It always surprises me what will work with a low ability group and what will not. Generally you have to hit the ability level spot on for the whole group for them to be able to grasp a concept (even if only momentarily).
Take indices. On one day grasping 3x3 = 3 squared = 9 was impossible, not to mention any attempts at 3^2 x 3^3 = 3^5. We went through a number of examples and by the end of the lesson I had 10 bored students and had lost half of my hair.
The next day I took a different investigative approach. This might be obvious to an experienced teacher but was fairly radical to me.
Sequence (imagine that ^3 is written as 3 superscripted):
a) Discuss nomenclature with notes (base, index, indicies, power, factor and power form)
b) Use calculator to evaluate single term powers - eg. 3^3 = ...
c) Add multiplying powers to the board (with positive index) - eg. 3^3 x 3^5 = ...
e) Look for a pattern in the numbers - supply the base after a few minutes.
f) Explain how multiplying powers works and supply notes including general forms
g) Rub off the answers, write as index addition - eg. 3^3 x 3^5 = 3^...+... = 3^8 = 6561
h) Add dividing powers to the board where answers are positive > 0 - eg. 3^5 ÷ 3^2 = ...
i) Look for a pattern in the numbers - supply the base after a few minutes.
j) Explain dividing powers, supply notes including general form (as ÷ and fraction)
k) Rub off the answers, write as index subtraction - eg. 3^5 ÷ 3^3 = 3^...-... = 3^2 = 9
l) Supply mixed problems
About 40 mins. I don't think I could have done this investigating factored form with these students as regrouping and cancelling bored them silly the previous day (I will revisit it later though). Using calculators to do the sum and examine the sum backwards worked far better. Special note was made from e) onwards about checking for same base, superscripting properly, neatness, identifying operator used in original sum and always referring back to general form to make sure the correct index operation is being done. By the end of class all 5 students were engaged and had grasped the concepts involved. yay!
Now some may ask 'why do index laws with a low ability group in yr 10?'. I suppose it is a philosophy problem put in place at uni. Students shouldn't have impoverished courses 'entertainment based/childcare oriented' purely because they are in a low ability group. If they could master simple algebra earlier in the year and ratios later in the year, I consider index laws and other more 'pure' maths well within their grasp even with behaviour difficulties. These students too should have the pleasure of mastering something that looks quite cool on paper, harder than they believe possible to learn and not feel inferior to peers when they walk into an upper school maths class.
Saturday, September 6, 2008
Friday, September 5, 2008
Longitude and Latitude problems
We revisited longitude and latitude today just prior to a quick quiz on Monday of elevation/depression, longitude/latitude and bearings problems.
Firstly the section that we did on angles(complementary/supplementary) and bearings seems to have resolved many of the angle addition/subtraction problems students encounter in longitude and latitude (this makes sense). The second was that teaching how to solve latitude problems before longitude problems is far easier than vice-versa (this was not expected).
Sequence used:
a) nomenclature & uses - great circles:longitude+equator, small circles:latitude
b) how to draw latitude problems - uses of front vs side views
c) find the radius of small circles - r(small circle) = r(great circle) cos (longitude)
d) how to find the circumference of small circles - C(small circle) = 2 x pi x r(small circle)
e) how to identify the angle travelled - reading diagrams carefully & common errors
f) how to calculate the distance travelled - angle / 360 x C(small circle)
The reasoning for the second finding is that students were happy to learn new skills (eg. solve latitude problems)...
... students were even happier to be told that longitude problems were easier than latitude problems (eg. remove step c), draw the diagram a little differently - front view edge marked)
.. rather than teach longitude first and say that latitude problems were more difficult (as you need to add step c) and have to think harder about the diagram).
All in all, it can be taught in a lesson to a good group in year 10, maybe a bit longer if proving step c), with practice for a couple of sessions. I never would have identified the second finding if I hadn't chosen the wrong question as an example. Nothing like a random event to improve your teaching and give an insight into student thinking.
Firstly the section that we did on angles(complementary/supplementary) and bearings seems to have resolved many of the angle addition/subtraction problems students encounter in longitude and latitude (this makes sense). The second was that teaching how to solve latitude problems before longitude problems is far easier than vice-versa (this was not expected).
Sequence used:
a) nomenclature & uses - great circles:longitude+equator, small circles:latitude
b) how to draw latitude problems - uses of front vs side views
c) find the radius of small circles - r(small circle) = r(great circle) cos (longitude)
d) how to find the circumference of small circles - C(small circle) = 2 x pi x r(small circle)
e) how to identify the angle travelled - reading diagrams carefully & common errors
f) how to calculate the distance travelled - angle / 360 x C(small circle)
The reasoning for the second finding is that students were happy to learn new skills (eg. solve latitude problems)...
... students were even happier to be told that longitude problems were easier than latitude problems (eg. remove step c), draw the diagram a little differently - front view edge marked)
.. rather than teach longitude first and say that latitude problems were more difficult (as you need to add step c) and have to think harder about the diagram).
All in all, it can be taught in a lesson to a good group in year 10, maybe a bit longer if proving step c), with practice for a couple of sessions. I never would have identified the second finding if I hadn't chosen the wrong question as an example. Nothing like a random event to improve your teaching and give an insight into student thinking.
Different approaches to supporting teachers
It is interesting to view different teaching styles and different ways of supporting teachers. Support staff such as team leaders and HODs are important parts of school machinery. I've been to a couple of schools and have made a few observations about how these support staff operate.
Type 1: Student focused (Soft and mushy).
The soft and mushy students support person always has the student in the forefront of their mind. They are 'friends' of the student, listen to their grievances and reason through their issues. Issues with this person relate to support of students based on student reporting of incidents especially as students often only relate parts that they remember and conveniently forget negative portions. Positives of this type of support staff is that many issues can become non-issues without further teacher intervention and they can negotiate middle-grounds where teachers and students both feel POV is acknowledged and resolution has been achieved. They also have great rapports with parents. Generally supporters of BMIS management techniques.
Type 2: Authoritative (Firm and stern)
For me, the easiest support person to deal with as many issues are black and white. They will investigate, report and resolve issues. In most cases will lean to the side of the teacher. Negatives is that some students will feel that their POV is not given enough weighting. Positive is that student POV is not given weighting over teacher and holistic classroom position. Middle ground resolution tends to focus on end results and measurable future performance. Generally supporters of the "teacher is boss" type mentality.
Type 3: Administrative (Paper pusher)
This is the worst type to my mind as nothing gets resolved but all paperwork is in order. Chaos tends to follow a support person of this type and responsibility is delegated to anyone but the support person for ultimate resolution of an issue. For specific issues they are often unavailable as they are pursuing "pet" projects. They tend to be active self promoters. The main negative is the sheer amount of unresolved issues pushed back onto teachers - students are not sent to support staff unless an unresolvable issue within the classroom has been encountered and pushing unresolvable situations back to teachers does not help maintain programme momentum. The only positive is that major incidents have well recorded backgrounds. Generally supporters of give anyone the responsibility as long as it is not me.
As I think of more I will add them to the list.
Type 1: Student focused (Soft and mushy).
The soft and mushy students support person always has the student in the forefront of their mind. They are 'friends' of the student, listen to their grievances and reason through their issues. Issues with this person relate to support of students based on student reporting of incidents especially as students often only relate parts that they remember and conveniently forget negative portions. Positives of this type of support staff is that many issues can become non-issues without further teacher intervention and they can negotiate middle-grounds where teachers and students both feel POV is acknowledged and resolution has been achieved. They also have great rapports with parents. Generally supporters of BMIS management techniques.
Type 2: Authoritative (Firm and stern)
For me, the easiest support person to deal with as many issues are black and white. They will investigate, report and resolve issues. In most cases will lean to the side of the teacher. Negatives is that some students will feel that their POV is not given enough weighting. Positive is that student POV is not given weighting over teacher and holistic classroom position. Middle ground resolution tends to focus on end results and measurable future performance. Generally supporters of the "teacher is boss" type mentality.
Type 3: Administrative (Paper pusher)
This is the worst type to my mind as nothing gets resolved but all paperwork is in order. Chaos tends to follow a support person of this type and responsibility is delegated to anyone but the support person for ultimate resolution of an issue. For specific issues they are often unavailable as they are pursuing "pet" projects. They tend to be active self promoters. The main negative is the sheer amount of unresolved issues pushed back onto teachers - students are not sent to support staff unless an unresolvable issue within the classroom has been encountered and pushing unresolvable situations back to teachers does not help maintain programme momentum. The only positive is that major incidents have well recorded backgrounds. Generally supporters of give anyone the responsibility as long as it is not me.
As I think of more I will add them to the list.
Labels:
administration,
support staff,
teaching
Thursday, September 4, 2008
Curriculum Council Moderation
Here are words that inspire fear in the most confident graduate teacher - "Moderation". We had ours and the one thing it showed was the need for experienced teachers to guide the less experienced teacher. Our most experienced teacher took the work of students, repackaged it to make it easy to be viewed and removed much of the stress.
I'm not saying that moderation was not stressful - the idea of redressing issues 3 weeks before the end of a course kept me up at night for a number of days. When it happened though, it was great to have recognised that the grading given was correct and also be given ideas about how to improve the course.
In my non-TEE course I now understand that they like to see context heavily developed into the course - coursework specially developed for the cohort. If this can be demonstrated in assignment pieces this can be a good thing.
Another insight was that moderators look at the intake as well as the results especially in TEE courses - to check if the students selected for courses has been done appropriately. It was interesting to hear of restrictions placed on student subject selection in other schools to (I imagine) protect school TEE rankings and student self esteem. As schools reduce the number of subjects on offer and students have reduced options, I wonder if we will see more issues in this area.
Our moderator liked to see cognitive type assessment. I shall seek out some more of this sort of thing (to be honest I have no idea what they are (isn't an investigation typically cognitive?) - but will ask around).
It shouldn't be underestimated the time it takes to prepare for moderation and the disruption it causes to other classes. I strongly suggest for portfolios of all assessment to be gathered and kept for all students in a class by the teacher. If you don't have these pre-done, prepare a couple of each for moderation or you may have your D turn into a C and have to find another portfolio at the last minute to fill the gap (...I wonder how I know this??).
Keeping portfolios from students is detrimental to test preparation (as you have the portfolios rather than students for study) but is far preferable than trying to gather materials in the lead up to moderation dates (especially as for us they fell just before the start of TEE mock exam preparation). After moderation dates portfolios can also be a great study tool for exams that careless students wouldn't have at the end of the year.
I'm not saying that moderation was not stressful - the idea of redressing issues 3 weeks before the end of a course kept me up at night for a number of days. When it happened though, it was great to have recognised that the grading given was correct and also be given ideas about how to improve the course.
In my non-TEE course I now understand that they like to see context heavily developed into the course - coursework specially developed for the cohort. If this can be demonstrated in assignment pieces this can be a good thing.
Another insight was that moderators look at the intake as well as the results especially in TEE courses - to check if the students selected for courses has been done appropriately. It was interesting to hear of restrictions placed on student subject selection in other schools to (I imagine) protect school TEE rankings and student self esteem. As schools reduce the number of subjects on offer and students have reduced options, I wonder if we will see more issues in this area.
Our moderator liked to see cognitive type assessment. I shall seek out some more of this sort of thing (to be honest I have no idea what they are (isn't an investigation typically cognitive?) - but will ask around).
It shouldn't be underestimated the time it takes to prepare for moderation and the disruption it causes to other classes. I strongly suggest for portfolios of all assessment to be gathered and kept for all students in a class by the teacher. If you don't have these pre-done, prepare a couple of each for moderation or you may have your D turn into a C and have to find another portfolio at the last minute to fill the gap (...I wonder how I know this??).
Keeping portfolios from students is detrimental to test preparation (as you have the portfolios rather than students for study) but is far preferable than trying to gather materials in the lead up to moderation dates (especially as for us they fell just before the start of TEE mock exam preparation). After moderation dates portfolios can also be a great study tool for exams that careless students wouldn't have at the end of the year.
Labels:
curriculum council,
moderation,
teaching
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