The Unit Programming BluesEvery time the holidays come round, I aim to sit down and write some units of work for the coming term. However, what invariably happens is I spend the first couple of hours banging my head off of the various piles of resources, faculty programs, syllabus documents and jotted-on bits of scrap paper. Then I go and whinge to my wife (poor love) about how I have no idea where to start. I'll then find my muse and spend another couple of hours writing notes about all the things I'd like to do in a particular topic only to find that I've spent all of my lesson time pontificating rather than actually coming up with decent learning activities for the students!
The next couple of days are spent cruising the web looking for "The Idiot's Guide to Planning a Unit of Work in Mathematics!"
I could give up and spend the remainder of the holidays doing something productive (there are any number of jobs around the house and garden), but I know that when I start back next term, I'll default to the easy option (notes, exercise, book-marking) and yet again, end up profoundly dissatisfied with my teaching and the students' learning (or lack of).
We must learn Mathematics because...? Just because!I think the major problem I have is that I don't have any faith in the "traditional" teaching format. My programs basically follow the typical (in my experience) format of "Whole number/ Patterns and algebra/ Perimeter and area/ etc." Most of the programs I've seen basically copy the syllabus document or reword it and I find it very difficult to get out of that mindset. Each topic is treated as a separate entity with a list of associated skills, knowledge and understandings. They may form an integral part of a larger whole but each is treated as an academic goal in itself.
The majority of available resources also seem to reflect this at a fundamental level. They seem to have been created to teach the skill. This would be okay, but there are very few explanations as to why the skill needs to be learned. Ultimately, most resources (including the Rationale on page 13 of the new NSW K-10 Mathematics Syllabus) seem to imply that the primary reason for learning mathematics is to learn mathematics. Very few students will end up studying Mathematics as a pure science, so why do I spend so much time teaching them as though that is where they are headed?
Where is the recognition that Mathematics is actually a tool?The vast majority of mathematical endeavour is a result of humanities' need to quantify. It has developed with the need to count, to measure, to trade, to predict and to build. It can be a purely academic exercise, but for most people it isn't. It is a tool that is pulled out and used to solve problems. After a while the individual recognises (maybe with some prodding from the teacher) that they can use the same tool in different situations and so the tool can be generalised.
Problem-based learningProblem-based learning seems a much better way of teaching Mathematics. It recognises that the tool was designed to help solve a problem. Students need to be presented with problems that result in the need to develop a new or modified tool. The problems must also be sufficiently interesting that the students have the desire to want to solve the problem. If we don't present students with appropriate problems to solve then they won't appreciate the value of the tool.
It seems to me that this is the way to actually encourage a love of mathematics and an interest in seeing how it works, hopefully leading on to further interest and a career in the field.
The problem with problem-based learningHaving been to a number of conferences, I know that there are teachers programming tasks that are successful in engaging and encouraging learning amongst their students. But what do their programs and scope and sequences look like?
We've got a copy of "The Case of the Mystery Bone." I've read it a number of times but never used it because, fun though it sounds, it doesn't fit neatly into our existing programmes. There are any number of interesting problem-based resources out there (101 Questions and Mathalicious spring to mind). But how do they fit into a full program? They appear to be stand-alone lessons rather than part of a coherent whole.
My problem is that I need a fully fleshed-out model of what a problem-based program looks like. How does the effective maths teacher or faculty approach the job? I think what is needed is for interesting problems to be created and explored; and the relevant skills, knowledge and understandings to be fleshed out to make a full unit. Having addressed a number of problems, the individual skills are then cross-referenced with the idea of seeing what is still left to teach from the syllabus