## Sunday, August 18, 2013

### Reflection 6 - August 17, 2013

Mathematics is the study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols.

“Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual ability in logical reasoning, spatial visualisation, analysis and abstract thought” CPDD MOE

Ms Peggy Foo taught on lesson study, enrichment lessons and about differentiated instruction. The activities are engaging, challenging and fun.

Activity: Card Trick
Arranging the cards in a row and moving cards which have been removed by moving them upwards and another method is to draw our thoughts on solving the ‘trick”

Implications for Instruction:
• Working with teachers
• Manipulation of poker cards
• Spelling the numbers,
• Challenging and interesting.
• Prior knowledge
• Patterning & generalization

Activity: Paper Art (cut out figures from paper

• Anticipate a pattern
• Relate similarities
• Simple to complex

What do you see?
• Describe
• Observe
• Visual

What do you think?
• Inferring from patterns
• Relationship, able to connect

How do you wonder?
• Reason
• Infer/generalization

Activity: Story- telling:
• Predict the story based on given words
• After reading - retell story through pictures or text

What have I learnt for this final session?
The following activities that reinforce what we as teachers and children need to develop for learning Mathematics:
• Card trick: Patterning and generalization
• Paper art: Visualization and patterning
• Story telling: Pattering and differentiation – content, process, product

### Reflection 5 - August 16, 2013

In the fifth session, though I am unable to attend, discussion with course mates, I understand that there is an additional way that children learns Mathematics which is communication.

The five learning ways in which children learn mathematical skills:
• Visualization
• Patterning
• Number sense
• Metacognition
• Communication

What have I learnt for this fifth session?
• 5 ways in which children learn mathematical skills.
• Functional Mathematics – money, time, weight
• Trigonometry – mathematics that deals with relations between the sides and angles of plane or spherical triangles and the calculations based on them

### Reflection 4 - August, 2013

For this fourth session, we revisit the ways the children learn about Mathematics and Richard Skemp who is pioneer in Mathematics Education who first integrated the disciplines of mathematics, education and psychology.

Children learn mathematical skills through:
• Visualization
• Patterning
• Number sense
• Metacognition

Richard Skemp:
• Instrumental Understanding – to know how to do a specific task quickly.
• Relational Understanding - can relate to what one know before, explore further, more concerned with the process
• Conventional Understanding – understand the meaning behind.

Dienes
• Systematic variation - experience variation through, for example, concrete tools, multiple representation of a concept

What have I learnt for this fourth session?
• Ways  in which children learn Mathematics
• Richard Skemp’s theory on understanding Mathematics
• Reinforcement on the approaches of teaching Mathematics to Children:

1. Scaffold, role model, explore
2. Concrete, pictorial, abstract
3. Systematic variation

### Reflection 3 - August 14, 2013

The definition of subitize defined in Dictionary.reference.com is to perceive at a glance the number of items presented, the limit for humans being about seven.

The following definitions and how to remember is from http://www.mathsisfun.com/numbers/cardinal-ordinal-nominal.html:

## Cardinal Numbers

• A Cardinal Number is a number that says how many of somethig there are, such as one, two, three, four, five.
• A Cardinal Number answers the question "How Many?" It does not have fractions or decimals, as it is only used for counting.
• How to remember: "Cardinal is Counting"

Nominal Numbers

## A Nominal Number is a number used only as a name, or to identify something (not as an actual value or position) How to remember: "Nominal is a Name".

What have I learnt for this third session?
• Subitizing in Mathematics
• Reinforcement of cardinal, ordinal and nominal numbers
• Revisit what I learned as a student on subtraction using fractions.

### Reflection 2 - August 13, 2013

For second session, we learn the usefulness of Ten Frames for teaching counting to children.  Besides, it is also used for teaching addition (add on)

Activity: Jack and the Beanstalk (using Ten Frames)

To find how many beans are there altogether?
• 3 Ten Frames - 5 beans, 6 beans and 7 beans in each frame respectively.
• Count in fives, then add 1 from 2nd frame and 2 from 3rd frame: 5, 10 , 15 + 1 + 2 = 18

The advantages of using the Ten Frames:
• Visualization
• Prior knowledge of numeral 1 to 10.
• Explore and arranging different ways to count in 5s (conserve)
• Putting 1 object (bean) on the frame develop one to one correspondence

What have I learnt for this second session?
Children learn mathematical skills through:
• Visualization
• Patterning
• Number sense
• Metacognition
Teachers to help them learn through:
• Scaffolding, modelling and explore
• Concrete, Pictorial and Abstract -
"The concept of prime numbers appears to be more readily grasped when the child, through construction, discovers that certain handfuls of beans cannot be laid out in completed rows and columns. Such quantities have either to be laid out in a single file or in an incomplete row-column design in which there is always one extra or one too few to fill the pattern. These patterns, the child learns, happen to be called prime. It is easy for the child to go from this step to the recognition that a multiple table, so called, is a record sheet of quantities in completed multiple rows and columns. Here is factoring, multiplication and primes in a construction that can be visualized." Brunner 1973.

### Reflection 1 - August 12, 2013

This evening was the first session for EDU Elementary Mathematics.  It's about how children learn Mathematics.  There were 3 lessons on problem solving.  Lesson 2 was about using a person's name to solve a Mathematical problem.  The activity is in about which letter is counted 99th in a name.  I chose this activity for my reflection as I find it very interesting and engaging to use a personal name as an activity to solve mathematical problem.

I use my own name to find which letter is counted 99th.  I count and write down the numbers in sets counting from left to right, then right to left for the next set till I reached 99.  As I was counting the sets half way through, I observed there was a pattern of numbers.  From the first letter of my name, I just need to add 14 to alternate set till I reach 99.  Upon realisation this pattern and reaching the number 99, the feeling was like the 'light bulb' in my mind lighted up and “ah.ha.. moment. Wow! “

What have I learnt for this first session?
• Concrete - counting the numbers
• Pictorial - writing the numerals in a row
• Abstract - seeing the pattern of 14 per alternate set in the mind.

## Monday, August 12, 2013

### Pre-course Reading - Chapter One and Two

Dear Parents,

To learn and teach Mathematics to children in the 21st Century, we have to understand our personal beliefs and perceptions.  It is no longer about drilling and doing numerous mathematics exercises through assessment books and homework.

It is through the five processes that are essential components of learning and teaching mathematics:
• Problem Solving – build new mathematical knowledge through problem solving
• Reasoning and Proof – develop and evaluate mathematical arguments and proofs
• Communication – talk about, write about, describe, and explain mathematical ideas to peers, teachers and others
• Connections – recognize and use connections among mathematical ideas, apply mathematics in contexts outside of mathematics
• Representation – create and use representations (graphs, symbols, charts, manipulative, diagrams) to express mathematical ideas and relationships

Through these processes, the benefits of relational understanding is rewarding and necessary:
• Effective learning of new concepts and procedures – actively building  their existing knowledge
• Less to remember -  information are stored and recall as single entities
• Increased retention and recall – able to retrieve ideas through reflection of ideas that are related
• Enhanced problem-solving abilities – better understanding of relationship between a situation and a context enable use of a particular approach to solve a problem
• Improved attitudes and beliefs – positive self-concept and confidence in his/her ability to learn and understand Mathematics. “I can do this! I understand!”

With this, it’s a departure from drilling methods, assessment books and homework.

Let’s make learning Mathematics fun and interesting!