Thursday, July 21, 2011

Games in mathematics

Developing strategic thinking in students is an emerging issue.  Living in a world of instant gratification, the ability to think is less prevalent in classes today.  The need for general knowledge seemingly has passed and rote learning tasks have been removed from WA curriculum.  There is little need to compete as everyone has access to the same information, gathered by Google, edited by Wikipedia.

In comes boardgames.  To play a boardgame a player needs to learn the rules and then work within the rules to seek advantage over competing players.  There is no prize other than the pleasure of learning and succeeding.  To succeed players must learn to strategise.

More than a few think I'm a more than bit nutty about games.  What I have found is that to engage students requires a wide variety of games and getting them to the point where they can open a box, read the rules and immerse themselves in a game is equivalent to the difficulty of getting a student to enjoy reading.  Similar to reading, success is based upon finding a related context.  Simpler gateway games can lead students to a love of thinking, not just success and winning.

To aid this below is my list of games that have been used successfully:

Gateway games
Pitchcar (7 players, <30 mins) 
Citadels (7 players, <30 mins)
7 Wonders (7 players, <30 mins)
Claustrophobia (2 players, <1hr)

Say Anything (5 players, <1 hr)
Apples to Apples (8 players, <1 hr)
Nuclear War (4 players, <1 hr)
Dixit (5 players, <1hr)
Lupus in Tabula (10 players, <1hr)
Carcassonne (4 players, <1 hr)
Ticket to ride, Europe (5 players, 1 hr)
Illuminati (7 players, 1+ hours)
Munchkin (7 players, <1 hr) 

Strategy Games
Through the ages (5 players, 3 hours) 
Indonesia (5 players, 3 hours)
Battlelore (2 players, <1 hr)
Space Hulk (2 players, <1.5hr)

Games currently under evaluation
Troyes (5 players, <1 hr)

Many games have been evaluated in establishing this list.  There are game links on the right hand side to help find and investigate these games further.


Tuesday, July 19, 2011

Professional Development

Any long time reader knows that I am a big critic of scheduled professional development days..  Most tend to be filled with administrative tasks and very little professional development is actually done.  Well, here I am now having to deliver a session to the local primary schools and I sit in the position of many presenters of not knowing what is expected by the primary teachers and having little time available to prepare a presentation of worth.

It's not that being asked to do it is a bad thing.  I am really looking forward to it.  My concern is that I could lose an opportunity to do it regularly by not being adequately prepared.  It's a bit of a fishing expedition as to how to create a closer relationship with the local primary schools.

On paper it should not be too hard.  Three of the five members of our maths department grew up in the area and two of them went to our school.  We relate to our kids.  The student profiles of our schools are very similar.  The results of both our schools are above like-schools in numeracy.  We both cater to the far ends of the student spectrum and have issues in the middle/bottom quadrant....  and we've taught much of the material now being pushed into primary.

I keep telling myself that it's only an hour.  It's an hour that could attract some of their top end to our school and give us an opportunity to do some extension work in primary.     I haven't done any adult training in the last five years other than practicum students and it's a little nerve wracking..   I hope at least some of the primary teachers are not as burned out with bad PD as I am and will see my ideas as worthy of consideration.

We'll wait and see.

Proofs in the classroom

Many of us have bad memories about proofs in the classroom and learned to switch off whenever they arrived.  After all, they were never assessed and the skill required always followed shortly after.   In texts today, the proofs are often missing and skills are instantly presented as the required content.

When writing assessment I tend to struggle with testing deep understanding vs trying to trick students into making mistakes.  I've read many external tests and they mainly use methods aimed at testing minute bits of content, "corners" of content areas rather than whether a topic is understood.  The wide splash of content that we are required to teach lends itself well to this method of assessment and it is quite easy to get a bell curve from it.

This is great for students that study hard and do lots of different types of questions.  It must be incredibly frustrating for naturally gifted mathematics students, the ones that enjoy delving into a new topic. I think this is where proofs need a more detailed treatment and where investigations in lower school can be repurposed.

The opportunity for delving into a topic is there for the picking.  Proofs for completing the square and Pythagoras' theorem are great ways of developing connections between geometric proofs and skills taught in classroom.  Developing conjectures about number patterns develops the idea of left hand side/right hand side of an equation and the setting up equations to solve problems.  Congruence, traversals of parallel lines and similarity are other topics that lend themselves well.

Having only taught upper school for awhile, it is interesting to see where the core ideas of geometric proof, exhaustion, counterexample, formal proof/conjecture/hypothesis and even induction can be introduced before year 11.  If 2C students can learn the idea of all but induction, there is little reason why we can't teach reasoning a little earlier.

Perhaps if they could reason more effectively they could then challenge their own results and complete investigations that developed into lasting learning events.

Saturday, July 9, 2011

Last day of term

The last day of term was a lot of fun.  The praccies wound up their classes and went off into the wide world.  Students went off for break... .. and a long two terms finished on programme with tasks completed.  All good so far.

We were very lucky this time with two great practicum students in Math, both very different and bringing something special to the profession. I said to mine about half way through prac to name ten things that she did better than me.  She never came back to me with that list but here is what I came up with.

She has strong organisational skills
She creates a fantastic working rapport with students
Each task is well monitored for progress (macro)
She reflects diligently on each lesson
She actively seeks to monitor the progress of each student (micro)
Colleagues enjoy interacting and assisting her with issues she has identified
She thoughtful and caring
She is fun to work with
She is prepared and willing to take risks to promote learning
She has a great and appropriate sense of humour

As you get further into teaching, sometimes it gets harder to maintain these things..  It can be great to look back and see how bright and bushy tailed you were when you started.  When times get tougher, you can reflect upon areas to focus upon to regain that initial vigor.  Be confident and know that those awful teenage years finish, slowly you gain confidence and independence... things improve as you go through your twenties and thirties (I can't speak for the forties!).

After talking with the maths department, I won the praccie competition this term.

Well done you two..  We look forward to hearing about your progress.


Monday, July 4, 2011

Developing educators

I've thought for a long time that we fail to appreciate that there are a range of teachers required in education as different teaching styles benefit different students.  Our teaching practicum system has a tendency to promote outgoing, gregarious teachers and discourage practicum teachers that are not.  This is a real shame as those that take time to build their skills and have a calling to teaching may need more help to get over that initial hurdle of conquering teaching practices and behaviour management but then excel in creating engaging, caring and developmentally appropriate learning environments.

I was once told that I had a lifetime of occupations crammed into my twenties, but even with this I barely made it through my ATP.   My final practicum was a train wreck (my only pass grade of my degree) but does this define me as a bad teacher five years later?  Well.. I'm still here and still improving my teaching.  I'm no teacher of the year but my classes are well defined, my students are achieving and as a team we are moving forward.  My growth from that point on ATP has been linear and I expect that to continue.

Sometimes I have to remind myself that the best teachers are not necessarily those that found things easy, but those that really had to deconstruct a problem, seek to understand it deeply and then work with others to find a solution.  This creates an understanding of the difficulty of capturing the nature of the learning problem.  It's hard to get this point across to practicum teachers as many come in expecting it to be as easy as we sometimes make it look, not realising that getting kids to the point where they engage fully may have taken a term (or in some cases a few years) of hard work, organising resources has taken hours of planning and that skills and knowledge used in the classroom took years of experimenting until things came together.  Reflection is a key component in this growth.

The first five years in teaching for me wasn't easy, but after the first couple of years, with good support it certainly is becoming easier.  It's one reason why I say seniority has its place.  You don't survive as a classroom teacher unless you can handle the pressure most of the time and have management structures to relieve the pressure for the remainder of the time.  Without a hierarchy of some nature, we can't give teachers time to grow, nurturing them in soft classes, mentoring them through difficulties without fear and then developing them into true educators.

Perhaps after a few more practicum students I'll think this is a load of drivel and that the system is right..  but I hope not.  I'd like to say that we can develop a system where students, teachers and administrators see teacher diversity as a key goal within the system.


Saying what we would like to say.. Even if it is a little exaggerated.

Sunday, July 3, 2011

My interactive whiteboard

The school has recently sprung for an interactive whiteboard for my classroom.  A Promethean 2.1m wide board.  We purchased it from Concept AV, who have successfully added themselves to my list of inept IT organisations.  At this stage, I can't recommend them.  In fact I probably can't recommend getting far enough away from them.. but that is my general comment about all IT people. 

To start with they didn't return calls.  We called them and said we had a budget, how much and when can you install.  "We'll get our sales team to call you."  Four calls later someone responds.  The salesperson comes and we explain where we want the points and where the board is to go.

Two guys turn up and it's a bit of a Laurel and Hardy show.  I'm not getting involved, I point them at the room and go to lunch.  I have no idea how they managed to get it up the stairs in one piece.  It's delivered but not installed.

We say to them, install on any day but x, because on that day we are having exams.  "Sure," they say, "We'll be there on day Y."  I move shelving (and 300 or so books and files) and move all my classes for the room to be free on day Y, lugging 30 texts from one room to the next.  Needless to say, no-one showed.

The next day we call them and find out that they are now coming on a new day.  No prizes for guessing which one - yep.. on our exam day.  After some gentle persuasion they say they'll come on another day.

On the new day, the installer turns up and insists that the point needs to go directly beneath the board (as opposed to the position discussed with the salesperson) and that it will cost extra to put it near the computer that will run the board.  "But that's ok, you can just run a cable around the edge of the room."  No it's not ok, the idea is that it is tidy and has as few visible cables as possible.  A workaround is devised using a double adaptor, more cost and some extra ducting.

I sit down to read the manuals supplied to learn how to use the board.  The aspect ratio isn't set correctly for my laptop and sound isn't working.   RTFM Russ..  but that's right, I can't.. they haven't left them or any other documentation on how to use it - all they have left is a software CD, some cables that won't work with my mac, the projector manual and its remote.  Rummage around on the web, locate the amplifier button (which is wedged against the shelving in a place I can't see without a mirror) and then play with the projector remote to fix the aspect ratio.  Installer says can't use USB for audio with mac.  BS, it does if set correctly and the amplifier is ON.  Go to the shops and buy the mac adaptor for video.  A whole heap of frustration that could have been avoided and prevented hours of fiddling and searching.

Two days later I inspect the setup and realise that there is no RCA adaptor for external video such as used by DVD players or games consoles despite the panel being designed to be used in this way.  "Why only a monitor port when the projector supports a range of outputs?" I ask the installer, "That's the way we do it in all schools".  Can I respectfully suggest it's a bloody stupid way.  So now I have to get up onto the projector, standing on a chair on a desk and run a cable down to the amplifier and the console for our Singstar competition at the end of the term.

In his technical wisdom he suggested using an analogue to digital converter and run the signal along the monitor cable.  Oh yes, and I used the last one I had of those just lying around yesterday nor does the Dick Smith shop around the corner have one.  I wasted another hour checking.

Next, I found that working on the laptop could be a pain especially when the laptop locked and required a password.  As my computer faces the room I needed a fliptop head to put the password in.  Solution: buy a wireless keyboard, $79.

Next challenge.  How to use the board effectively.  It's dropping some of my writing due to lag (it wasn't before, I don't know what's changed, my new mac pro seems fine), so I suppose I'll have to figure out what is causing that too.

So, tips for those getting an interactive whiteboard working.

a) find an organisation that returns calls
b) be very clear about where you want your computer and the connection point to go and request to get it installed there
c) ensure that they install it where your want it
d) ensure you have all the cabling you need to make it work
e) find someone that knows about the board and get them to show you how it works
f) get an RCA cable run from the connection point to the projector and the amplifier on the whiteboard
g) get a wireless keyboard (the apple one is great)

It just reminds me that getting IT implemented so that it works is not a simple task and requires someone with IT skills to be working on both sides of the equation - someone knowledgeable is required on both the buyer and sellers side to get an effective solution.

Saturday, July 2, 2011

State of mathematics education

Interesting article on the state of mathematics education in the SMH.