas with the other students in the class"


• Initially, do not ask students questions in front of the entire class but rather move to students and when they have an answer that is correct, ask them individually if they can share that with the class as this will give the student confidence in their ability.


• Have students work in small groups so that they do not have to talk in front of the entire class, but the setting can be more informal, which will give a greater chance of them contributing.

2. Mathematics Teaching and learning to rech beyond the basics (Kaye Stacey, University of Melbourne)

Year 8 textbook study found good proofs if rules as well as the rules themselves, but once the rue was learnt, the derivations we not referred to again. I do not think that this is a problem - once you understand the derivation, there is no need to repeat this for no purpose. Instead students should be given the opportunity to discover this for themselves in the first instance.

 

There does seem to be a slight improve on the "shallow teaching syndrome", which could be a result of the wonderful applets that can be found on the Internet to help explain rules and the derivation of them.

 

The important point was made that we need to use these derivations more as a thinking tool than simply an explanation tool.

 

Implications

• We need to let students explore the content, make their own connections and attempt to come to their own rules and relationships, thus creating a thinking opportunity.

3. What TIMMS and PISA can tell us

PISA: In 28 out of 41 countries, boys scored had higher 'Mathematical Literacy'. Interestingly there was NO OVERALL GENDER BIAS in Australia. However, boys in Australia were stronger at Space, Shape and Uncertainty.

 

TIMMS reveals that 15 year old girls in Australia had much lower self-belief of their Mathematical capabilities than boys. PISA: Interestingly, although indigenous students scored a whole proficiency band lower than non-indigenous (on average), there were no gender differences in terms of their self belief.

 

Implications:

• Why do non-indigenous girls have lower self belief? I teach boys only, so I can capitalise on their possibly over inflated self belief, but as a society this is a concerning trend as we need strong males and females in mathematical and scientific professions.

 

 

 

Posted with Blogsy