My prac student is to deliver the right angle trigonometry unit and I was thinking about all the little things that I like to emphasize to students.
The first thing I would like him to consider is to design the course to make connections to previous courses of work (prior learning) especially with regard to language. Mathematics has such a rich history of precise language that it is important to identify ideas correctly to students in a manner that ties together topics to promote abstraction.
For instance before actually doing anything, we need to remind students what the LHS and RHS of an equation is, and how to identify the subject of the equation that we want to work with. Then we might think about how to eliminate coefficients and pronumerals/variables from one side on an equation, transpose terms/pronumerals/variables and multiplying through/simplifying to remove a denominator. What can we substitute into an equation? How do we solve the equation? Do we need simultaneous equations? We need to use every opportunity to reinforce concepts learned in previous algebra topics.
We have geometry prior learning to consider, three internal angles = 180°, a right angled triangle has one internal angle 90°. Line properties give us complementary, corresponding, co-interior, supplementary, adjacent, vertically opposite, exterior, alternate angles. Also the types of triangles, isosceles, equilateral and scalene help us find other angles. Circle geometry gives us tangents, subtended angles, cyclic quadrilaterals. Properties of 3D shapes!
Only after we consider possible connections to prior learning can we think about actually teaching the relatively small amount of new material. Without these connections we are just teaching students a new trick that will be forgotten immediately after assessment (a key issue exacerbated by the increased assessment required by OBE reporting requirements).
We have to introduce a range of new ideas such as opposite, adjacent and hypotenuse for right angled triangles. We have equations such as Pythagoras' and the three trigonometric ratios. .. and the dreaded bugbear bearings (until vectors makes bearings look easy!!)
We have conventions such as labelling the hypotenuse 'c' and the remaining sides a, b for Pythagoras' theorem problems and opp, adj and hyp in trigonometric problems.
We have good practice such as always writing the symbolic form of a trigonometric equation before substituting values, labelling diagrams, identifying right angles.
We have acronyms to help us remember trigonometric ratios SOH, CAH, TOA.
What is the correct sequence for introducing the material? What resources can we use or have available?
So now prac student, your job is to help students see how their prior learning is necessary to solve these problems!
Wednesday, June 10, 2009
Touchy.. Touchy...
Often speaking at school you think.. bloody hell.. that's not what I meant.
This seems to happen to me a lot as I am a bit introspective at times but will say what I think - and subsequently seem to live with a constant case of foot-in-mouth.
A couple of students came to me and said, "such and such teacher just doesn't understand.. I ask them for help and they don't listen." I sat down and talked with them about the kind of questions they were asking and it turned out to be a conversation like "I just don't understand anything!", to which even I would respond, "then go back to primary. I can't help you either." I then talked to the students about leading questions, redrafting and investigated what they did know. By the end of it, we realised that they had actually learnt a lot from the teacher already and that the angst they were feeling was that they now had to use this knowledge and that this required work.
.. so I said to myself... job well done.. and mentioned it to the teacher and asked if students resubmitting redrafted work was a problem and discussed the conversation I had with the kids.. this was turned on me as, "don't you think I provide scaffolding for my kids." OMG.. I'd just been praising this teacher to students and pointing out what they had already learned!
Another case in point occurred when I was asked did I have a preference to teaching boys or girls, to which I responded I thought I had a bit more experience teaching girls, therefore found it a bit easier.. to which the scamp teacher cheekily replied.. "I find boys easier to teach, are you saying I have less experience with girls?" ARGH!!!
These were jokey experiences, but sadly in teaching often analysis of our strengths and weaknesses, or sharing our ideas is seen as a prelude to punitive action to rectify a perceived issue. This fear often hampers any reform process and causes much angst with regards to performance management issues.
Oh and don't even think about robust discussion or sharing subject passion or investigating your own perceived flaws.
One of the ways of stopping teacher close mindedness is to nip it in the bud with practicum students and promote sharing of ideas (using new media where a young group of teachers is not at hand) to ensure that we become collegiate as a profession and welcome self and group analysis as a way of improving our performance. With many of our experienced teachers on the verge of retirement beaten down by OBE we will need to accelerate the speed that teachers become competent and we can no longer rely on the "closed door, hide in our classroom and teach ourselves" method of learning. It's inefficient, in a world where people change careers like underwear, it is also impractical.
That's my rant for today.
This seems to happen to me a lot as I am a bit introspective at times but will say what I think - and subsequently seem to live with a constant case of foot-in-mouth.
A couple of students came to me and said, "such and such teacher just doesn't understand.. I ask them for help and they don't listen." I sat down and talked with them about the kind of questions they were asking and it turned out to be a conversation like "I just don't understand anything!", to which even I would respond, "then go back to primary. I can't help you either." I then talked to the students about leading questions, redrafting and investigated what they did know. By the end of it, we realised that they had actually learnt a lot from the teacher already and that the angst they were feeling was that they now had to use this knowledge and that this required work.
.. so I said to myself... job well done.. and mentioned it to the teacher and asked if students resubmitting redrafted work was a problem and discussed the conversation I had with the kids.. this was turned on me as, "don't you think I provide scaffolding for my kids." OMG.. I'd just been praising this teacher to students and pointing out what they had already learned!
Another case in point occurred when I was asked did I have a preference to teaching boys or girls, to which I responded I thought I had a bit more experience teaching girls, therefore found it a bit easier.. to which the scamp teacher cheekily replied.. "I find boys easier to teach, are you saying I have less experience with girls?" ARGH!!!
These were jokey experiences, but sadly in teaching often analysis of our strengths and weaknesses, or sharing our ideas is seen as a prelude to punitive action to rectify a perceived issue. This fear often hampers any reform process and causes much angst with regards to performance management issues.
Oh and don't even think about robust discussion or sharing subject passion or investigating your own perceived flaws.
One of the ways of stopping teacher close mindedness is to nip it in the bud with practicum students and promote sharing of ideas (using new media where a young group of teachers is not at hand) to ensure that we become collegiate as a profession and welcome self and group analysis as a way of improving our performance. With many of our experienced teachers on the verge of retirement beaten down by OBE we will need to accelerate the speed that teachers become competent and we can no longer rely on the "closed door, hide in our classroom and teach ourselves" method of learning. It's inefficient, in a world where people change careers like underwear, it is also impractical.
That's my rant for today.
Labels:
teaching
Friday, June 5, 2009
Unrealistic expectations and belief
As a teacher you hold fragile confidence in your hand every day. Belief in a student is a powerful thing, it can set a child on the path of success and make them believe in their own futures.
When we get caught up in grades and league tables and moderated scores and all other such associated bulldust we forget what a powerful thing belief is. When we believe in the person miracles are possible.
When we don't let students try, succeed and fail, we fail our students. Failure is important when seeking the utmost of our ability.
School is not about high stakes testing, nor about consequences. It is about creating a safe environment for our kids to explore their limits and seek excellence. Sometimes as a society I think we have forgotten this.
...as teachers we see the evidence of our beliefs every day.. as well as the consequences when our belief fails.
It's something to ponder.
When we get caught up in grades and league tables and moderated scores and all other such associated bulldust we forget what a powerful thing belief is. When we believe in the person miracles are possible.
When we don't let students try, succeed and fail, we fail our students. Failure is important when seeking the utmost of our ability.
School is not about high stakes testing, nor about consequences. It is about creating a safe environment for our kids to explore their limits and seek excellence. Sometimes as a society I think we have forgotten this.
...as teachers we see the evidence of our beliefs every day.. as well as the consequences when our belief fails.
It's something to ponder.
Labels:
expectations
Monday, June 1, 2009
The meaning of life
Today, I was talking about the meaning of life with my daughter..
Her response was definitely, "GOOP!".
..and how true she is. We start out as goop, we end as goop and we goop about a lot in between.
In fact there is very little that can't be explained by the word goop..
but.. I was unsure if she was interpreting our existence as part of a predestined global goop entity rather than as individual gooplets with free destiny. Does she lean more towards intelligent goop design or a more darwinistic goop approach? I'll have to check with her later.
Very thought provoking little 3 month old Mackenzie! Maybe she can explain it to me when she learns her second word.
Her response was definitely, "GOOP!".
..and how true she is. We start out as goop, we end as goop and we goop about a lot in between.
In fact there is very little that can't be explained by the word goop..
but.. I was unsure if she was interpreting our existence as part of a predestined global goop entity rather than as individual gooplets with free destiny. Does she lean more towards intelligent goop design or a more darwinistic goop approach? I'll have to check with her later.
Very thought provoking little 3 month old Mackenzie! Maybe she can explain it to me when she learns her second word.
Labels:
funny
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