Thursday, August 26, 2010

Geography Lesson @ S1-01: Demographic Transition Model

Attended the lesson by Aurelius this afternoon. It was the 2nd time... er I should say the 3rd time I heard about similar thing - Population Pyramid and the Demographic Transition Model (DTM). Thanks to James, too :) The preliminary introduction of the big topic during the meeting :)

The purpose is not just a lesson visit to see how lessons could be further sharpened, but also for us to learn and possibly surface good classroom practices. Hence, it's also part of my learning journey :)

The lesson started off by helping students to understand what it meant by "Trend". I was still quite puzzle over why the teacher needed to take length to explain the word. Well, I think that's where I learnt that it's important to explain the words with a relevant context even though it might be just a simple word.

For example, in Maths, we ask students to observe trends or patterns established by numbers. However, in this subject, to describe a trend, it's more than words, but in broad areas like "form", "functionalities". It seems to be a different kind of 'animal' in another subject.

1. Understanding of Trend... with Phone as an example

The Form
  • "Old phones are bulkier and newer phones are much more smaller and light"
  • TR: What else do you see in the outlook?
  • The screens of the newer phone gets bigger.
  • The old phone - keypads are big big while the new ones touch touch
  • The new ones are more stylish ?
  • Nowadays have lots of functions like internet... now only can call
2. Next, looking at Population Pyramid:

So, there were so much to get out of the population pyramid!
Not just superificial information based on comparison of the bars. There were so much to get out of it, when breaking the pyramid into 3 tiers!

Here were some questions and responses. Indeed, I was impressed by some of the questions and responses from the students :)

  • TR: Tell me what's the birth rate like for Congo?
  • High Infant mortality rate
  • TR: What group are we talking at the middle tier?
  • Death Rate.
  • Ties back to the field work out there
  • Harsh brought up a possible observation (which could probably be used to argue about the trend) that it could be in the past that the birth rate was not that high. Hence, resulting the concave shape
Next, by comparing the birth rate of India and Congo; both countries have high birth rate; but India's might not be as high

Another question was asked:
Which group actually has a larger group of people in the society working?
  • For India, the change of population from one group to another (upwards) is quite minimal, as compared to Congo.
  • By comparing the "tip" of each pyramid, one is able to tell people from which country live longer.
Other observations of low birth rate:

  • Because living standard is high, and therefore have less children.
  • Does it mean that in a develop country, the country will spend less in infant or children?
  • The parents tend to spend more money on the children because they have less children.
  • So, it doesn't necessary mean there's less money spend on infants.

Into the next activity, which was to draw distinguishing features of both developed and less developed countries throuh 3 pictures (which broadly focused on transport, standard of living and infrastructure). I think it would be easier for students to remember if these 3 broad areas were articulated at the start of the task. Some responses from students include:

  • The road is pretty rough and that means the government might have spent less money in its infrastructure.
  • The picture with a truck carrying more people - Soh Fan: Because the population was very dense. The crowd in the tiny truck. So, it means that they don't have money to spend on taxis.
  • Ziying: Why is it that while the country is poor, there's such high birth rate
  • Mayur: It's because the survival rate of their children is low

Moving on to the Demographic Transition Model

Here's an interesting explanation about the DTM?

  • Stage 1: High birth rate & High Death Rate (e.g. tribal society)
  • Stage 2: With a bit of technology, but people still cling to their culture... better living, better food... need people to work... so still high population, and birth rate start to grow
  • Stage 3: Start to have stage 3, death rate has dropped... death rate is low... however, birth rate starts to drop
  • Stage 4: Standard of living has gone up, people also doesn't want to bear so much children.

Tuesday, August 24, 2010

Maths Lesson @ S1-03 - Relationship between 2 Linear Graphs and a Quadratic Graph

Today attended the lesson by Jason... which led the students to see what the link between 2 linear equations with a quadratic equation.

The scaffold came through several activities:

(1) The first activity of this lesson is to find a linear equation when given 2 points.

If A (2, -2) and B (-2, 4), find the equation of the line AB.
And hence, state the value of the x-intercpet and y-intercept.

Students were able to use the formula to find the gradient using the formula,
(y2-y1)/(x2-x1), which is - 3/2.

One question from the student was...
"when m could be written as 6/(-4) and subsequently (-3)/2.
So, does it matter where the negative sign is? Is it with numerator or the denominator?"
Hm... while the response to the student was, "It doesn't matter..."
Well, I think it's where the students always get confuse over... at any level.
So, would writing - 3/2 helps? Maybe... when the negative sign belongs to the entire fraction 3/2.

It was also noted that students were introduced to the fact that the y-intercept can be expressed as (0, c) that is, when the x coordinate is zero.
Well, this is an important concept that students must understand.

To find the y-intercept, it was quite obvious that students knew that they would substitute any of the coordinate to the "half-found" equation: y = -3/2 x + c

(2) Indeed, I enjoyed the next part of the activity :) an interesting one - getting students to learn the 'beauty' of expressing the equation in the form of x/a + y/b = 1

I could not recall my teacher was able to explain so clearly what's the significance of expressing a linear equation in the form x/a + y/b = 1
Hm... I think this was introduced in Secondary 3 Additional Mathematics then. The key deliverable at this point, I guess is leading the students to be able to how the x- and y-intercepts could be so well represented in an equation expressed in the form of x/a + y/b = 1

The process to elicit responses from students really made their minds spin. Hahah...

The best part is really asking the students "Why" the a is the intercept and why b is the y-intercept... and how they derive the explanation through application of the following concepts and solve algebraically:
  • what happens to the equation when the line cuts the y axis (i.e. to find the y-intercept)? i.e. x coordinate = 0, hence y = b.
  • similarly, to show why a is the x intercept. The same concept applies: when the line cuts x axis, the value of y is zero. Hence x/a + 0/b = 1; therefore, x = a.

It really required them to have solid understanding of the intercepts (i.e. the y-coordinate of the x-intercept is zero while x coordinate of the y-intercept is zero, too).

  • It sounds easy, but definitely not something simple for a 13-year old mind who just started to touch-base with the Cartesian Coordinate Geometry.
  • Indeed, I'm really curious to find out how many in the class would be able to explain...
(3) The 3rd part was something new to me... which did not cross my mind in the past until the recent discussion when Sarah proposed the possibility of looking at the relationship between linear lines and parabolas, focusing at the roots.

In fact, I like it very much... it's like gaining enlightenment at this age - making new discovery in what I was familiar with!

Students observation, for students to the relationships of lines passing through the same point:
What kind of lines pass through the point (-2, 0)?
  • What kind of gradient and y-intercepts do we get?

2 linear equations contributed by students:
  • y = x + 2 [root = -2]
  • y = x - 4 [root = 4]
  • y = (x + 2)(x - 4) [roots = -2 and 4]

Why is the roots (x-intercepts) of the straight lines are the same as the roots of the parabola?
I guess that's where technology came in very handy that allows students to see how the lines coincide with each other.

Of course, the other part was when students were guided to check out the "signs" of the gradient and y-intercepts at the 4 different quadrants.

By the way, I wonder, after this first introduction, how many students were able to explain the process they went through in this activity.
All in all, I enjoyed this very energetic lesson :)
  • The explanation was clear... though it's a bit quick in the pace.
  • On the other hand, I think too much things were packed into this 1-hour lesson.
  • Perhaps some breathing space for the students to attempt some tasks would help to check their understanding.