Learning Elementary Mathematics has finally come to an end however, the journey to pursue more insights to deepen the content on the subject matter continues.

The three things that I have learnt during these 6 days:

1. Language and mathematical instructions

As teachers equip themselves with enough content knowledge to guide the children acccordingly, they have to be aware of the importance of giving explicit instructions. Mathematical verbs such as compare, divide and subtract give children a better usage of the terms as they experience with the various mathematical activities. The incorrect usage of the words "less" and "lesser" was also highlighted to ensure such mistakes should be avoided.

2. Dienes Zolton theory of variability

The choice of materials and examples plan for the activities is carefully and purposefully selected to give children with variations in the tasks.

3. Four critical questions in planning a lesson

The following questions guide a teacher as she plans her activities:

a) What is it that I want the children to learn?

b) How do I know children have learn?

c) What do I do if I have struggling children?

d) What do I do if I have advance children?

These are the two questions I wish to ask:

1. Is it incorrect for teachers to use the term "oblong" in replacement of "rectangle"?

2. How do I ensure that a child is able to conceptualize the number sense?

# EDU 330 Elementary Mathematics

## Monday, 23 July 2012

### Use of Technology in Mathematics

The vivid images and sound effects make the learning both interactive and effective as a follow up to the concept or topic that is introduced.

For an example, the concept on subtraction can be further enhanced by the famous Nursery rhyme entitled, "Five Little Ducks".

The following video clips from the YouTube can be used for the activity to engage children in their sing-a-long as well as enhancing on a concept learnt.

### Day 4: 19 July 2012 - A New Learning That Surprises Me

Geometry

Learning shapes can be equally be a mind-stretcher for you

when you get to explore with cutting a shape to form a new particular shape of the same area. That was exactly the experience I went through and was totally awed by the experiential learning.

Once again we were subtly challenged to give many different ways of forming a rectangle of a similar area from the original trapezium given. The surprise came when we google the definition of a rectangle that mentioned, "A rectangle is any quadrilateral with 4 right angles." With reference to that, my coursemates and I learnt that a SQUARE is a RECTANGLE. Therefore, it is best to prevent giving shapes like squares and rectangles on paper activities for children to identify any one of the two shapes mentioned.

It took Dr Yeap a few attempts to convince the statement though until we succumbed to the fact and took a mind shift to accept what the norm had taught us. It will be useful to read the van Hiele levels of geometric thoughts on page 403 of the text to gain more insights.

Learning shapes can be equally be a mind-stretcher for you

when you get to explore with cutting a shape to form a new particular shape of the same area. That was exactly the experience I went through and was totally awed by the experiential learning.

Once again we were subtly challenged to give many different ways of forming a rectangle of a similar area from the original trapezium given. The surprise came when we google the definition of a rectangle that mentioned, "A rectangle is any quadrilateral with 4 right angles." With reference to that, my coursemates and I learnt that a SQUARE is a RECTANGLE. Therefore, it is best to prevent giving shapes like squares and rectangles on paper activities for children to identify any one of the two shapes mentioned.

It took Dr Yeap a few attempts to convince the statement though until we succumbed to the fact and took a mind shift to accept what the norm had taught us. It will be useful to read the van Hiele levels of geometric thoughts on page 403 of the text to gain more insights.

### Day 2: 17 July 2012 - Chapter 8 to 13

Relationships Between Numbers 1 Through 10

As children are facilitated and taught to solve problems, simultaneously, they are also trained to look out for patterns and number sense thus developing the visualization skills. With the acquired concept of cardinality and counting meaningfully, children could develop the following number relationships that are useful:

Besides being able to count on one or two more or count back one or two, children should know that 5 is 1 more than 4 and also 2 less than 7. Hence, children's numeric relationship is developed.

Grouping of items or variables in 5s or 10s is is an ideal strategy to help children when counting big quantity. For example, 1 group of 5 and 2 things or 1 group 10 and 6 things. The ten-frame model can be an aid to demonstrate the relationship.

Similar to number bonds, children will be able to see a number that is made up of 2 or more parts.

As children are facilitated and taught to solve problems, simultaneously, they are also trained to look out for patterns and number sense thus developing the visualization skills. With the acquired concept of cardinality and counting meaningfully, children could develop the following number relationships that are useful:

**1. One and two more, one and two less**Besides being able to count on one or two more or count back one or two, children should know that 5 is 1 more than 4 and also 2 less than 7. Hence, children's numeric relationship is developed.

**2. Anchors of 5 and 10**Grouping of items or variables in 5s or 10s is is an ideal strategy to help children when counting big quantity. For example, 1 group of 5 and 2 things or 1 group 10 and 6 things. The ten-frame model can be an aid to demonstrate the relationship.

**3. Part-part-whole relationship**Similar to number bonds, children will be able to see a number that is made up of 2 or more parts.

### Day 1: 16 July 2012 - Inspirational and Interesting

As a student, I will always look forward to the teacher who will be conducting the lesson. Not by their physical attributes but rather how much I could connect in the class and make my learning a worthwhile one. In my opinion, an efficient teacher is very important to engage the students and inspire them with the gained knowledge that is delivered. A U.S. educator once quoted, "A teacher who is attempting to teach without inspiring the pupil with a desire to learn is hammering on a cold nail" (Horace Mann 1796 - 1859).

Having said that, the content alone is insufficient to ensure learning takes place. Besides the series of nteresting hands-on exercises, I must thank Dr Yeap for being very loud and clear in his explanations throughout the entire class. I could sense his energy and excitement in his lesson delivery that is engaging as well as mind boggling. Most importantly, he gives a different perspective towards the learning of Mathematics.Somewhat like a young learner, I was amused by the Spell Number Name (Card) activity. Interestingly, it was not simply magical however more into challenging you to see the pattern in the card arrangement.

Having said that, the content alone is insufficient to ensure learning takes place. Besides the series of nteresting hands-on exercises, I must thank Dr Yeap for being very loud and clear in his explanations throughout the entire class. I could sense his energy and excitement in his lesson delivery that is engaging as well as mind boggling. Most importantly, he gives a different perspective towards the learning of Mathematics.Somewhat like a young learner, I was amused by the Spell Number Name (Card) activity. Interestingly, it was not simply magical however more into challenging you to see the pattern in the card arrangement.

## Monday, 16 July 2012

### Chapter 2: Exploring What It Is to Teach and Do Mathematics

__Reading Reflections__
Moving on to Chapter 2, I was amazed by the explanation
given about the co-relation between science and mathematics. While one is a
process of finding out or making sense, the other is the science of concepts
and processes that have pattern and logical order. Therefore, mathematics
learning is the process of finding and exploring the patterns and order, and then
making sense of them.

I am greatly motivated by this statement by Van de
Walle, Karp & Bay-Williams, 2010 that states, “Even the youngest
schoolchildren can and should be involved in the science of pattern and order.”
However, my biggest challenge would be to find out how I could teach children
doing mathematics and engaging them in the science of pattern and order. As far
as I could recall my younger days of learning mathematics, often I could not
see these patterns and logical order nor find meanings. The hardest and most
inefficient way for me to learn mathematics was then by memorization and that had
resulted in me struggling to understand the concepts as they became more
difficult.

In order to develop the life-long learning for
children in the twenty-first century, it is mentioned that besides providing
materials and activities for children’s exploration, children have to be
engaged in a higher-level thinking when teachers pose questions using
mathematical verbs such as compare, explain and describe that encourage
children to make connections and understand the mathematics they are exploring.

With reference to children’s learning styles,
teachers should continuously provide opportunities for them to connect ideas
and build new knowledge. Children are actively participating in mathematics
discussions where they reflect and learn through the errors they make.

## Sunday, 15 July 2012

### Chapter 1: Teaching Mathematics in the 21st century

__Reading Reflections__
Chapter 1 reveals the series of changes that have
taken place in the mathematics education. It is a constant effort by the
National Council of Teachers of Mathematics (NCTM) to enhance the teaching and
learning of the subject matter since the past two decades. It seems change is
here to stay and much prominent and excessively discussed in this twenty-first
century. In the education sector, change is inevitable in order to achieve and sustain
the quality standards that will benefit both teachers and students alike.

As a practitioner in the early childhood education,
I am an advocate for a holistic development of the children through a
curriculum that is well-balanced and integrated. Therefore, teaching
mathematics to these preschoolers takes a paradigm shift and now, we could take
reference from the reformed Principles and Standards for School Mathematics
(NCTM, 2000).

The six principles form the pillars of the
Principles and Standards for School Mathematics and I wish to highlight the
teaching principle that mentions the critical roles of teachers to provide the
learning experiences to deliver high quality mathematics education. Teachers
who are equipped with the knowledge of how their children learn mathematics
will then “select meaningful instructional tasks and generalizable strategies
to enhance learning” (Van de Walle, Karp & Bay-Williams, 2010). Teachers
are the catalysts to facilitate the entire learning. “Their actions are what
encourage students to think, questions, solve problems and discuss their ideas,
strategies, and solutions” (NCTM, p.18). Opportunities for discussion and
sharing of ideas should be made available for children to get affirmation of
their learning.

That leads me to discuss one of the five process
standards that are equally important. The Connections standard has stated that
there should be connection within and among mathematical ideas so children will
see that each topic is a build on from the previous topic learnt. Similarly, mathematics
learning should be connected to the real world thus making it significant to
apply in children’s daily activities.

At this juncture, I strongly feel that regardless
of what subject or concepts taught teachers must ensure that children are able
to make connections and relate to their everyday lives. In this manner, learning will be meaningful for them.

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