The geometry of learning

One thing that education seems so big on is the notion of "planning". What tends to happen is that it is done in a decontextualised, prescription fashion with little consideration for the fact that there are real students in the class. This is not helped by teachers college templates which reduce a lesson into small chunks organised literally down to the minute. There is little room for the real life contingencies of a classroom of students. The alternative to this situation today seems to be an increase in explicitly identifying learning intentions (which teachers do according to curricula mandates) and then co-constructing the success criteria for these intentions with the students. This is a solution to the problem that in our factory model of schooling students seem to have little idea about why they are there. The idea is that if it is made explicit to students why they are there, and if they are involved in the development of identifying what will count as success of the original learning intention, better learning will occur. I have used and continue to use this method with some classes but I am far from convinced that it can harness the collective intelligence of a classroom body. It seems to be based on the individualist notion that learning is an activity that predominantly occurs within the individual brains (minds) of students. There is little sense of what Sylvia Ashton Warner referred to as the organic, conversational aspects of education. So, my concerns are as follows:

• The explicit statement of learning intentions might mean that teachers focus on achieving them rather than participating in the life of the classroom and "expanding the space of the possible" (Engaging Minds, 2nd edition)
• They feel like a glossed up return to 'behavioural outcomes' and behaviourism couched in constructivist speak.
• You can have technically brilliant learning intentions and success criteria and no real engagement in learning

The problem is that everyone knows that a good teacher has "outcomes" in mind. In that sense what I have described is a very good method to ensure that the teacher has given some thought to what they are actually trying to achieve. But the teacher giving thought to what they want to teach within the framework of learning intentions and success criteria might mean that ONLY what they intend is learnt and at the expense of far more sophisticated learning possibilities that emerge during the course of the lesson. Put more simply, I wonder if the lesson becomes goal-driven rather than possibility-for-new-ways-of-looking-at-the-world-driven. Brent Davis reminds us of the difference between prescriptive curriculum and proscriptive curriculum. A prescriptive curriculum is when what is to be learnt has already been determined. It is a representationist theory of knowledge that assumes learning is about the individual conforming to an already pregiven reality. A proscriptive theory of curriculum is one which sees education as "a participation in the ever unfolding project of becoming capable of new, perhaps as-yet unimaginable possibilities" (Engaging Minds 2nd editon). This is when education actually becomes interesting and the image of a fractal (top right) can, I think, help to serve as a metaphor for "planning".

Here are a few features of a fractal:

• You get incredible complexity from incredible simplicity in a very short time. By simply iterating lines of increasingly smaller sizes you get the image above
• Change is non-linear in that it is growth oriented rather than goal oriented. In this respect it is heavily supported by neo-darwinian theories of evolution, ecological theories of learning and recent research into how the brain works
  
• There is self-similarity across scale. This means that some smaller parts retain the same pattern as the whole

So how are these ideas useful when teachers think about planning?

Firstly, with an attitude towards what might happen in the classroom and the presentation of resources that allow for new interpretive possibilities we teachers don't need to spend hours making plans for the students to follow. Complexity will arise if we create the conditions for it. There is more to this but I'll leave it at that for now.

Secondly, if change is non-linear we simply cannot determine goals of learning. This is not to say we can't expect an inquiry or assignment to be finished at a certain time, but we can't legislate what learning will occur. Perhaps we can guess what might occur, but unless we are to treat the brain as something other than a biological organism subject to the tendencies of evolution, we cannot predetermine what is to be learnt without killing the possibility for new something new and novel being "constructed".

Third, obviously there needs to be a goal in the broad sense of something that orients and constrains. With out a really clear idea of what could happen chaos will quickly ensue. By critiquing a common method of planning I am not saying that teachers can't afford not to be prepared. They need to be highly prepared for the contingencies of what could happen and have learning activities that anticipate the needs of the classroom culture.

Some ideas about integrating

We are currently in the stage of preparing for next year's first topic on "food". On its own such a suggestion is merely a context which could quickly descend into what Beane refers to as multidisciplinary integration. But we may have found a way to make it a source of some really critical and creative thinking that doesn't lead teachers to fear about "what they'll teach" on the first day if they are to totally leave it to the students. What we are going to do, and especially me as the Social Studies teacher, is spend 2-3 weeks making "food" problematic. I need to keep probing students so they can make a tentative response to the question "why would we want to learn about food?" or "Why is it socially significant?". I intend to collect some materials that might disrupt or "perturb" their thinking; I need to try and make what is familiar strange, with the explicit purpose behind it all of giving them ideas to launch their own inquiry. Some ideas of what I could use to do this:

• Howard Kunstler's stuff on the importance of living locally

• Morgan Spurlock's Macdonalds documentary

• A guest speaker such as someone from the green party talking about GE

• Some readings/data of world poverty, the food crisis

• Some excerpts from the book "The ethics of what we eat"

Perhaps the first homework session is to have students talk to their parents and grandparents about why you might learn about food and they write ideas on some pieces of paper which go up onto a "problem wall".

What is going to make this successful is the cooperation we have among the four core teachers. Once we have given them some ideas about why you might study food we will create "inquiry" slots in the timetable where they can work on it. This is where we have struggled so far this year though. An inquiry is quite tiring and we all worry that the students might not cover the areas we are required to teach. We hope to get around this by having timetabled "skills" or "new ideas" sessions. For example, the maths teacher might say to the class "today (or this week) I am going to teach you 3 different ways to do a graph". Or they might respond to their own observations, (or even better the students' request) with a more teacher led lesson. The students would then be encouraged, with that new knowledge, to think about how they could potentially use that in their inquiry. They don't have to though. As a social studies teacher I might take a concept or theory from an Achievement Objective, perhaps something like globalisation and introduce this as a useful concept to be applied, if it works within the context of a specific inquiry. The point is that we are feeding them new ideas in order to deepen their inquiry.

The overall intent of this particular unit of work is that they they have to curate an exhibition using the model of a science fair. Invites are sent to their parents and they can come in for an hour and eat organic nibbles after school and see what their kids have produced. This is a positive form of extrinsic motivation. Someone would need to design the invitation, we would need to think about what the exhibition is called, we would need to go to an exhibition and think about what makes a good one, how does text flow with images and with an artifact.... This could all be done in the "new ideas" sessions and could involve some great collaboration with the English and Social Studies teacher.

Curriculum integration versus Multidisciplinary "integration"

Our experiment with trying to integrate the four core subjects around a common theme has started to become more and more interesting as more teachers are about to get involved in 2009. I am not convinced many teachers, myself included, fully appreciate the radical changes required for what James A Beane calls "curriculum integration". It is quite different from teachers selecting themes and making sure any overlaps that could occur between what happens, do actually occur. Student-centred curriculum integration according to Beane is much more than this which he refers to as "multi-disciplinary education" with no real democratic mandate. What is required instead is for teachers to help students generate genuine problems and then have students explore these. The subject teachers provide expertise when asked and when it is required or arrange the expertise from the community. There are a whole lot of practical issues at stake here. But here is an illustration of what I think it could mean.

Recently a teacher started teaching a unit on world religions. There was considerable fuss from some students about this because they were anti religion and didn't want it "forced down their throat". In a teacher-centred approach, the problem is one of behaviour management. Kids need to sit down and listen to what we have to say about world religions. In a student-centred approach the real life issues and beliefs the students have about religion are your first resource.
There is a lot of talk about "diagnostic assessment" in order to gather "base line data" about what students already know, as if knowledge is somehow a static thing which needs to be lifted from their individual brain. Personally I have done a lot of this without really knowing why and have never looked at it again.

For this religion topic each group was given a large piece of paper with some questions such as "Religion should be taught at this school", "religion should not be taught at this school", "what does Sept 11 have to do with religion", "what are some world problems associated with religion" "what benefits does religion offer to the world". Each kid had a vivid and responded and the paper was passed around until each group had their paper back with everyone's comments. A student centred approach suddenly makes this diagnostic assessment critical to what happens next. A teacher centred approach would not have done this and would have answered a whole lot of unasked questions. As Karl Popper says, "Never answer unasked questions!!" The responses from students were of course extremely interesting unlike much diagnostic testing which is very boring.

The problem here though is what next? I am still working this one out. Students don't know what they don't know. I think they need a few things thrown at them before choosing a problem which they inquire into. For example, they could be given some accounts of some controversial religious issues such as the Danish cartoons, the Sudanese teddy bear named Muhammed or the issues of banning headscarfs and Christian scarfs in schools. The teacher needs to listen to see what happens. Perhaps next they could be introduced to Dawkins and atheism, since many are so concerned about it. We have a staff member who is happy to come and talk to them about atheism and religion. The difficulty is when to stop introducing them, perturbing them, shaking them up a bit and let them actually start inquiring into a problem with an authentic outcome.

When they have enough ideas to explore something it starts to get exciting. I love the idea of the extreme atheist who made a comment about the "pathetic" denial of evolution investigating evolution, creationism and intelligient design. There were some students who were very insightful about the discrimation many Muslims suffered after the Sept 11 attacks. They could go to the local Mosque and interview them down there, see if it is still hapeening in NZ and write up the results in an article. Of course the major difficulty is the timetable which operates in 1 hour blocks but this is being changed for our school next year.

Perhaps the journalism teacher, also their dean, could help with producing a class magazine with all their articles. These are only some ideas but this is when education becomes exciting. We lecture when the students ask for it, which they will. We teach skills when they stumble, which they will. We discovered that even the most able students found something as easy as summarising the class' responses to a key question extremely difficult. That's when you have a lesson of how to summarise information and discuss why this might be a useful skill.

James A Beane is right though. Simply encouraging overlaps between the material that teachers "cover" is hardly going to change much.

Integrating subjects

Although I don't like the idea of any kind of universal theory or method working for all people at all times I think these are four good steps for how to integrate in a way that is authentic and useful and helps to break down the barriers that education erects between different disciplines or subjects.

1) Develop a real world question with students
2) Make sure everyone, teachers and students, understand how the core subjects can contribute to a sophisticated exploration of this question
3) In class learn the skills and knowledge that each subject can offer in regards to the main question
4) Provide an opportunity for students to use this new learning to explore the question in new and creative ways.