Sunday, 18 August 2013

Maths - Day 6 Blog

How to use Children's Books to Teach Maths?

After reading the story book, we would encourage children to retell the story in round robin through

1) pictures
2) texts

The class teacher can design a mathematical task for the children.

She must always bear in mind - 'How can this mathematical task be differentiated for different


Differentiation Instruction (by Tomlinson)

1) By content

2) By process

3) By product



Children's literature is an effective tool for mathematics instruction because it:
  • incorporates stories into the teaching and learning of mathematics
  • introduces math concepts and contexts in a motivating manner
  • acts as a source for generating problems and building problem solving skills
  • helps build a conceptual understanding of math skills through illustrations

What Is Differentiated Instruction?

Differentiation means tailoring instruction to meet individual needs. Whether teachers differentiate content, process, products, or the learning environment, the use of ongoing assessment and flexible grouping makes this a successful approach to instruction.
At its most basic level, differentiation consists of the efforts of teachers to respond to variance among learners in the classroom. Whenever a teacher reaches out to an individual or small group to vary his or her teaching in order to create the best learning experience possible, that teacher is differentiating instruction.
Teachers can differentiate at least four classroom elements based on student readiness, interest, or learning profile:
  • Content – what the student needs to learn or how the student will get access to the information;
  • Process – activities in which the student engages in order to make sense of or master the content;
  • Products – culminating projects that ask the student to rehearse, apply, and extend what he or she has learned in a unit; and
  • Learning environment – the way the classroom works and feels.

So enjoy reading and have fun with Maths ....

Math - Day 5 Blog

Properties of a Parallelogram

How to solve this PSLE question ?

I realized that we (girls) could have solved this problem faster and easier if we knew the 

properties of a parallelogram.


more ...

A 4-sided flat shape with straight sides where opposite sides are parallel.

* opposite sides are equal in length, and
* opposite angles are equal (angles "a" are the same, and angles "b" are the same)

NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

We finally solved the problem ! 

Math - Day 4 Blog

Pick's Theorem 

Pick's Theorem was first published in 1899 by Georg Alexander Pick. The theorem gives an 

important formula for the area of lattice polygons.

A geoboard  is a good way to explore these lattice polygons. A geoboard is a piece of wood 

or board with pegs or nails arranged in a regular grid. The board represents a section of the 

plane and the pegs or nails are the lattice points. Children can stretch rubber bands over the 

lattice points to create polygons. 

These strange shapes above are examples of  lattice polygons, which is a polygon whose lies 

on points in the plane that have integral coordinates.

How to calculate its area?

By simply counting the lattice points! Count the number of lattice points on the boundary of the 

polygon (b) and the number of lattice points inside the polygon (i), then the area (A) of the 

polygon is given by Pick's Theorem

                                                            Area (A) = i +(b/2) - 1

What will children learn from this activity?

Children will learn

1) to look at the number relationships to determine Pick's theorem

2) to use this theorem to predict the area of more complex shapes

Math - Day 2 Blog

Teaching Ten Frame - More and Less

This video is about teaching children and parents about 'a ten frame'.

A ten frame is a simple math tool that helps children :

1) keep track of counting
2) see number relationships
3) learn addition to 10 
4) understand place value

Working on ten frame is an opportunity that will help children become better at counting as well as indicating quantities accurately.

Math - Day 3 Blog

Matching Skills

To Teachers and Parents,

Q : How to teach 'matching' and 'sorting' to children in the correct order? 

*Do you want to play the game first? (Click the two characters to switch) 

Matching and Sorting (Each day there is a variation)

a) Day 1 - match by type, colour, orientation or size

b) Day 2 - match

c) Day 3 - match by Colour                                                            

d) Day 4 - match by Design - Reception

e) Day 5 - match by Design - Production - children are asked to colour.

f) Day 6 - match by Functions

g) Day 7 - sort one out

h) Day 8 - sort which is essentially many-to-one matching

i) Day 9 - sort - generalizing to less familiar situations

The benefits of matching and sorting help children to improve in their thinking skill, logical skill, visual skill, mathematical skill and receptiveness.


Wednesday, 14 August 2013

Reflection (1)

It has been a long long time since I played with tangrams. I always marvel how my kindergarten children played with it. They always feel very proud with their 'masterpieces'.

It has been a very interesting evening, learning about tangrams, guess and check, equal parts question and MOE maths syllabus expectation.

I have a good time fiddling and rotating the tangrams. I believe the benefits of playing with tangrams will help our children to share and talk about the shapes and pictures they have made. I believe as our children explore, they will become more familiar with the size and the shape orientation of the pieces. Then they may begin to discover the properties and the relationship between and among the seven pieces.

As what Dr Yeap summarizes the three ways of teaching (methods):
1) Do not do anything - let the children explore
2) Scaffolding
3) Role model

I like the idea of the 'Journal'. P1 children are asked/encouraged to pen what they have learned in the journal - 'Journal is the Mathematics'. I believe this method is quite effective. It will indeed help the P1 children to learn, revise and reflect on the concepts. In the long run, this method will actually help to build their maths foundation well.

Sunday, 11 August 2013

Pre-course reading Chaps 1 & 2

Chapter 1 and 2

In chapter one, I have comprehended that the five content strands defined by Principles and Standards are number and operation, algebra, geometry, measurement and, data analysis and probability.
According to the authors, these five content strands are emphasized differently in different grade bands. In comparison, in Singapore context, number and operations are very heavily emphasized in primary school and algebra is seen to be taught in secondary school onwards.
According to the Principles and Standards, the five process standards are referred to 'the mathematical processes through which students should acquire and use mathematical knowledge' (p. 3). The five process standards consist of problem solving, reasoning and proof, communication, connections and representation. According to the authors, 'To teach in a way that reflects these process standards is one of the best definitions of what it means to teach 'according to the standards'' (p. 4).
In this chapter, I have learned and perceived that to become a teacher of mathematics, 'She needs to have a very good knowledge of mathematics. She needs to be persistent and have a positive attitude toward the subject of mathematics. She must always be ready for change. Most importantly, she must have a reflective disposition to make time to be self conscious and reflective' (p.10).
In chapter two, according to the authors, this chapter focuses on 'learning theories of teaching developmentally and the knowledge necessary for students to learn mathematics with understanding' (p.13).
I fully agree with the authors in order to help student learn mathematics 'the importance of both words in 'productive struggle'- students must have the tools and prior knowledge to solve problem, and not be given a problem that is out of reach, or they will struggle without being productive' (p.15).
I have also learned that according to the constructivism and sociocultural theories, 'the best learning opportunities takes place when the teacher encourages and engages the students in using their own knowledge and experience to solve problems through social interactions and reflection' (p. 29).
(Walle, J. V., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching
            developmentally (8th Edition). New Jersey: Pearson Education.)