Week 5 on the course was devoted to the mid-term exams in all the academic subjects; so no lectures or seminars.
In Week 6 we got stuck into more algebraic tools and methods; namely polynomial division, factor theorem and remainder theorem. Read on for more details.
This was the second week of geometry (following on from straight lines last week) and we looked at some of the properties of circles.
This week has been all about quadratic functions and equations. Read on below the fold for more details.
The first formal week of teaching has ended for my 14th cohort of Foundation students at INTO Newcastle University. The first week often feels like a bit of a drag; we're often skimming through topics that they should be completely familiar with. Not all of my students have arrived in the UK so I'm not launching straight into stuff that'll be assessed on the exams immediately.
Details of each session below the break.
On the eve of a new academic year of teaching and as usual I'm worried about getting the balance right. It's the usual conflict. Students are required to know the subject well enough to pass exams at various points during the next 8 months. There are various methods and techniques I can employ to ensure this happens. But if that was was the only focus of the course then I'd be guilty of "teaching to the test". Students would probably pass the exams but they'd be ill-equipped to handle new material or cope with even small variations on what they've already seen.
As a maths teacher I want my students to be independent learners. For me that means they are able learn from their mistakes and that they have strategies for thinking about and solving mathematics problems in a very general way. The intensity of my course - the amount of time allocated and the material that the students are expected to know - means that I definitely won't get enough sessions emphasising skills required to be an independent learner.
In practice what will probably happen is that I build some kind of activity into most classes where I get the students thinking about how to solve a problem that isn't textbook. There are plenty of teachers blogging about how to do this and lots of real world scientific examples to draw on.
Anyway, I'll record the best examples of my strategies here!
Course notes from my session called "Astrometry" at NASTRO are available by clicking the link.
The PDF has Flash animations from University of Nebraska-Lincoln embedded in it. When you open it, you'll have to enable them to run. It usually means clicking a little toolbar at the top of the talk. For best results press ctrl-L to view in full screen after you've done that.
You can view the Flash animations online if you prefer. These are the ones I showed during the talk:
Altitude/Azimuth (Horizon coordinates)
Right Ascension / Declination (Equatorial coordinates)
Coordinate Systems Comparison
There are loads more at the UNL website on other topics. Enjoy!
I was introduced to the joys of LaTeX (and TeX) by my PhD supervisor about 13 years ago. When it came to writing up scientific reports and documents Microsoft Word just didn't cut it; documents with inline equations in Word just looked bad. Things may have improved since then (I'm not convinced) but polished, beautifully typeset documents come from LaTeX.
However, LaTeX has a steep learning curve. You have to write code in LaTeX (to produce everything from headers, footnotes, bold text, equations, etc) and then compile the document to see how it looks. LaTeX is best described as WYSIWYM (What You See Is What You Mean). LaTeX's internal algorithms deal with the best places for page breaks, positioning diagrams, equations, footnotes and so on. This is not the same as Word (or equivalent), with its WYSIWYG (What You See Is What You Get) interface and bewildering choices of styles for everything.
Now to the point.
LaTeX has a steep learning curve - no doubt about it. In recent years there have been attempts to put a nice front end on it. Something between Word (with it's shortcuts and buttons) and raw LaTeX (with the actual coding hidden from view but not inaccessible and still easily customisable).
My favourite editor - by a mile - is called LyX. I like it because it's free and easy to use. I wrote my mathematics textbook using LyX. All of my course notes were produced with it. Any time I need a diagram or figure for an exam paper....I write the code to produce it. Just to give you an idea how I use it, here's an example: a slab of graph paper with an irregular shaded region. This was part of a question about using Simpson's rule to compute areas.
To produce this diagram I called the package "pst-plot" in the LaTeX preamble within LyX:
and in the document window I placed some ERT (evil red text - raw LaTeX!)
...and LyX outputs a hires plot to the exact specifications I need.
It's easy to get started - just go to the LyX website and download the latest stable version (currently 2.10).
An 3am start for me. A mad dash to the airport by taxi on another hot day. A plane from Sibu to Kuala Lumpur. Another plane to Singapore (we only found out at the airport that we'd be going to Singapore rather than directly to Johor Bahru). We cleared immigration at Singapore by midday and were driven by taxi back into Malaysia.
We arrived at Foon Yew High School in barely on time in the early afternoon. Four mini classrooms were laid out in the school hall. Unfortunately no projector or whiteboard available to anyone. This pretty much ruled out the lessons I'd been using up until that point. With only minutes until the arrival of my first class of 40 students I decided to do an impromptu session on design considerations in aeronautical engineering and their subsequent impact on experimental test flights.
In other words I just spent the next hour and half making paper aeroplanes with kids. A competition to see who could design a plane to travel furthest in a straight line. After the play-off style tournament the students were allowed to tweak the design before trying again. I got them to come up with branding and logos for their designs (in everyday parlance - they coloured their planes in).
And that was it - the end of the STEM sessions. On Friday we're heading back to Singapore. Only admin, networking and paperwork left on this trip now. And still...no stars at night.
Well my plan to post a blog entry every day was derailed by the rubbish wifi in each hotel. Honestly! Don't promote your hotel as having wifi if the service is this bad. Better to say you don't have it and not disappoint your guests! Rant over :-) All this travelling seems to blend the days together in my memory. Here's a quick catchup on what's happened so far...
On Tuesday I was at Chung Hwa High School in Miri. Only time for one session so I did the Buffon's needle experiment. After several hundred needle throws we got pi to be 2.9. We talked about reasons why the experiment might give a different value to the actual value (3.1, to one decimal place).
With less than a week to go I'm just about settled on the sessions I'm going to do in Malaysia. Here's a brief summary.
A mathematical experiment to determine the value of pi. Needles, or an equivalent (cotton buds, matches, hot-dogs) are thrown onto a surface with regularly spaced lines. The ratio between needles touching and not touching can be used to estimate pi.
This lesson covers a suite of mathematical skills: data collection and analysis, probability, trigonometry, calculus and Monte Carlo methods.
This is a surprising (to most people) result concerning the distribution of first digits in many samples of data. For example, in lists containing asteroid diameters in meters, isotope half lives in seconds, student heights in mm your intuition might tell you that you're just as likely to get a 1, 4 or a 9 as the first digit. A physicist called Frank Benford discovered that not only was intuition wrong about that, but that the distribution of first digits followed a beautiful mathematical pattern.
This lesson requires a bit of data analysis and unit conversions. The mathematical explanation of why Benford's law works is fairly complicated. I'm planning to just give the hand waving version using concepts they'll "get" like percentage change frequency distribution of digits in the integers.
Benford's law in mathematically interesting in its own right but it has practical applications in terms of fraud detection. It's easy to detect when books have been cooked with numbers that human generated. If you're going to do it - you'll need to know about Benford :-)
Where are the aliens?
I've done this presentation so many times with the astronomy club. I'll start by asking the students whether or not they think life exists beyond the Earth and perhaps if any of them can give a persuasive reason for their position. Usually the majority response is "Yes" and the reason is version of "because the universe is so big". The obvious question is well, where are the aliens? Then I'll do a brief summary on the search of extrasolar planets and the history of SETI. In other words, present the students with the evidence and have a discussion which attempts to resolve the apparent paradox between widespread planetary systems and no evidence of intelligent life beyond the Earth.
3D Tour of the Solar System
This is another popular astronomy presentation with NASTRO. I'll run with this one when I've got 15-20 minutes only. Lot's of pretty pictures and I'll get the students to tell me what they know about the solar system as we go. And on top of that...it really is 3D (well, red-blue anaglyph).
Dr Adrian Jannetta
Guitar strummin' explorer of the universe. Mild mannered maths teacher by day and astronomer by night.