Recently I was asked to include a copy of the Trigonometry Unit Circle in a Year 10 Extension Maths exam. When I went looking for a good one on the Internet, I found plenty of Unit circles that were good for concept teaching, but weren't very detailed. Some had no angle labels at all.

We also had one that had been hand drawn and scanned, but it wasn't very accurate or neat. That unfortunately was the one I used, as the exam timetable was approaching fast.

So once I had some free time, I scratched one together using SageMath.

# An Australian Teacher

Advanced resources and utilities for the classroom and teacher

## Monday, 21 September 2015

## Sunday, 22 March 2015

### MathJax for the win.

Just a little note that I use MathJax for my mathematical posts, and this is the ONLY scripting (so far) that I throw into my blog.

Here are some of the resources I use for MathJax:

http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference

http://www.suluclac.com/Wiki+MathJax+Syntax

and here's how I add it:

http://mathjaxtest.blogspot.com.au/

The one thing missing in this post, however, is that you need to close the </script> tag. :/

Here are some of the resources I use for MathJax:

http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference

http://www.suluclac.com/Wiki+MathJax+Syntax

and here's how I add it:

http://mathjaxtest.blogspot.com.au/

The one thing missing in this post, however, is that you need to close the </script> tag. :/

### Why does e = 2.71828183? Or how e SHOULD have been discovered.

This is an interesting exercise to do with higher level mathematical students - it shows them that the value of $e$ can be derived purely from it's differential properties.

So we start with the fundamental property of $e$, that $D(e^x)_x = e^x$.

In short, we're looking for the

(As noted in previous posts, I'm using a differential format similar to sagemath's default format.)

So we start with the fundamental property of $e$, that $D(e^x)_x = e^x$.

In short, we're looking for the

__- what function stays unchanged.__**identity function of differentiation**(As noted in previous posts, I'm using a differential format similar to sagemath's default format.)

## Monday, 24 November 2014

### Science Posters

Okay, thought I'd dig these out of the digital attic. The following are links to two science posters I made some time ago.

They are licenced under Creative Commons (Attribution and Share Alike) so feel free to print share.

They are licenced under Creative Commons (Attribution and Share Alike) so feel free to print share.

## Wednesday, 16 April 2014

### Biovisions

These are some great biology videos from Harvard University.

Biovisions - Inner Life of a Cell

https://www.youtube.com/watch?v=wJyUtbn0O5Y

Biovisions - Powering the Cell: Mitochondria

https://www.youtube.com/watch?v=RrS2uROUjK4

and a lot more available at:

http://multimedia.mcb.harvard.edu/media.html

The Youtube versions are better for a projector screen than the ones you can get on the Harvard site. (Larger and clearer).

Inner Life of a Cell is a

Biovisions - Inner Life of a Cell

https://www.youtube.com/watch?v=wJyUtbn0O5Y

Biovisions - Powering the Cell: Mitochondria

https://www.youtube.com/watch?v=RrS2uROUjK4

and a lot more available at:

http://multimedia.mcb.harvard.edu/media.html

The Youtube versions are better for a projector screen than the ones you can get on the Harvard site. (Larger and clearer).

Inner Life of a Cell is a

__great__way to introduce cell parts, either for juniors and seniors.## Sunday, 2 June 2013

### Alternative Conceptions

One of the basic facts of science and mathematical education is that you have to deal with Alternative Conceptions in your students.

Basically humans are very good at finding patterns in the world, but we're

The following link lists a series of common Alternative Conceptions.

Basically humans are very good at finding patterns in the world, but we're

__very__reluctant to give up on discovered patterns, even with plenty of evidence that they don't work. We also have a weird tendency to only seek evidence that confirms our theory, and discount or dismiss evidence that rules our theory out.The following link lists a series of common Alternative Conceptions.

### Van Der Graaf Machine - Preparation and Safety

Van Der Graaf machines are awesome - impressive as all hell, and allow you to investigate and demonstrate a large varieties of electrical physics concepts.

Typically I'm very much against the inductive-learning-good, deductive-learning-bad philosophy that has seemed to invade modern scientific theory. It takes too much time if done every lesson, it does little to correct pervasive alternative conceptions and it ignores half of how science works.

But a mixture of inductive and deductive learning

Typically I'm very much against the inductive-learning-good, deductive-learning-bad philosophy that has seemed to invade modern scientific theory. It takes too much time if done every lesson, it does little to correct pervasive alternative conceptions and it ignores half of how science works.

But a mixture of inductive and deductive learning

__works__for Van Der Graaf machines. At the bottom of this post are some investigations that can be done. With good timing and a dollop (5 minutes) of deductive-style learning, you can complete most of them in a single one hour lesson.
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