Open learning targets

Click to get math mind maps from The PiFactory

The PiFactory’s student-friendly math learning targets, from the TARGETmath database, are now online as the project slowly moves towards going open source.

The several hundred learning targets, covering pre-algebra to advanced algebra, can be searched here. Many of the targets are also grouped by learning unit.

All the targets are written in the form I can…

For teachers the targets make up a handy To-Do list of stuff to be covered. For students they summarize what needs to be learned. The order of the targets roughly reflects what a student needs to understand before they can move on to later targets.

In the TARGETmath database the learning targets are at the core of a system that links nearly 2,000 questions + notes, builds assignments and gives descriptive feedback and revision advice to students. TARGETmath can be downloaded for macs.

Mindmaps, or concept maps, for many groups of targets are also available from The Pifactory to complement the targets. There’s a thumbnail of the logarithm mindmap at the top of this page.

It is expected that the textbook notes attached to the targets will be available online soon, followed by linked questions.

No prizes in points

WHEN I was training to be a math teacher in Britain some years ago there was a popular satirical BBC radio program called I’m sorry I haven’t a clue, presented by legendary jazz trumpeter Humphrey Lyttelton.

Humph arbitrarily awarded points for no apparent reason. The rules of the games were far from clear.

And although the audience shouted “points mean prizes…” on cue, no one ever knew what the prizes were. The only real prize for all concerned being an addictive dose of hilarious nonsense that was also a biting weekly commentary on current events.

Reflecting on the issue of grading, I’m reminded of this farce.

Three years ago I decided to completely abandon all grading based on points, marks, percentages or letters. The only numbers in my classroom would be in the math my students and I were working on, and not in any assessment. I felt naked.

But since then, this simple decision has lead me radically to re-assess everything that goes on in our classroom — from testing, homework policies, seating plans, late work, make-up work, behavior management to the really important question… the very essence of what it is my students and I are trying to achieve in our thinking laboratory.

Now my assessment focuses on observation, listening, discussion, collaboration and increasingly on students’ own assessment of progress. I hope the result is a focus on what we’re trying to think about in the classroom, free of the diversion of worrying about some ill-defined percentage.

The prize is the achievement of just trying to get it.

Feedback is verbal and descriptive, striving to help the student find some way of constructing their own meaning and paths to mathematical thinking.

I changed career to be a math teacher at the age of 50. UK educationists were encouraging new math teachers to abandon the traditional mark-book full of numbers. Numbers have no place in assessment and feedback in the math classroom was the argument.

It was summed up: Students who get nines and tens out of ten, nearly always get nines and tens. It may make them — and their parents — happy, but the points don’t motivate them to seek out new challenges or how to improve. They coast, complacently.

Those who get sevens or sixes… well, they’re passing. They just need to survive the you-could-try-harder talk. But how to try harder? To do what, exactly?

Those with the fives, fours, threes… confused, disappointed, frightened, feeling an inexplicable shame, they give up and cover-up as best they can. I was given a class into which such kids had been herded: “Hi,” they said, “we’re the dumb class.” I felt ashamed.

Numbers in assessment de-motivate, set student against student and encourage assessment as a process of ranking and sorting.

Adding some words of encouragement to the numbers also seems to make little difference. Students still focus on the numbers, despite their lack of any real meaning. Changing the numbers to letter-grades, doesn’t shift the focus to learning either.

Only when you take away the numbers, and letter grades, and replace them with phrases such as, “well done, now you need to work on… the distributive property” does motivation get turned round.

A target, a goal, something to focus on finally clears the clouds of confusion for the student. Now the student can see just what to do to improve. With student self-esteem no longer punctured by the stark moral judgement of a number or letter dripping with blood-red ink, students are free to focus on what they need to do to improve… and work cooperatively together to collaborate and help each other.