Now don't get me wrong, I try to remedy this, and (I hope) I'm improving my teaching towards this end all the time. I don't just tell pupils about mean, median and mode and expect them to remember. I give them problems like this one, that lend themselves to the different averages and play around with the numbers. We create a need for more than one average. I love the WCYDWT model for its multiple entry points, which is a neat way to give interesting problems to people not in the top set. However, I have never felt that I can stray too far from the standard teaching model or the standard curriculum. Why? Well this is what the school, my head of department, parents and pupils expect from me. They want 'exam readiness', they want regular standardised tests, etc. Maybe I just feel insecure as a first-year teacher, but I honestly don't think I could keep my job if I tried to teach maths differently. In fact, I've never been in a school that I think would employ a teacher like this.
All this when so much in my school is ripe for this style. For one, this is the first school I've been to where the maths teachers actually enjoy doing maths. We regularly have discussions about UKMT maths challenge questions, project euler, or interesting textbook questions (yes they do exist, though you have to do the further maths A level to get to them). We have books like 'What is mathematics' lying around that are actually read. Also, our pupils are bright and I mean really bright. Their grasp of language alone is so good that most can make fairly convincing arguments in their first year.
So here are the questions that will be going round in my head for God knows how long:
- Will I ever be able to teach my pupils in this way, without meaningless definitions and magic formulas? How?
- How can I convince others that this is a good idea?
- How can I become good at it without really being able to practice and have no other experience than reading about it online?
* Will I ever be able to teach my pupils in this way, without meaningless definitions and magic formulas? How?
ReplyDeleteTeaching it? Maybe not, to begin with.
Using it? I'm sure you can. Maybe do 'Applications of...' lessons after teaching specific units, if you get the chance? It gives you the opportunity to outline the enjoyment of maths rather than just the necessity.
* How can I convince others that this is a good idea?
Ask a colleague to critique a lesson that you've planned? Ask them if they think it's a good idea, and ask them if they would like to share the resource/idea if they show an interest?
* How can I become good at it without really being able to practice and have no other experience than reading about it online?
With the 'Applications of...' lessons, you'll be able to get practice, and slowly build a resource bank too.
Eventually, after introducing it gradually, more kids might respond to it, and maybe you'll be able to teach lessons like it, rather than facilitate pupils applying their knowledge.
Really tough questions here, Phil. For me, before I could teach math via inquiry, I had to practice learning math via inquiry, which meant developing and solving problems for myself (often the kind of posts you'll find under the WCYDWT heading). I did that and I noticed the procedures and questions I encountered en route to a solution. Slowly I was able to invoke those same procedures and questions with my students in class. Good luck!
ReplyDeleteThanks for the comments guys.
ReplyDeleteMr Taylor said:
Ask a colleague to critique a lesson that you've planned?
I do try to use the occasional inquiry style lesson, but I always do it covertly. My department wants straight-forward lessons that they know will produce results come exam time, so I don't feel like I can share these ideas with other staff.
I also have trouble convincing the pupils that these kind of lessons are a good idea. They are not used to it. They all want more structure and are completely uncomfortable dealing with uncertainty. I'm hoping that this will change as I become better at selling the question and they become more used to the style.
Dan Meyer said...
For me, before I could teach math via inquiry, I had to practice learning math via inquiry, which meant developing and solving problems for myself (often the kind of posts you'll find under the WCYDWT heading).
Hmm, maybe coming across your blog and the edublog community as a whole has been a mixed blessing then. The ideas and discussions going on there have given me a passion for improvement and an idea of the kind of teacher I want to be. On the other hand it could be that fast-tracking the initial process of creating my own wcydwt problems by using other peoples' means that I'm skipping an important part of the process.
I definitely learn a lot from my inquiry lessons (particularly when they fail), and I'm not ready to give up on them. I'm just struggling at the moment to see how they fit into the school system I am in.