At play in mathland

I recently started a separate blog At Play in Mathland to store and share maths problems I like.

Mathland is like Homer Simpson's Land of Chocolate - except with maths.

In words of Seymour Papert, "If we all learned mathematics in math land, we would all learn mathematics perfectly well".

With apologies to Matt Groening.

SBAR with light bulbs and spanners

So how has my experiment with Standards Based Assessment and Reporting been going? Here is the first in a series of reflections.

Half way into my first year using outcomes sheets with my students as the basis for Standards Based Assessment and Reporting, I realised the outcome lists I was making every few weeks were really just a list of skills I expected students to master. When the penny finally dropped that skills were only one part of Working Mathematically, I realised my outcomes sheets had to change.

Here is my first attempt to be different - which I've been doing now with my outcomes sheets for a few months:

Click on the image for a full sized image.

The key idea is to separate outcomes into the categories of the Working Mathematically proficiencies:

A light bulb icon indicates an outcome that requires some new understanding of an important idea.


A spanner icon indicates a skill to be acquired - 'fluency' in the Australian Curriculum description.

A balance scale indicates that a reasoning process is being used.

How has using light bulbs and spanners changed teaching and learning in my classroom?

• Clearly showing the understanding and reasoning outcomes forces me to focus on these important elements. If I find my outcomes sheet for a new topic is full of spanners and no light bulbs or balance scales, I know I've made an unbalanced teaching sequence.
• It sends a clear message to the students that understanding and reasoning are important - it's not enough to just be able to mechanically follow a process to get an answer to an exercise. I will be expecting them to be able to explain and reason.
• Any time during a lesson when I'm about to introduce or consolidate the development of an understanding outcome, I stop for a moment, and point to it on the outcomes sheet, making it very clear to students were are working on a "light bulb" outcome. I emphasise this means it's a time for quality intellectual engagement: thinking, listening and asking questions. While we can get the idea behind a skill outcome by reading a text book, or perhaps watching Salman Khan do it on YouTube, the understanding outcomes are much better learnt interacting with peers and the teacher.

Where is Problem Solving?
The big challenge I'm facing now is how to integrate the problem solving proficiency into a set of outcomes related to a content heavy topic.  What this really reflects is the fact that real problem solving (beyond just "harder skills questions") aren't yet integrated into my content heavy program. For now, I'm experimenting with specific Problem Solving lessons which stand outside the regular content sequence - and that's something I'm going to work on in 2012.

You may notice the outcome sheet above doesn't make provision for recording quiz results - which you would normally see on my sheets. That's because for this course I'm actually not permitted to use SBG, but have to follow a statewide assessment method and schedule. But this doesn't stop me using the idea of standards, or using them for formative assessment. More on this in the next few posts.

In my toolkit: JFileSync

Been a while between posts - school year is getting very busy and as usual I'm trying to do too many things. 

The problem: I have three Windows computers I use all the time, in conjunction with an array of USB portable disk drives. I want to be able to use which ever computer or disk drive I have at the time, while keeping everything in sync. To make thing harder, I don't have admin rights to some of those computers (read: school issued laptop *).

The solution. A free open-source Java application called JFileSync.

Some tips to make the data management painless:

• Nominate a portable USB disk drive as your master data repository. Give it a name - this gives it a distinct identity, helping you form a mental image of the data store as a distinct entity. I call mine 'wombat' - and I have stuck a label on it.
• Carry your portable USB disk drive in a protective case. They are robust, but still vulnerable.
• Don't use a USB memory stick as your master data store - while they are convenient, they are also fragile. I have seen several teachers lose their entire collection of vital documents when their USB memory stick died. Just too fragile - a zap and they are dead.
• Any time I sit in front of a computer, I plug in that drive and immediately run JFileSynch to resynch that computer to the current state of my USB disk drive.
• I work on the computer's local drive.
• When I'm about to leave that computer, I run JFileSyn again to get my USB disk drive up to date.

If I don't have my USB disk drive on me, or I forget the ocassional JFileSync, it's usually fine to just resynch the next time - JFileSync will 'do the right thing'. The only challenge is if I edit the same file on another device - because JFileSynch will not merge files - and then you have to think. Best not to do that.

I've been using JFileSync now for three years and couldn't recommend it highly enough. And as a side benefit, I have four copies of my data in several locations. If worst comes to worst, there should always be a place I can recover my data (barring an asteroid strike on Sydney - in which case I'm dead anyway).

* If you have a NSW DEC laptop: JFileSync is a java app - so you can just put the Java file somewhere on your laptop and run it any time - no install required.