A paucity of posts

I've been neglecting this blog quite badly. I had intended to post semi-regularly about my studies toward a Bachelor of Teaching but I've dropped the ball fairly thoroughly. As an attempt at redressing the balance, I'll post several entries over the next few days.

Tags: Meta

Resources for Teaching Pythagoras' Theorem

I've decided to make the lesson plans, materials and such I write freely available under an Attribution, NonCommerical, ShareAlike license from Creative Commons.

The first lot of material I'm making available are the lesson plans for teaching Pythagoras' Theorem that I developed last semester (and wrote about using). If you're interested in teaching, mathematics, or teaching mathematics why not have a look at my free lesson plans.

Tags: Education Plans Mathematics

Inclusive Education

I'm currently sitting in a lecture about inclusion and inclusive schooling. We're discussing a case-study about a primary school class and approaches that we might take to differentiating our curriculum and practice for students with disabilities. In particular we're considering a hypothetical student with Down Syndrome in a grade 5/6 class. We've had some interesting points raised including the inherent inclusivity of the Essential Learnings and the possible effects of differentiating the curriculum (will we be, in effect, "dumbing down" the curriculum?).

More later.

Tags: Inclusion Education Teaching

LaTeX output for HsColour

On a somewhat related subject to my last post (the one about LaTeX), I've just started working on adding LaTeX support to hscolour. The structure of the program has made it easy to add support for LaTeX output: all I had to do is add two items to a pattern match (for option handling), and define a function to render the code to LaTeX (plus a few helpers to escape LaTeX special characters, etc.).

Once I've managed to get it working adequately, I'll submit a darcs patch to the maintainer.

See also Malcolm's posts about hscolour: one and two.

Tags: Haskell LaTeX

Wanted: LaTeX packages

I've got a hankering to dig out my incomplete thesis and polish it off as an excuse to really get up to speed with LaTeX. As such, I'm looking for LaTeX packages that accomplish a number of tasks:

Unicode and symbols

The main thing I'm after is a package that will allow me to '∧' instead of '\wedge' in my LaTeX source and have it Just Work^(TM). A single package that provides consistent symbol handling would be nice too.

Metadata support

While hyperref can be used to add PDF metadata, and xmpincl can include an RDF license when using pdftex, you still need to do it all yourself. It'd be nice if there was a module that would do it for you.

Font handling

A single, consistent way to handle real fonts. I like Computer Modern as much as the next person, but once in a while I'd like to be able to use another font without having to wrestle with TeX.

I'll admit that most of my desire for packages to address these issues is probably an issue more of my knowledge of existing code than that code's availability, but it'd be nice if there was a little more consistency in my LaTeX environment and a lot more consistency in Google's LaTeX search results.

Tags: LaTeX Wishlist

An Interesting Find

One of my house-mates made an interesting find yesterday: a 36 inch folding ruler. After a bit of cleaning up (it was caked with grease and grime) it's presented as being even more curious.

It is constructed of four wooden segments of equal length joined with what I assume to be brass pins and hinges. Both sides bear scales. The inside face has a single scale on the lower edge with inches and sixteenths marked. The outside face bears an inch scale marked on both edges and three different sub-inch scales: the bottom edge is marked in inches and eighths, the first seventeen inches of the top edge are marked inches and twelfths, the last seventeen inches of the top edge are marked in inches and tenths, and the middle two inches of the top edge are unmarked as the hinge makes them unusable as a line or measure.

The ruler has a number of markings in addition to the scales marked: each of the sub inch scales are labelled with the appropriate number, and each face bears a "3FT" before the brass end cap. The outside face bears what may be some manufacturers marks between the thirteen and sixteen inch marks. While they are too faint to make out with any degree of certainty, the first appears to be a rectangular border containing an entirely illegible first line and a second line: "LUCAS". The second might be "made in England" but is even fainter than the first and only "and" may be made out reliably. The third mark is quite easily made out and reads "354".

I had a bit of a poke around on eBay and did a bit of Googling, but haven't been able to find out much. Any information would be appreciated.

Tags: Picture Curious Object

The Other Shoe Drops

Today was the third day of Professional Experience One and the other shoe dropped. Continuing with the material I've planned, the first class ripped along, even those who were absent yesterday and needed to catchup.

The second class was another matter entirely. A number of them managed to finish everything and I was really happy with three or four of them in that we've managed to resolve their initial confusions and get them to the point where they are completing problems quicker than 90% of the class. Other students in this class managed to avoid completing much at all, even when I was stood next to them trying to find out if they needed assistance or were just being lazy. Some of this is to be expected (they were distracted by an event being held after my class), but I'm not sure how I'll be able to get through to them if they're like this tomorrow.

Tags: Education Teaching Practicum

Categories and Tags

I've added support for tags to this blog using Del.icio.us. New posts will be tagged with links to the appropriate tag on my Del.icio.us account and readers with Javascript enabled should see a list of categories at the top of the right-hand column.

I'll need to experiment some more before I make up my mind just how useful this'll be.

Update: It looks like Technorati has managed to index the tags on the last two posts.

Tags: Blog Meta Organisation

Teaching; A Second Reaction

My second day of teaching went quite a bit better than the first. I managed to address quite a few of the points my colleague teacher raised yesterday as well as improving my structure and delivery. Where yesterday the way I presented the examples and instructions wasn't as effective as it should have been introducing a new unit of work (I think that I was still stuck in 'university seminar' mode rather than 'high-school lesson' mode), I think that the main thing lacking today was the polish that will come with experience. One reflection of this is that the comments provided by my colleague teacher amount to one-and-a-bit pages today rather than the three pages of notes on yesterday's lessons.

The most glaring omissions yesterday were:

1. my lack of action toward learning the students names;
2. my poor use of the whiteboard to reinforce and record explanations; and
3. the structure of the lesson.

I started addressing the first two points more adequately today, but I need to pay more attention to the third. One way this came out was in my use of examples. As my colleague teacher pointed out to me, we should use examples and explanations to 'scaffold' the students understanding: we explain a concept; they practice it; we extend the concept; they practice this extension... Today, I explained a concept (deriving the length of one side of a right triangle given the length of the other two sides), and then asked them to do some problems about concept that is not related (or, rather, not related in a way immediately obvious to high-school students). This resulted in a bit of confusion which I needed to resolve by explaining in a lot more detail.

Tomorrow, I'll try to focus on my structure ('scaffolding' is the key word here) and learning the students' names.

Tags: Education Teaching Practicum

Teaching; A First Reaction

Today was the first day of my first block of professional experience at a high-school in Tasmania. I'm teaching a unit on Pythagoras' Theorem (which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides usually written: a2+b2=c2) to two classes.

I introduced the topic by drawing a right triangle on the board, labelling its angles A, B, and C in ascending order, then labelling the sides a, b, and c after their opposite angle. C is obviously the right angle, and c is the hypotenuse. I then stated the proposition that: a2+b2=c2; illustrated that proposition by way of drawing a triangle abc with a square of the appropriate size on each side and proposed that we would, as a group, be proving that it is true (that it is a theorem).

I introduced the students to two different dissection proofs of Pythagoras' Theorem:

1. The first dissects two squares (a+b)2, one into a2, b2 and four triangles 0.5ab; and the other into c2 and four triangles 0.5ab. We can describe the relationship between the areas of the two squares as a2+b2+2ab = c2+2ab. The 2ab on each side cancel each other out (being trivially equal) and we are left with a2+b2=c2. Q.E.D.
2. The second proof beings with a diagram of the square c2 (drawn using four right triangles arranged within a square (a+b)2). If we draw within the c2 four right triangles arranged to leave a gap in the centre (a square of (b-a)2). These five pieces taken from c2 can be rearranged to form a2+b2. Q.E.D.

These two proofs can be seen at the Digital Mathematics Archive's page of dissection proofs of Pythagoras' Theorem. The first proof can be seen in the second diagram on that page, and the second proof is illustrated (in the same way I explained it) in the sixth diagram. Both classes managed to complete both of these proofs in just over 40 minutes, though I think that the first group may have suffered due to my nervousness.

My colleague teacher (who usually teaches these classes) gave me a lot of feedback on my performance. I managed to miss many, many, many of the little bits and pieces that keep things together:

1. introducing myself;
2. beginning with a question (to find out what they already know and get them thinking about the topic);
3. writing pertinent terms on the board (like "Pythagoras' Theorem" for example);
4. structuring the lesson into 'direction' and 'doing' blocks effectively; and
5. three pages of other bits and pieces.

Hopefully, I'll be able to resolve most of them by the end of this two week placement.

Tags: Education Teaching Practicum