**Chapter 1**

As mathematics education around the world undergo changes,
it becomes inevitable that teachers have to be on top of things, mainly in the
methods used to teach the subject as well as the content that is being taught. With
the National
Council of Teachers of Mathematics (NCTM) emphasising that “mathematics taught at each grade level
needs to focus, go into more depth, and explicitly show connections” (p. 2), more changes can be expected over the
next few years. Going “back to basics - reading, writing and arithmetic” (p. 1)
and the work of theorist, Jean Piaget also helped to focus research on how
students can best learn mathematics.

I have also observed significant adjustments in the way
mathematics is taught in the schools in Singapore based on the curriculum of my
two older children. In fact, it has
recently been reported that pupils entering primary
school next year will be given more breathing room to grasp basic numeracy skills
as the Ministry of Education (MOE) plans to drop part of the Primary 1
mathematics syllabus as part of its regular curriculum review.

It is important for schools to enforce and intertwine the
six principles and standards for school mathematics in their programme. These
principles which include

1.
Equity

2.
Teaching
3.
Learning

4.
Curriculum

5.
Assessment

6. Technology

will act as a guide and provide some form of direction
for teachers of mathematics. Of all the
six principles, I feel that the teaching aspect is the most important. As more
children of diverse learning abilities are integrated in schools, it is
necessary for a teacher to firstly, find out what her student’s needs and
understanding are before proceeding with ways to help them. I had a very poor
understanding of mathematical concepts even in primary school. I do not ever
recall my teacher having a keen interest and awareness in my individual
development, and selecting “meaningful strategies” to support my learning. Math
was taught one way - my teacher talked and I listened. There was not much
hands-on or interaction amongst the students, let alone the teacher. She left
me very much on my own to fend for myself. So yes, you can see why mathematics
has never been my first love. However, I must admit the teachers of today are more
proactive and responsive to the different challenges and uncertainties. Added emphasis
is also now placed on teacher’s education, teaching approach, and curriculum
content.

A teacher of mathematics has to be flexible, and vary her
knowledge of any mathematics content to fit the different learning styles of
her children in the class. She must be equipped with the necessary strategies to
counter any hindrance that might slow her down. She has to be diligent and persistent
when faced with any challenging cases. Having a positive attitude and being
ready for changes are also crucial skills for today’s teachers of
mathematics. More important, making time
to be reflective and being self-conscious allows such teachers to relook at
which areas need improvement or reflect on accomplishments and plan their own
growth. I aspire to be that teacher and not let what happened to me in school years
ago rub off on the children I am teaching now.

I must admit I was very sceptical when I saw teachings of
fractions (decimal, percents, ratio), and algebraic thinking included in some
of the sessions of the course outline. I asked myself why we needed to learn
all this when I was only teaching in a pre-school. As I read on, I realised
that these topics were parts of the five content standards. Each standard had a
set of goals that was relevant to all grade bands but with different emphasis,
and exclusive to only what students of that level needed to know. This provided
me with a better picture about why my daughter could not initially do well in
even very simple mathematical topics in primary school. Her lack of
understanding of a concept, and the ability to connect new ideas to existing
conceptual webs were the main reasons. These days she is much better, thanks to
a teacher who helped her “think and reason mathematically” and “connect within
and among mathematical ideas” (pp. 3-4).

** ****Chapter 2**

Children’s interest in maths begins with me. I create a
classroom environment that is conducive for children can take risks and share
their mathematical ideas. I am aware that some children in my class take a
longer time than others to grasp concepts. I use various tools and
manipulatives as aides to represent the concept in the math corner for children
to explore and enhance their learning. I
feel children pick up concepts faster when I use more concrete tools. Children
are also encouraged to learn to evaluate their own ideas and those of others, scaffold
each other’s learning, make decisions, test them, and develop reasoning and
sense-making skills. I must admit I am still working on how to balance
“productive struggle.” I often step in to show or explain to the children how
to solve a problem too quickly.

The attached pictures show how using different tools and
manipulatives can give children a clearer picture of various math concepts and help
them understand patterning and matching numeracy to number words.
I seem to be able to relate to what Lesh and his
colleagues said, “that children who have difficulty translating a concept from
one representation to another also have difficulty solving problems and
understanding computations” (p. 24). I had a very weak understanding of concepts
e.g. I may be tested on the same concept but once the equation changed
slightly, I could not solve it. My reaction was exactly what was stated on page
27 – “I can’t remember the way to do this type of problem.” Very seldom did I
have a “can do” attitude (p. 28). I lack that perseverance and confidence. I did
not understand the ideas and they did not make any sense to me. Hence, I feared
the subject and tried to avoid doing my math homework or copied where possible.

I learn mathematics the instrumental manner – “endless
list of isolated skills, concepts, rules, and symbols that must be refreshed
regularly and often seem overwhelming to keep straight” (p. 29). As I look back
now, I wonder if this inability to do mathematics came about because of my lack
of interest or perhaps practice or could it have been a shortage of
opportunities and adequate support from the teachers to learn mathematics.

The book talks about employing “invented strategies” (p.
27) and the use of flexibility to compute an answer which I totally agree.
However, in the case of my daughter when she employed a different method to get
her answer, her math teacher insisted that she use the way she taught her to
get the answer. My daughter became confused and found it difficult to
understand the method her teacher was using. She did not like the topic after
that because of the “lack of retention and increased errors” (p. 27) when she
used her teacher’s method. Overall, developing mathematical proficiency has
more useful and worthwhile benefits for both the teacher and the student. It
plays a significant role in art, science, language arts, and social studies. Indeed,
knowing how to do mathematics indisputably connects one to the real world.