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.