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