Month: July 2014
I learnt a lot about the world of maths about how simple questions can lead to confusing answers. It was crazy to believe something that leads to infinity ends up to be a completely strange and random number.
Paradoxes: When Mathematics Doesn’t Make Sense is such an intresting subject as it goes on and on about stuff that end up leading you to something you won’t expect and that just doesn’t make sense.
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When trying to learn something new, it’s really important to think about what you’re thinking. The fancy name for this is metacognition. The way to do it is to ask yourself questions like:
What new concepts/skills did I learn?
How does this relate to things I already know?What old ideas have been challenged?
Was anything surprising?
Was anything particularly difficult to understand?
This is just a starting point. I’m really looking forward to reading and engaging with your thoughts!
Exploring Mathematics is an elective semester course offered to Stage 5 (Year 9-10) students at Cherrybrook Technology High School.
To understand what this course is, you must first understand what it is not:
- This course is not about acceleration (learning content from years 11-12 in advance so that you will be more familiar with it when you encounter it in the future). In fact, topics in the Stage 6 mathematics subjects have been intentionally avoided so that they can be given their proper introduction in the Preliminary and HSC courses.
- This course is not like your regular mathematics class in its classroom activities or its assessments. In fact, there is a very conscious emphasis on branches of mathematics that are not understood through repetitive exercises, nor assessed in traditional examination formats.
By contrast, the goals of this course are:
After a pretty intense Term 2, I’ve hit the ground running in Term 3. Highlights include: preparing a new Year 8 program aligned to the NSW Syllabus for the Australian Curriculum; motivating my year 12s to make the most of their final term in school with a stirring story from the 2000 Sydney Olympics; and having a cracker of an introductory lesson to the Stage 5 elective maths course that I’ve started teaching this semester!
A brief note about that last point: the elective course (open to year 9-10 students) is called Exploring Mathematics, and it’s an incredibly exciting opportunity for me. It provides the chance to dig into all kinds of maths that have to be passed over in the BOS mathematics courses (due to lack of time, difficulty of assessment, and a variety of other factors). I intend for it to feature fairly prominently on this site; Í’ll write more details about this in the future as everything is still is in a state of flux for now.
What’s on the cards for your Term 3?
I’m a pretty slow thinker. In an argument, I’m that guy who comes up with the perfectly witty comeback… about two hours after the conversation is over. This doesn’t just happen to me in social settings – it also happens to me in the classroom! Often I’ll teach through a skill or concept only to realise, after the lesson is over, that there was something else I should have said, or some other analogy that would have been immensely helpful, which would have added valuable insight or made things clearer.
Something like that happened when I taught this lesson on congruence transformations:
In geometry, a congruence transformation is – roughly speaking – a way that we can change (“transform”) a figure in such a way that it is still the same shape and size (“congruent”). There are three main kinds of transformation that we cover in year 7: translation (sliding the shape to a different position), reflection (flipping a shape over) and rotation (spinning the shape around).
After introducing the idea of transformations and how they work, we start to think about “composite transformations” – what happens when you combine more than one transformation and consider the total effect from original to final image. An interesting fact emerges: that not all transformations are created equal. In fact, one of the transformations is more simple and basic than the others. One transformation can be used to create each of the other two. Which do you think it is?
It turns out that the most basic transformation is reflection. You can make translation and rotation out of a series of reflections, but not the other way around; though it’s counter-intuitive, reflection is the most basic kind of geometric transformation. Perhaps that’s why reflectional symmetry is so deeply ingrained into our natural sense of beauty.