Any long time reader knows that I am a big critic of scheduled professional development days.. Most tend to be filled with administrative tasks and very little professional development is actually done. Well, here I am now having to deliver a session to the local primary schools and I sit in the position of many presenters of not knowing what is expected by the primary teachers and having little time available to prepare a presentation of worth.
It's not that being asked to do it is a bad thing. I am really looking forward to it. My concern is that I could lose an opportunity to do it regularly by not being adequately prepared. It's a bit of a fishing expedition as to how to create a closer relationship with the local primary schools.
On paper it should not be too hard. Three of the five members of our maths department grew up in the area and two of them went to our school. We relate to our kids. The student profiles of our schools are very similar. The results of both our schools are above like-schools in numeracy. We both cater to the far ends of the student spectrum and have issues in the middle/bottom quadrant.... and we've taught much of the material now being pushed into primary.
I keep telling myself that it's only an hour. It's an hour that could attract some of their top end to our school and give us an opportunity to do some extension work in primary. I haven't done any adult training in the last five years other than practicum students and it's a little nerve wracking.. I hope at least some of the primary teachers are not as burned out with bad PD as I am and will see my ideas as worthy of consideration.
We'll wait and see.
Tuesday, July 19, 2011
Proofs in the classroom
Many of us have bad memories about proofs in the classroom and learned to switch off whenever they arrived. After all, they were never assessed and the skill required always followed shortly after. In texts today, the proofs are often missing and skills are instantly presented as the required content.
When writing assessment I tend to struggle with testing deep understanding vs trying to trick students into making mistakes. I've read many external tests and they mainly use methods aimed at testing minute bits of content, "corners" of content areas rather than whether a topic is understood. The wide splash of content that we are required to teach lends itself well to this method of assessment and it is quite easy to get a bell curve from it.
This is great for students that study hard and do lots of different types of questions. It must be incredibly frustrating for naturally gifted mathematics students, the ones that enjoy delving into a new topic. I think this is where proofs need a more detailed treatment and where investigations in lower school can be repurposed.
The opportunity for delving into a topic is there for the picking. Proofs for completing the square and Pythagoras' theorem are great ways of developing connections between geometric proofs and skills taught in classroom. Developing conjectures about number patterns develops the idea of left hand side/right hand side of an equation and the setting up equations to solve problems. Congruence, traversals of parallel lines and similarity are other topics that lend themselves well.
Having only taught upper school for awhile, it is interesting to see where the core ideas of geometric proof, exhaustion, counterexample, formal proof/conjecture/hypothesis and even induction can be introduced before year 11. If 2C students can learn the idea of all but induction, there is little reason why we can't teach reasoning a little earlier.
Perhaps if they could reason more effectively they could then challenge their own results and complete investigations that developed into lasting learning events.
When writing assessment I tend to struggle with testing deep understanding vs trying to trick students into making mistakes. I've read many external tests and they mainly use methods aimed at testing minute bits of content, "corners" of content areas rather than whether a topic is understood. The wide splash of content that we are required to teach lends itself well to this method of assessment and it is quite easy to get a bell curve from it.
This is great for students that study hard and do lots of different types of questions. It must be incredibly frustrating for naturally gifted mathematics students, the ones that enjoy delving into a new topic. I think this is where proofs need a more detailed treatment and where investigations in lower school can be repurposed.
The opportunity for delving into a topic is there for the picking. Proofs for completing the square and Pythagoras' theorem are great ways of developing connections between geometric proofs and skills taught in classroom. Developing conjectures about number patterns develops the idea of left hand side/right hand side of an equation and the setting up equations to solve problems. Congruence, traversals of parallel lines and similarity are other topics that lend themselves well.
Having only taught upper school for awhile, it is interesting to see where the core ideas of geometric proof, exhaustion, counterexample, formal proof/conjecture/hypothesis and even induction can be introduced before year 11. If 2C students can learn the idea of all but induction, there is little reason why we can't teach reasoning a little earlier.
Perhaps if they could reason more effectively they could then challenge their own results and complete investigations that developed into lasting learning events.
Labels:
daily reflection
Saturday, July 9, 2011
Last day of term
The last day of term was a lot of fun. The praccies wound up their classes and went off into the wide world. Students went off for break... .. and a long two terms finished on programme with tasks completed. All good so far.
We were very lucky this time with two great practicum students in Math, both very different and bringing something special to the profession. I said to mine about half way through prac to name ten things that she did better than me. She never came back to me with that list but here is what I came up with.
She has strong organisational skills
She creates a fantastic working rapport with students
Each task is well monitored for progress (macro)
She reflects diligently on each lesson
She actively seeks to monitor the progress of each student (micro)
Colleagues enjoy interacting and assisting her with issues she has identified
She thoughtful and caring
She is fun to work with
She is prepared and willing to take risks to promote learning
She has a great and appropriate sense of humour
As you get further into teaching, sometimes it gets harder to maintain these things.. It can be great to look back and see how bright and bushy tailed you were when you started. When times get tougher, you can reflect upon areas to focus upon to regain that initial vigor. Be confident and know that those awful teenage years finish, slowly you gain confidence and independence... things improve as you go through your twenties and thirties (I can't speak for the forties!).
After talking with the maths department, I won the praccie competition this term.
Well done you two.. We look forward to hearing about your progress.
Russell.
We were very lucky this time with two great practicum students in Math, both very different and bringing something special to the profession. I said to mine about half way through prac to name ten things that she did better than me. She never came back to me with that list but here is what I came up with.
She has strong organisational skills
She creates a fantastic working rapport with students
Each task is well monitored for progress (macro)
She reflects diligently on each lesson
She actively seeks to monitor the progress of each student (micro)
Colleagues enjoy interacting and assisting her with issues she has identified
She thoughtful and caring
She is fun to work with
She is prepared and willing to take risks to promote learning
She has a great and appropriate sense of humour
As you get further into teaching, sometimes it gets harder to maintain these things.. It can be great to look back and see how bright and bushy tailed you were when you started. When times get tougher, you can reflect upon areas to focus upon to regain that initial vigor. Be confident and know that those awful teenage years finish, slowly you gain confidence and independence... things improve as you go through your twenties and thirties (I can't speak for the forties!).
After talking with the maths department, I won the praccie competition this term.
Well done you two.. We look forward to hearing about your progress.
Russell.
Labels:
daily reflection
Monday, July 4, 2011
Developing educators
I've thought for a long time that we fail to appreciate that there are a range of teachers required in education as different teaching styles benefit different students. Our teaching practicum system has a tendency to promote outgoing, gregarious teachers and discourage practicum teachers that are not. This is a real shame as those that take time to build their skills and have a calling to teaching may need more help to get over that initial hurdle of conquering teaching practices and behaviour management but then excel in creating engaging, caring and developmentally appropriate learning environments.
I was once told that I had a lifetime of occupations crammed into my twenties, but even with this I barely made it through my ATP. My final practicum was a train wreck (my only pass grade of my degree) but does this define me as a bad teacher five years later? Well.. I'm still here and still improving my teaching. I'm no teacher of the year but my classes are well defined, my students are achieving and as a team we are moving forward. My growth from that point on ATP has been linear and I expect that to continue.
Sometimes I have to remind myself that the best teachers are not necessarily those that found things easy, but those that really had to deconstruct a problem, seek to understand it deeply and then work with others to find a solution. This creates an understanding of the difficulty of capturing the nature of the learning problem. It's hard to get this point across to practicum teachers as many come in expecting it to be as easy as we sometimes make it look, not realising that getting kids to the point where they engage fully may have taken a term (or in some cases a few years) of hard work, organising resources has taken hours of planning and that skills and knowledge used in the classroom took years of experimenting until things came together. Reflection is a key component in this growth.
The first five years in teaching for me wasn't easy, but after the first couple of years, with good support it certainly is becoming easier. It's one reason why I say seniority has its place. You don't survive as a classroom teacher unless you can handle the pressure most of the time and have management structures to relieve the pressure for the remainder of the time. Without a hierarchy of some nature, we can't give teachers time to grow, nurturing them in soft classes, mentoring them through difficulties without fear and then developing them into true educators.
Perhaps after a few more practicum students I'll think this is a load of drivel and that the system is right.. but I hope not. I'd like to say that we can develop a system where students, teachers and administrators see teacher diversity as a key goal within the system.
I was once told that I had a lifetime of occupations crammed into my twenties, but even with this I barely made it through my ATP. My final practicum was a train wreck (my only pass grade of my degree) but does this define me as a bad teacher five years later? Well.. I'm still here and still improving my teaching. I'm no teacher of the year but my classes are well defined, my students are achieving and as a team we are moving forward. My growth from that point on ATP has been linear and I expect that to continue.
Sometimes I have to remind myself that the best teachers are not necessarily those that found things easy, but those that really had to deconstruct a problem, seek to understand it deeply and then work with others to find a solution. This creates an understanding of the difficulty of capturing the nature of the learning problem. It's hard to get this point across to practicum teachers as many come in expecting it to be as easy as we sometimes make it look, not realising that getting kids to the point where they engage fully may have taken a term (or in some cases a few years) of hard work, organising resources has taken hours of planning and that skills and knowledge used in the classroom took years of experimenting until things came together. Reflection is a key component in this growth.
The first five years in teaching for me wasn't easy, but after the first couple of years, with good support it certainly is becoming easier. It's one reason why I say seniority has its place. You don't survive as a classroom teacher unless you can handle the pressure most of the time and have management structures to relieve the pressure for the remainder of the time. Without a hierarchy of some nature, we can't give teachers time to grow, nurturing them in soft classes, mentoring them through difficulties without fear and then developing them into true educators.
Perhaps after a few more practicum students I'll think this is a load of drivel and that the system is right.. but I hope not. I'd like to say that we can develop a system where students, teachers and administrators see teacher diversity as a key goal within the system.
Labels:
daily reflection
Subscribe to:
Posts (Atom)