My emphasis for the last week has been on establishing an idea of "one" with my year 9 academic class. We examined how our idea of one influences how we deal with fractions and algebra.
Firstly we looked at common denominator problems and examined in more detail the method for adding fractions with different denominators.
A common idea is to find common multiples or factors of the denominator and then multiply both the numerator and denominator of the fractions until common denominators are found.
eg. 1/2 + 1/3 -> common denominator of 6 (LCM of 2 and 3)
We then need to find equivalent fractions with denominators of six.
eg 1/2 x 3/3 = 3/6
1/3 x 2/2 = 2/6
Now we have common denominators we can add the fractions..
eg 2/6 + 3/6 = 5/6
But.. why does multiplying by 2/2 and 3/3 work??? Understanding "One" is the answer!!!
1/2 x 1 = 1/2
3/3 = 1
Therefore by substitution 1/2 x 3/3 is just multiplying 1/2 by one. Any number multiplied by one is equal to the original value thus any resulting fraction must be equal to 1/2!
This illustrates two different ideas related to one.. "Multiplying by One" and "Dividing a number by itself".
We also looked at cancelling and why it works..
2m / 3m, we commonly use the skill cancel the m's and 2/3 is what is left.
By re-examining how multiplication works with fractions we find that we can rewrite
2m/3m
as
2/3 x m/m
..but we know that anything divided by itself is 1 (other than zero of course!)
Therefore we can simplify to
2/3 x 1
and we know that anything multiplied by one is equal to the original value.... thus we can see why cancelling works..
Quite a fun little lesson.
Russ.
Saturday, February 12, 2011
Moderation - advice for new players.
Moderation is the local equivalent of peer assessment at a teacher level. If your class is small (less than 12), it is assumed that it is too difficult to give fair grades thus you need to find other small schools to check your grades against. If you are having trouble locating a group tell your HoD/TiC then contact the curriculum council.
Moderation sounds like a pain (and it is) but there is one major advantage. Generally, not always, when you do this you share assessment. This means that you may only need to write half (or a third/less depending on the number of schools involved in your group) of the assessment for the course. If your group has teachers that are organised it can create some great discussion and access to course materials that are often hard to find (such as investigations). Sometimes teachers are not organised, are difficult by nature or have a different opinion to you as to the content and difficulty level of assessment. When they are a combination of these you end up with conflict. Especially if assessment is given late and other participants do not have time to check the difficulty level and breadth of assessment. This is reasonably rare and you can always decline letting them into your next small group. It's in nobody's interest to have a slacker in your group. If you are the slacker for a good reason (such as sickness at home or an unrealistic load at school) then make sure you nurture a good relationship with the rest of the group. Don't let the resentment fester.
If you are terrible at investigations (I own up to this one, I rarely get the difficulty level right), then ask for a later investigation in the year and start now, using your mentor teacher as a guide for where to go with the project. Hunt around for one that hasn't been done for a few years at your school. There are some fantastic investigations being dreamed up at the moment as teachers are finally finding that they have more time with courses bedding down.
Last but not least are the technical issues. Sort out whether you are running concurrent or sequential. Ensure that you know what the weightings are for each assessment and where the marks are coming from (take home and/or validation). Check if notes or calculators are allowed in each assessment. Send your marks to all members of your group and check where your students lie - this will change your approach during semester. Agree on grade cutoffs for semester 1 well before the end of term 3.
Have Fun.
Russ.
Moderation sounds like a pain (and it is) but there is one major advantage. Generally, not always, when you do this you share assessment. This means that you may only need to write half (or a third/less depending on the number of schools involved in your group) of the assessment for the course. If your group has teachers that are organised it can create some great discussion and access to course materials that are often hard to find (such as investigations). Sometimes teachers are not organised, are difficult by nature or have a different opinion to you as to the content and difficulty level of assessment. When they are a combination of these you end up with conflict. Especially if assessment is given late and other participants do not have time to check the difficulty level and breadth of assessment. This is reasonably rare and you can always decline letting them into your next small group. It's in nobody's interest to have a slacker in your group. If you are the slacker for a good reason (such as sickness at home or an unrealistic load at school) then make sure you nurture a good relationship with the rest of the group. Don't let the resentment fester.
If you are terrible at investigations (I own up to this one, I rarely get the difficulty level right), then ask for a later investigation in the year and start now, using your mentor teacher as a guide for where to go with the project. Hunt around for one that hasn't been done for a few years at your school. There are some fantastic investigations being dreamed up at the moment as teachers are finally finding that they have more time with courses bedding down.
Last but not least are the technical issues. Sort out whether you are running concurrent or sequential. Ensure that you know what the weightings are for each assessment and where the marks are coming from (take home and/or validation). Check if notes or calculators are allowed in each assessment. Send your marks to all members of your group and check where your students lie - this will change your approach during semester. Agree on grade cutoffs for semester 1 well before the end of term 3.
Have Fun.
Russ.
Labels:
moderation
Tuesday, February 8, 2011
Bullying
In a school with strong personalities, bullying can be a real problem. Typically physical bullying with the boys and psychological bullying with the girls. Bullying can and does break good students. A success story of our school is the lack of bullying despite public perception.
It is one area of the school where the middle school and the counselling group excels. The kids that come through to the senior school typically aren't bullies; those that try get counselled to death and the source of their bullying painfully exposed. I can't imagine being told "you are a bully and you need to have a look at yourself" is a wonderful experience.
There is always room for improvement. Especially with new kids. Assimilation can be tenuous at time especially in well settled groups. Each teacher needs to be conscious of isolates within a class and subtly discourage them. Each teacher needs to be conscious of niggles that rise during the year. Each year an issue defines a group: race issues, bitchiness, physical agression, complacency, lack of work ethic, teacher conflicts, lower than expected performance. How we deal with those issues makes or breaks a year group.
A nice thing is that regardless smart students at our school are looked up to - there are safe areas in the school for them, for the weird kids, for the popular kids, for the sporty kids. Inside a class anyone can answer a question without fear of a smartness stigma. Amongst all the "over" worldliness of our kids is an innocence that comes with a lack of funds and a questionable future. There are few students that have a future guaranteed by a parent's bank account. Education is one pathway out of the poverty trap. It's a source of pure hope.
It's a real responsibility to find a pathway for this hope through education into the workforce for each of our kids, whether VET or TEE and we all have a part to play.
It is one area of the school where the middle school and the counselling group excels. The kids that come through to the senior school typically aren't bullies; those that try get counselled to death and the source of their bullying painfully exposed. I can't imagine being told "you are a bully and you need to have a look at yourself" is a wonderful experience.
There is always room for improvement. Especially with new kids. Assimilation can be tenuous at time especially in well settled groups. Each teacher needs to be conscious of isolates within a class and subtly discourage them. Each teacher needs to be conscious of niggles that rise during the year. Each year an issue defines a group: race issues, bitchiness, physical agression, complacency, lack of work ethic, teacher conflicts, lower than expected performance. How we deal with those issues makes or breaks a year group.
A nice thing is that regardless smart students at our school are looked up to - there are safe areas in the school for them, for the weird kids, for the popular kids, for the sporty kids. Inside a class anyone can answer a question without fear of a smartness stigma. Amongst all the "over" worldliness of our kids is an innocence that comes with a lack of funds and a questionable future. There are few students that have a future guaranteed by a parent's bank account. Education is one pathway out of the poverty trap. It's a source of pure hope.
It's a real responsibility to find a pathway for this hope through education into the workforce for each of our kids, whether VET or TEE and we all have a part to play.
Labels:
bullying
Monday, February 7, 2011
NAPLAN preparation
There are lots of times you are surprised as a teacher. Today I did some NAPLAN revision of decimal numbers with my year 9 class. It really surprised me how difficult students find the concept of decimal numbers.
Here's something to try with your child.
Draw a number line and place 4.5 at one end and 4.6 at the other.
Place a marker in the middle and ask your child what number would go there.
The answer is 4.55 and many students may get this right, but many would not be 100% sure.
Split the number line again so that it is now in four equal sections. Ask your student to label the new sections.
You may get a wide variety of answers and weird looks.
The answer is 4.5, 4.525, 4.55, 4.575 and 4.6
If your child cannot do this they are not alone. Try again using whole numbers and break it into ten equal sections. Try asking for points between intervals.
Errors like these indicate an issue with both division and place value. It can easily be remedied with some place value exercises (to check if they understand that 4.6 is bigger than 4.59), some estimation exercises (to check if their answers are feasible/reasonable), determining how to find the width of set intervals (using division), learning how to add on intervals and how to find midpoints of intervals.
Here's something to try with your child.
Draw a number line and place 4.5 at one end and 4.6 at the other.
Place a marker in the middle and ask your child what number would go there.
The answer is 4.55 and many students may get this right, but many would not be 100% sure.
Split the number line again so that it is now in four equal sections. Ask your student to label the new sections.
You may get a wide variety of answers and weird looks.
The answer is 4.5, 4.525, 4.55, 4.575 and 4.6
If your child cannot do this they are not alone. Try again using whole numbers and break it into ten equal sections. Try asking for points between intervals.
Errors like these indicate an issue with both division and place value. It can easily be remedied with some place value exercises (to check if they understand that 4.6 is bigger than 4.59), some estimation exercises (to check if their answers are feasible/reasonable), determining how to find the width of set intervals (using division), learning how to add on intervals and how to find midpoints of intervals.
Labels:
number
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