Reflections

Session 1 : 22 August 2011

Doing Math but "not doing Math"

Thanks to Dr Yeap, I now have the opportunity to enjoy the process of maths rather than my schooling days (I am now 54 yrs old) of hating math because it is always about who has the right answers first. Those days, I never heard of pattern, making connections.... All I remembered was "just learn the steps by heart"; "recite your multiplcation tables"; "don't ask me why like that. You will get the right answers. Just follow steps. "
Lesson 1: Name Problem
Lesson 2: Sound of Numbers
Lesson 3: 5+6+7
Lesson 4: Arrange the cards
Lesson 5: Number Titles Puzzles

I enjoyed the above hands-on lessons very much and could feel my brain nuerons zapping to make connections, searching for patterns, count, adding, taking away and so on.

My key take-away is how Dr Yeap conducted the lessons, his materials used, his prompts and others. He uses very accurate instructions, prompts and queations which I as a teacher will borrow and use. Some of these are:
> "write down and make a list and then models how to do it".
> "look for a pattern in the ones place".
> "are your sure? Explain"
> "do you think so? Why? How come?"
> "You are correct. Tell us how you know".

My mindset for maths has now taken a new perspective. I now do not see Math as Math, but "Mathematics is an excellent vehicle for the development and improvement of  intellectual competence ... ". (MOE)

As a teacher in early childhood education, my philosophy has always been to give the children "opportunity" to explore and construct to learn.
Process is more important than the product.

I will definitely share the following information with my colleagues.

How Do You Use Numbers? (The Uses of Nymbers)

1) Rote Counting

2) Rational Counting

- cardical number (number of items counted)

- ordinal number (position in space and position in time)

- nominal number (number used to identify. e.g. bus number)

- measurement number (continuous qualtity and infinite quabtity)
- proportion ( from Session 5)

Know That The following Pre-requisite Skills Are Needed For  Counting 
- be able to classify

- be able to do rote counting

- understand and appreciate that the last number uttered is the number of item 

  being counted.

- have one-to-one correspondence

Other useful termologies/teacher tips

- number fact

- count all

- count on

- cummutative property of addition (5+7 is the same is 7+5)

- skip counting (2s. 5s, 10s ...)

- conservation of numbers (move them around but quantity remains)

- Initially, always use identical objects for counting, then move on to

  introduce change ot colour. You can only count things that are in the same 

  set. You cannot add oranges to apples, unless you change the unit to fruits.

- ten-frame cards which are cheap to produce, are useful for  training children 

  to see pattern and develop number sense.

Wow! I am more confident teaching children Maths already and am eager to use these activities.

Session 2 : 23 August 2011

"Subitize" was the word of the day. According to Dr Yeap, if you look at the thing and know the numbers without the need to count them, you can subitize.

I really enjoyed the "Holiday Games" . The "magic" with the die was really fun, but most importantly, the children would like "myself " in the class, observed and discovered the patterns and the numerical logic behind it.

Some Big Ideas :

• Thinking skills
• Problem solving skills
• Meta Cognition - manage information
• Looking for patterns
• Communication - justification / representation / reasoning
• Visualization
• Number sense
• Generalization

Session 3 : 24 August 2011

This evening, I felt creative and had sense of visualisation. I totally enjoyed it and would like my children to experience this achievement. Using 5 cubes, many different "toys" were constructed.

This task teaches conservation of number. No matter how they are arranged, the number of cubes remains the same.

Peggy shared with us "Lesson Study", "Mathematical Investigation" and "Recent PD Trends". These were comforting to me - our future generations should be in good hands. Yes. Learning is a continuum.

Session 4 : 25 August 2011

"Word Problems Disected" - Addition and Subtraction (Lesson 15)
There are three types of word problems, namely:

• Change
• Part/Whole
• Compare

All word problems have a situation, an initial amount, a change amount and a final quantity. This simple explanation meant a lot to me.

Children may be overwhelmed by the sentences in the problem. As a preschool teacher, I will address their fear and spur them to explore. Model them to do  one sentence at a time, using appropriate concrete manipulatives .

Example of Change Situation:

Tommy has 31 marbles. (concrete quantities)

He gave Peter 19 marbles.

How many marbles has he left?

Example of Change Situation:

Rashda had $37 in her bank. (continuous quantities)

She spent $19 on books.

How much money has she left?

Example of Part/Whole Situation:

There are 37 children in a class.

19 are boys. How manay girls are they?

Example of Comparison Situation:

I have 37 pens. I have 10 pens more than you.

How many do you have?

Lesson 16 : Equal Parts

I had to re-learn. Thanks to Dr. Yeap I will now avoid using the incorrect terms.

Key learning points:

• When you can make equal parts, you can name them
• The name is "one half " "one third" "one fourth".... (Not one upon four...)
• Fraction as part of a whole
• Fraction as part of a set
• Being equal doesn't need to be of the same shape
• Being equal need not be identical parts

Session 5 : 26 August 2011

It was Visualization Galore"
Lessons 17, 18, 19 & 20 had me on the edge of my chair visualizing.
Division of fractions and looking at area.

• How many fourths can you make from a piece of square paper?
• In one how many one fourths are there?
• One unit can cut into equal units. Once they are equal, we can rename it.

• Two methods of dividing fractions (i) model method and (ii) change to whole number method
• 5 Transformation of shape # reflect # rotate # translate (no change to the shape) #stretch #shear (will change the shape)

• Polygon is a closed figure  

Lesson 20

Pick's Theorem on calculating the area of a figure was discussed. His theory was interesting, but what another possible idea suggested in class was even more amazing.

Lesson 21

Graph Making (also covered during last session)
Revision was given to my priior knowledge that there are 5 common types of graph namely, Picture Graph, Bar Graph, Line Graph and Pie Graph.
What I did not know:

• Width of Bar Graphs must be equal (best used for category data)
• Histogram - the area counts and must be arranged in order. (best for continuous data)
• Line Graph is best used for plotting time concerns
• In pie graph the area of each sector makes the calculation. If comparing data, diameter of pie grpah must reflect the difference of toal being compared. 

Session 6 : 30 August 2011

This last session primary focused on Assessment. Dr. Yeap through his in-class task, showed us how assessment need not be paper and pencil test alone. Oral test/interviews as well as observation during classroom time are also assessment opportunities. One candid example was "Telling time". Why make the chidren draw hour hand, minutes hand, when one can simply ask them to TELL you the time.

Task at the MRT

A group task was given where we had to calculate the height between the basement level and the street level.
There were four flights of steps as seen in drawing below. 3 were of 16 steps each and one of 14 steps. The height of each step is 15cm.  Therefore 16 x 3 + 14 = 62 steps . 15 x 62 = 930cm.
Therefore, the height between the basement level and the street level is 930cm.

"Thank you Dr. Yeap". What I feared of math has been erased and I am finding and seeing more math in the world around me. Hope to have you "solve my problems" in the "Developing problem solving skills" module.