Friday, June 01, 2007

Maths Teachers Conference 2007

On the whole, feel that the conference was not solid enough... in fact, throughout the whole day, thought only 2 items worth the time and travelling - (i) Guest Lecture by Prof Jin Akiyama - 7 Questions for Mathematics Teachers (ii) Workshop S3 by A/P Yap Sook Fwe - Data Analysis with IT). Thought they are the saving grace of the event.

The Opening 0845 - 0915: In fact, there wasn't much for this session, especially when I was seated in LT12... watching the 'live' broadcast - it's like what mentioned to the team, perhaps, we could just turn up during tea break. Nevermind, one learning point - never never let an opening ceremony to 'stand-alone' as a session. It vows to generate lots of grumbling... especially when people have to travel from all over the island to a ulu-ulu place in the west...

Keynote (Secondary)1a on Mathematical Literacy - the Case of Quantitative Reasoning (Dr Liu Yan): Don't quite appreciate the lecture. Hm... maybe I 'operated' at a slower frequency... Thought that the context of the presentation was not well set out. It was too quick, esp at the beginning. Probably there's an assumption knowing what's "Quantitative Reasoning".

At the start, there was an attempt to break down the terms "Quantitative Literacy" (as a lead to the reasoning):

  • "Quantitative literacy" has been defined from various perspectives - as a set of basic skills, higher order thinking skills, or even ICT related tools. It touches on a several elements, that includes Confidence in Mathematics, Cultural Appreciation (of course, ie. Maths), Data Interpretation, Number Sense, Logical Thinking, Practical skills, Decision making... and more (that I wasn't quick enough to jot down).

  • "Quantitative" is used interchangeably with "Mathematics"

  • "Literacy" can also be simply interpreted as the minimum ability to read, write and calculate.

Moving on to "Quantitative Reasoning", which is the key of the entire presentation:

  • It comes in 4 combinations - with 4 magic words - combine, compare, additively & multiplicatively: (i) Combine quantities additively (ii) Compare quantities multiplicatively (iii) Combine quantitites additively (iv) Compare quantities multiplicatively.

  • There, they moved on to analyse pupils' responses to problem questions in little 'packets'.

  • It's amazing that a simple word problem can be broken down into "Quantities" and "Quantitative Relationships" {ok, from this part of the presentation, "I'm back" again}.

  • So, what I could conclude from this presentation is: No matter how simple a task is, it can still be broken down into parts we never thought of - and for the sake to understand how the young children work, it worth the time and effort and the extent of such research(?). Well, I guess that's what 'mathematicians' are for - to devote time to ask why and investigate. On the other hand, having gone through discussions at work, just wonder, do findings from just "16" students can justify any solid conclusion?

2 questions used in the research:

  • Q1: A group of tourist paid $200 for admission to a theme park. Adults paid $8 each and children $4 each. If there were 7 more adults than children, how many adults and children are there in a group?

  • Q2: In a certain town, 2/3 of adult men are married to 3/5 of the adult women. What fraction of adults in the town are married?

I think my key takeaway is really... to realise how powerful the model method is, to solve Q2. Of course, it is also the thinking process that I went through in the course of solving the problem - a fair bit of interpretation and careful manipulation of the fractions and pieces.

Keynote (Secondary) 1b on Multiple "Literacies" of Representations - the Case of Model Method and Letter Symbolic Algebra (AP Ng Swee Fong):

This keynote deals with something closer to the hearts of secondary school maths teachers, in particular those who teach Sec 1. Being one, I know how painful it is to convince and 'convert' a model user to a 'letter symbolic algebra' user. Like what Prof Ng shared, often secondary school teachers are not aimed with enough reasons to convince the pupils the necessity of using letter symbolic algebra. I guess, partly because being trained in secondary maths in the early years, we were not exposed to the model method - be it in our school days or during our training days at NIE. So, we don't know much of the model method - its strengths and weaknesses! Of course, after a while, we found one reasons to convince pupils something that models can't do - in the presence of negative numbers! In the first place, there were times we wonder... hey, we learnt the letter symbolic algebra since young - in primary schools! So, why can't pupils nowadays do the same too?

On one hand, it seems like pupils are the "immigrant" to the world of letter symbolic algebra... on the other hand, we, teachers are the immigrant to the model method, too!

One thing caught me in surprise was the use of Functional Magnetic Resonance Imaging Method! Wah! The study of how the brain works come into play! Though find the reasoning pretty force-fitting... but it tells one thing: "Think out-of-the-box" to look at other possibilities! OK, what this study shows is , using the letter symbolic algebra method is more cognitively demanding, as compared to using the model method. Just wonder, when this model method was introduced, are there already studies that highlights this aspect?

In fact, AP Ng mentioned casually that perhaps the model method would be suitable for the primary school children since it is a less demanding in solving problems... So... our brains can weather more demands, compared to the younger generations nowadays???

One website on modeling (prototype):

Guest Lecture on 7 Questions for Mathematics Teachers (by Prof Jin Akiyama)

Mathematics came alive in this session! Have not been so engaged with a Mathematics-related talk, since the Stiatistics session at NIE during my DDM course. Wah! Maths everywhere, who would have link 'chim' ideas of ellipses to 'satelite dish' in Singapore? Who would have brought in some much manipulatives to the class to do mathematical experiment? "You mean mathematical experiment in class?", one will give you that 'look'.

A couple of interesting ideas:

  • Circles inscribed within quadrilateral. But is it true? Try it! Rotate a 'quadrilateral' on a circular disc at high speed. If we see a circle - yes! Also, to explore the sum of lengths of opposite sides - they are the same! Hey, I guess not many of us know.
  • The use of models to learn statistics! BTW, I like the tower-like model to learn multiplication. That's fun and I would love to own one :D
  • The amazing means to find the minimum network connecting all points on a plane - with just soap water!
  • Everything about Maths become so exciting!

More info...

Workshop S3: Data Analysis with IT by AP Yap Sook Fwe

This is an introductory session (to me) on the box-and-whisker plot.
Something new, yet is made easy to understand :D

One thing pointed out was to look out the type of data given:
  • Catagorical data: example - survey data. Appropriate representation includes bar chart, pictograph and Pie Chart.
  • Numerical Data: where the 'horizontal axis is usually number.

The hands-on session using winstat is helpful. In fact, it is a freeware that's pretty to use.

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