Monday, July 23, 2012

The use of technology

Living in an IT savvy era where the technology is constantly improving and upgrading, it is necessary that teachers utilize technology in their teaching to provide children with a different medium of learning. Children of the later generations are exposed to technological gadgets more than they are exposed to books, thus, they are certainly not new to computers, laptops, or even touch pads. 

Personally, I would love to use technology in my lessons as I know that my students would be very excited and happy to be learning through a different approach. Through learning software, the concepts would be presented in a more visual way and less explaining is required from the teacher. Rather, the teacher could perform more demonstrations as she teaches with the software to allow a better understanding for the children. However the use of such software should be done during the middle of teaching a concept as they are pictorial to absent; children have to be exposed to the concrete part of learning prior to this stage. This could therefore be used for follow up activities to reinforce the concepts being taught to them previously or in extending their learning to another level. 

Unfortunately, my centre does not possess such resources and software in which I could utilize in my teaching, thus I am unable to share a personal experience of using technology to conduct lessons. I am however, supportive of using technology in my lessons and would be keen to purchase any useful software if I am able to get it at affordable rates. :)

Final blog entry

3 things learnt

First thing that I have learned is that the main goal of teaching mathematics to  young children is to train their minds; to prepare their minds for visualizing different concepts, see and recognise patterns and to have a good sense of numbers.

Teaching Mathematics to young children develops their ability to view things from different perspectives and to cultivate good thinking skills which enables them to think “out of the box” and be creative in their problem solving strategies. Children need to know that “whatever I don’t know, I can start with what I know”. It is important that children are equipped with such life skills as sharpening the mind and improving oneself is a constant pattern of human civilization and evolution. It also trains children to be independent in their learning and create a learning pattern of their own which is something that teachers had not taught them before. In addition, we must remember that we are to portray mathematical problems in a purposeful manner that stimulates their thinking to help them extend what they already knew to discover what they do not. Thus, as generations of children get smarter, all the more they should be provided with such opportunities for learning and development.

Second thing that I have learned is the importance of using the right language during the process of teaching mathematics. 

I have learnt that the same nouns must be used carefully and properly during maths questions so as to avoid confusion in children with regards to concepts like addition and subtraction. As teachers, I have learnt that we must be mindful of the language we used while conversing and teaching children mathematics as we do not want to inculcate the incorrect impression of concepts to children since young. The use of language to connect math concepts and children’s understanding is a significance aspect that we must take note of the very moment children start acquiring skills and knowledge on maths.

Lastly the third thing that I have learned is that visualization is a skill that can be systematically developed. 

A child with good visualization skills will be able to interpret and infer indirect problems as he possesses the ability to see things that are difficult to see. This is how we should want our young learners to be when learning mathematics instead of just providing them with the solutions and standard formulae without giving them the opportunities to explore different ideas. In order to do that, children must learn math concepts through the Concrete-Pictoral-Abstract (CPA) way. Visualization is a crucial element of a good preschool Mathematics curriculum, therefore, with that in mind, I am able to improve on the current mathematics curriculum in my centre by incorporating more activities for children to develop the skill of visualization. 

2 Questions:

  • How do I teach Maths to a young learner who is showing signs of resistant to learning Maths? For example, he just does not want to participate in Math learning activities during lessons and is behaving restlessly.

  • At what age can a child start learning simple Mathematics concepts (i.e counting, shapes etc) without facing the risk of being confused?

Thursday, July 19, 2012

Reflection for class on 19/07

"Whatever that can be measured is not important, whatever that is important cannot be measured" -Einstein

I have been hearing this quote since the first day of class but i did not realise the real meaning until yesterday's session. Indeed, in the journey of learning Maths, it is the process that counts. The process of learning Maths is to train and develop young learners into critical thinkers and equipping them with the necessary strategies to problem solve. More often that not, teachers and parents are guilty of taking children straight to the end product of learning Maths, which is obtaining the correct answers, without even giving them the opportunities to make mistakes and develop strategies. 

Personally, I am also guilty of the above to a certain extent at times. I always thought that learning some concepts of Maths, has to be, to a certain extent, via memory work (i.e multiplication tables and number bonds) and that was what I was brought up doing too. Yesterday's session had proven my mindset wrong and I was surprised and amazed by the different strategies that young learners could use to approach the concept of multiplication and number bonds directly or indirectly. 

As a Math teacher, I now understand that apart from introducing to young learners the concepts of Maths, it is also significance that I guide them through the process of learning it through the CPA approach with plenty of hands on activities for exploration and experimentation. 

Most importantly, I am really glad that I have cleared the doubts of preschool children doing assessment books and am clear of the importance of them not doing it. I am able to explain my rationale to parents in future should there be queries about it. 

Wednesday, July 18, 2012

Reflections for classes on 17/7 and 18/7

During these two sessions, I have learnt so much more about whole numbers and fractions. I have learnt how I could teach the concept of whole numbers by paying attention to the four big ideas in whole numbers.

To my amazement, whole numbers is actually a very interesting topic to teach and learn about. I realised that my pedagogy for teaching the concept of whole numbers could be improved on tremendously with the knowledge gained from yesterday's class. I am inspired by the open ended activities presented to us in class and I have come up with some ideas of activities that I could present to young children in my Math classes. 

I find myself getting excited about teaching Maths to my children and students. I might even stretch my capacity to teach Maths by teaching primary school maths. I am slowly seeing the importance of Maths in the development of young children as the process of learning Math would craft their thinking skills for future use in their education journey. 

For today's lesson (18/7), I have learnt that brain development is dependent on muscular development. The more a child engages in physical play during his infant and toddler years, the better his brain muscles develops. I am really intrigued by this fact and further convinced that play is indeed crucial and effective in a child's development! 

This module is rekindling my love for Maths and I look forward to every lesson as I never fail to go home with powerful insights! 

Monday, July 16, 2012

Lesson one 16 July 2012

Yesterday's session was fun and enjoyable, much to my surprise. To me, I have always felt that Maths lessons are boring and heavily loaded with calculations and problem sums. As a result, I did not really anticipate the start of this course, much less having great expectations of it. 

But I was wrong. Totally wrong! My impression of teaching Maths has changed. My knowledge towards mathematical terms and concepts have also been reinforced and widen. After yesterday's session, I learnt that in order to create a mathematical environment for students, teachers must pose purposeful problems to them and allow children the freedom to explore the different ways in solving the problem. Teachers must also be flexible and open minded towards the different solutions that students are able to come up with through their critical thinking, brainstorming and communication with one another. 

Most importantly, I was inspired by the simplicity of materials that teachers could use in order to teach maths; all we require is a tinge of creativity and viola! We could be on our way to discovering the different concepts in Mathematics. I have learnt that there is no definite solution for a math problem and students need to understand that too. Maths is an curriculum integrated with language and other areas of development, thus teaching and learning maths can also be through a holistic approach. 

Despite being physically tired after a day's work, I actually find myself being engaged by the hands on activities like a child and being very motivated to search for the solutions to the problems posed to us in class. I believe that that should be the kind of response that we teachers should impose on our students to create an interesting and inspirational Math learning journey for them. 

Saturday, July 14, 2012


As a learner, I feel that I am able to grasp Mathematical concepts best when I am giving opportunities to go through stages of trial and error and explore the contents of each concept. I believe that peer learning and support is very important when learning about Maths as this acts as a moral support to me and also enable me to learn through social interactions. Both chapters have provided me with an insight of the principles, the process standards of mathematics education and what it means to learn about mathematics, which is I feel could be used as a guide to maintain and upgrade the mathematics curriculum and my teaching strategies respectively. 

Maths is everywhere! It depends on how the teacher establishes meaningful activities and strategies to enhance the children’s learning. Teaching Mathematics to young children has to be done through concrete objects, where children could see the concepts being taught to them. Learning about Mathematics can be done anywhere and anytime and there are no fixed methods of teaching concepts of Mathematics.

I could relate closely to the five process standards as some of which are what I have been doing all these while during my journey of teaching Mathematics to the kindergarten children. My lessons are executed in such a way that there is a fair balance of small group learning and individual learning activities. 

This child is displaying her understanding of tens and ones with the use of counters 

These girls are learning about the concept of measurement and volume through a water play activity

Children applying the concept of one to one correspondence in groups with use of cubes

Being a Math teacher myself, I recognise the importance of giving my students the opportunity to learn Math in an interesting, fun and enriching manner. Mathematics is a subject that can be quite a challenge to teach as it involves the process of analysing, thinking and brainstorming on the different concepts. Kindergarten children might find the above processes a challenge and might even lose their interest in learning mathematics if the teacher does not deliver it through a less daunting and enjoyable manner. As a result, I always try my very best to deliver my lessons to the best of my ability, using a variety of tools and activities to illustrate the mathematical concepts being taught. 

Lastly, learning about Mathematics is essential in the development of young children as it teaches them problem solving skills, challenges their logical thinking and reasoning, enables them to make connections between different concepts by identifying patterns and engages them in active learning as they learn how to express abstract mathematical ideas and display Maths concepts with the use of concrete objects. 

Key Ideas

Key Ideas from Chapter 1: 

The Six Principles for School Mathematics

  • The Equity Principle
  • The Curriculum Principle
  • The Teaching Principle 
  • The Learning Principle
  • The Assessment Principle
  • The Technology Principle
The Five Process Standards for School Mathematics 

  • Problem Solving Standard
  • Reasoning and Proof Standard
  • Communication Standard
  • Connections Standard
  • Representation Standard
Six Major Necessary Components for Students to Develop Mathematical Understanding

Create an environment that offers equal opportunities for all to learn

Focus on a balance of conceptual understanding and procedural fluency 

Ensure active student engagement in the NCTM process standards

Use technology to enhance understanding

Incorporate multiple assessments aligned with instructional goals and mathematical practices

Help students recognise the power of sound reasoning and mathematical intergrity

Key Ideas from Chapter 2:

The Classroom Environment for Doing Mathematics

  • Persistence, effort and concentration are important in learning mathematics
  • Students share their ideas
  • Students listen to each other
  • Errors are opportunities for learning 
  • Students look for and discuss connections
Problem Based Teaching Strategies formed by Constructivist and Socialcultural Perspectives

Build New Knowledge from Prior Knowledge

Provide Opportunities to Discuss Mathematics

Build in Opportunities for Reflective Thought

Encourage Multiple Approaches

Engage Students in Productive Struggle

Treat Errors as Opportunities for Learning

Scaffold New Content

Honor Diversity

Strands of Mathematical Proficiency

Conceptual Understanding: Comprehension of mathematical concepts, operations and relations

Procedural Fluency: Skill in carrying out procedures flexibly, accurately, efficiently and appropriately

Strategic Competence: Ability to formulate, represent, and solve mathematical problems

Adaptive Reasoning: Capacity for logical thought, reflection, explanation and justification

Productive Disposition: Habitual inclination to see mathematics as sensible, useful and worthwhile, coupled with a belief in diligence and one's own efficacy