Friday, February 19, 2010

Time continued...

We were working on applying time calculations today, so I posed a question:

"If [student A] was given detention for 1.4 hours and [student B] was given detention 1 hour 25 minutes detention, who would be in detention the longest?"

Students had a guess and then they reviewed the caterpillar for converting between time units.

We then did a number of calculations with some templates to show how a calculation could be constructed.
Eg
3.4 hours = _______ x ________ mins
= ______________ mins
2 122 131 sec = ________ ÷ _________ ÷ _______ ÷ _______ days
= ____ days
1 hour 20 mins = ________ x _________ + ________ mins
= ______________ mins
After we did that, students were just given a range of questions to solve without the templates.
Eg.
2.8 hours = ___________ minutes
12 hrs 12 minutes = ______ hours
12 hrs 12 minutes = ______ days
Then we revisited our original detention problem and a range of similar problems.
Students then practiced with math-joke type connect-the-answer-with-the-question exercise (the old worksheet with a bad, bad mathematics joke at the bottom to solve). Students were able to solve the majority of problems.
yay!
There's nothing to say that with a stronger group I couldn't have taught the same topic by teaching basic time facts (such as 60sec = 1 minute) and then relied on their application of multiplication and division, but in this case I'm glad I didn't do that, the look on the faces of my students when they realised time calculations made sense (that they had found difficult over a long period) was priceless.




Wednesday, February 17, 2010

Teaching Elapsed Time

Teaching time is always a little problematic with a class, as some students will have this well and truly conquered by year 10 and others will struggle.

Elapsed time is a difficult topic for many as it drags in a lot of sub topics. With each step it is important to draw student's attention to possible mistakes and also to any parallels with an analogue clock.

A common method is to find the number of hours elapsed and then add the remaining minutes on either side (eg. for 2.14 to 4.15: 2.14 -> 3.00 -> 4.00 -> 4.15 would be 46min + 1 hour + 15 mins = 2 hours 1 minute)

The usual approach is to
a) draw a number line
Issues: Students don't relate a number line with time, and commonly place decimal marks (eg. 10 between each hour) rather than 12 (for 5 minute intervals).
b) place the start and finish time on the number line.
Issues: Students don't realise that the start time and end time have to be placed in that order. Eg. if the start time is 8am and the end time is 7am they want to put 7am first on the number line.
c) mark on the hour after the start time and the hour before the start time
Issues: Students have difficulty adding the two times inside the interval. If 7.30am is the start time, they might add 7.00am instead of 8am or for a 4.30 finish time they might add 5.00pm or 3pm.
d) mark on midday and midnight if they lie between the start and finish time
Issues: This is problematic especially with times over 12 hours where both midday and midnight are involved. Students are often not sure whether 12pm or 12am is midday or midnight. They also get confused moving from 12am to 1 am (counter-intuitive).
e) calculate the time between each number on the timeline
Issues: This is the bugbear of the exercise. Students are not sure of the answer counting up to the nearest hour and counting back to the previous hour. Eg Finding the time between 1.17am and 2am or 4.00pm and 4.55pm. Many issues here are related to issues in part c)
f) add the elapsed times
Issues: Students write times such as 7hrs 85 minutes not realising 85mins is greater than an hour.

An alternate approach is to go up in hours and add the remainder (eg. 2.14-> 3.14 -> 4.14 -> 4.15 = 2 hours 1 minute). This may help struggling students and reduce the amount of calculation required.

Monday, February 15, 2010

Heroes in mathematics education

There are some heroes in mathematics education in Perth. They're the ones that share their resources freely, commit to projects and help out. Most are quiet, private and retiring soon. I feel sorry for the public heroes like Rom Cirillo at Curriculum council who is trying to help everyone and is succeeding most of the time. If only there were four of him.

Then there's those that are paid to help and are more talk, little knowledge and bugger all action. I've labelled them the West Australian New Kurriculum Education Resource (the acronym is all important - feel free to put it after your name - no charge!). They join TDC's, MAWA and teaching groups and are paid to produce resources and assistance. All too often they send out untried resources that cause confusion and show their lack of knowledge, they provide advice that is the flavour of the month and denigrate anything functional (their favourite seems to be the Saddler texts). Their advice is ill researched and they often don't answer the question posed. I often have a good laugh at their email sigs that are fourteen lines long outlining their projects as if this means something.

Numeracy consultant, Leaders Facilitator, Specialist teacher, TDC coordinator (yawn - and all in one sig!). It seems rampant self aggrandisement. I've seen title based nonsense before in IT, it's not something we need in teaching. The word 'consultant' brings about shudders - tell me what you're doing and then I'll record it so that you will know what you are doing (and charge at $400 per hour), tell you how the latest fad might help and provide insanely conservative advice as any real advice I give could lead to litigation that might hold them responsible.

One only has to look at how well these experts do during in school PD to realise how out of touch they are.

No thank you.

To me - it makes more sense to signoff Mathematics teacher. Add BEd, if you need qualifications. Sometimes I might add senior school to make it easier to find me within the school. Anything more seeks to diminish the reputation of a classroom teacher.

Give me a teacher that can teach a TEE student and a year 8 effectively any day (or a primary equivalent).

Show me a "super teacher" and I'll show you an idiot. Teaching is too wide a profession with too many different contexts to be an effective specialist or specialist trainer. To specialise is to remove yourself from the coalface and limit your student involvement (eg. reduce your ability to teach). I fail to see how this is a good thing.

Sunday, February 14, 2010

Creating a positive learning environment

Positioning kids for learning is an underestimated part of teaching programmes. If a student understands that creating a good impression is important, then this creates a pattern of behaviour that can continue throughout the year.

As a form teacher, it's important to remind kids of this, take a personal interest in their successes and reinforce disappointment when they step out of line. This creates a culture of success and reinforces the positives.

It can also snap a student out of negative behaviour before it becomes habitual.

Homework is one of those things that needs to be positioned early. It is time consuming to check homework daily, but initially there is no way around it. There needs to be real punishment for non compliance (I use check ability -> detention until complete -> blue note with letter for non-attendance -> phone call -> demotion to lower class). The letter part is my favourite as I can suggest a number of activities that might be suspended such as PS3/Wii/XBox, MSN, TV, sport, going out etc. until regular homework becomes established. Diaries and journals play an important part in this process to keep parents informed.

I have heard that imposing homework is too difficult (and it is difficult if done in year 10, without having the habit instilled earlier) but without it, we are expecting low SES kids to perform with potentially 3 hours per night less work completed compared to independent schools. This means state school kids are expecting to compete with 2/3 the effective work time.