"a dialogue with students which involves meta cognition (thinking about their own thinking) and meta-conceptions (students thinking about their own knowledge and understanding of concepts)"earlier posts:
meta-dialogues are hard to establish
initiating a meta-dialogue
fractions in real life
My quest for meta-dialogue in teaching fractions has merged with the broader issue of redefining power relationships between myself as teacher and my students. This is as it must be in the modern world, where the "cool" thing to say is "school sux" and "maths is boring". Not only students say this, School (and teachers) have many critics.
Students are going to be reluctant about revealing what they know and especially what they don't know about fractions, or anything else, unless they feel some sense of personal ownership of the physical and psychological space - including the meanings that are transacted, the humour, encouragement for speaking your thoughts etc. What is the word for this overall environment? I'm not sure - trust, empowerment, rapport, engagement? Whatever you call it, it is the secret ingredient (xxx) to the successful classroom / teacher. If it is present you can feel it shortly after entering the room.
And that ingredient (xxx) is (initially) built through wide ranging negotiations that recognise (some, not all) student rights and are perceived to be fair and reasonable. I say some student rights because the teacher retains overall responsibility for educational goals.
It works much better in a primary or middle school environment where the teacher has the same group of students for multiple lessons. In my case it's a year 8 group for homegroup, maths and science. Increasing of contact time is one essential factor for improving teacher-student relationships.
What NOT to do:
Don't stay in the regular routine of teacher out the front lecturing and setting exercises through a textbook. But it remains OK to do this sometimes, particularly in the early stages of getting to know a group. I'm not arguing for complete negation of traditional methods
Retain some traditional control:
As a teacher of maths and science I have my own agenda. I am not aiming for student empowerment in some generalised sense based on their current understanding of the world. My goal is to engage students deeply in maths and science activities and learning, which I see as important for them.
Sometimes I do find it necessary to being strict and insisting that students stay "on task". I also think that students sometimes use "fun" as a means of avoiding things they don't understand and at their current stage don't see much point in learning. For example, recently I was doing a more or less traditional sort of lesson about converting improper fractions to mixed numbers and there was all sorts of avoidance through fun happening in the room. When I got strict about it I found that only 2 students in the class knew how to do it. Since I have my own agenda and beliefs (that fraction knowledge is important) I insisted in authoritarian fashion that we deal with it.
What student's have pushed for, at this stage:
Student's asked me if they could go outside and I agreed but before we go out I negotiate with them an educational activity that we can do outside. Everyone has to agree, otherwise we don't go out.
The first time we went out, each student had to find a "real life fraction" outside (fractions in real life). After that I promised the class I would take them outside at least once a week. The second time we did a penalty shootout competition where each student had to measure their best effort. The going outside activities have been very successful in terms transforming the class attitude to maths. "Maths can be fun".
The most difficult issue for me has been some students saying they have become sick of using Scratch. I realise now that I pushed it too hard and in a didactic fashion at the start, rather than letting them discover and explore it more in combination with other software. (which is what I would do if I had my time over again). So, at this stage I have backed off a little on Scratch use and we are exploring other software as well. This is not something I really want to do from an educational perspective (so I haven't stopped using Scratch altogether) but something I feel I have to do since the reaction against Scratch use has been strong and persistent.
New, different things I have encouraged:
I have continually invited students to come out the front, borrow my markers and write exemplars or answers to questions on the white board. eg. "Who can write an improper fraction on the board?" I push those who haven't written much on the board to have a go.
I have asked my students to teach fractions to students from another class. Initially, they only had to administer a pre-test but then step by step I ask them to take more responsibility. They are now at the stage of writing their own fraction questions and programming them in Scratch.
At first students liked the idea of administering a test to other students but as I asked them to do more teaching there was some resistance. We discussed this. The best I could do was to explain my position that I felt being a teacher was one of the best ways of learning. Some students still don't like the responsibility so the acceptance is grudging. Nevertheless, I recently noticed some stats on this about which methods promote understanding, quoted in a comment by Tortuga on OLPC news:
By compiling various research sources a breakdown was arrived at that looks like this: Lecture (5%); Reading (10%); Audio Visual (20%); Demonstration (30%); Discussion group (50%); Practice by doing (75%) and Teaching others (90%). This reinforces the concept that students need to be turned into teachers.Another thing I have done a little of and which I might do more of is change the seating arrangements around, eg. put the table in a square with everyone facing inwards for a good group discussion environment.
It's a complex dance of when and over what issues to concede teacher power and when to exert teacher power in striving to develop students to become more engaged and deeply involved in maths learning.