Three things that I have learnt during these 6 days of Math module would be CPA approach, seeing problems in a different perspective and the importance the way instructions were given to the children.  All the quizzes had definitely made me kills a lot of my brain cells and losing handful of hairs while I struggled to work them out! From what I went through, Math is not a mundane subject and had been fun with a lot of exploring and possibilities! I think my past experiences with Math and the way my Math teachers taught me during my school days had somehow diminished my interest in Math. I am glad to have that interest rekindled back at this time. At this moment, one thing that I have in mind would be how much should the teacher use concrete objects vs technologies in her class? Interactive boards and iPad are gaining so much popularity in young children hence those definitely would be able to sustain children's interest longer than concrete objects. With time constraint, should the teacher use lesser time for concrete materials and more than modern tech ogives to enhance children's learning?

Technology is the application of scientific knowledge to practical problems. In the 21st century, humans have created and depended on modern technologies to do a lot of problem solving. To move forward with times, children should be exposed to the use of technology tools in the classrooms. Although it should not replace the traditional method of teaching in the classrooms, it serve as an additional tool for reinforcement of what has been taught to deepen children's understanding. Ideally, it should be a combination of the use of technologies and teacher's teaching pedagogy. Internet has countless useful resourecs and webpages for children to enhance their learning skills. Cameras and video camera have widely been used for documenting purposes. My favorite technology at present would be iPad. It is learning at my convenience-anytime and anywhere. Interactive board is my second favorite use of technology in class. However, even though these technologies provide the convenience,at the end of the day, a teacher's touch would still be the best. While these modern gadgets would not be able to give you reassurance and the personal touch, the teacher is always there for children's social/emotional aspect.

Tonight, I've learned something that I thought was what it should be for the past 15 years in my teaching. A simple square and rectangle have shaken my years of foundation on shapes and my ,'now doubtful' ,knowledge on how well I really know my shapes. 'A square has 4 equal sides. A rectangle has 2 long sides and two short sides' type of explanation must now be banished from my thinking! So the conclusion to this :
A square is a rectangle!

As I read from chapter 8 onwards, I realized that young children need plenty of opportunities to explore numbers and its operational sense. Using the Bruner theory of CPA approach, concrete materials works best for young children to explore the possibilities of the outcome of a problem. I feel that teachers have to instill a relational understanding instead of instrumental understanding (Skemp, 1978) for our children these days. Manipulative tools like Number frames can help to develop early numbers sense which allows the children to see the relationship between the numbers thus developing the flexibility when working with numbers. As they develop number sense, they will also begin to see the connections and relationships between the numbers and its operations.

It's magic! Unbelievable! Regardless of the number of letters in all names, 99th appeared to be the 3rd(ordinal number)letter in almost all names. Hmm, although it didnt make sense but I discovered number patterns while trying out on my name. May's method worked for me! 
 Another interesting idea-spelling obedient numbers! I'm going to try this with my K2 kiddos! They'll love the challenge! But before they learn the secret, I'm going to put on my magician hat and robe and amaze them with my 'obedient numbers' card game. More class activities coming up! I can't wait! The only thing I shan't be clapping my hands for will be the 10 minutes quiz..

Mathematics is all about making sense of events of patterns and order. It is a series of activity of generating strategies, seeking solutions and evaluating whether it make sense. In Chapter 2, I learnt 3 big ideas:  

• the meaning behind doing Mathematics
• importance of connecting existing ideas to new skills (blue dots and red dots)
• learning theories of Piaget on constructivist theory and Vygotsky's sociocultural theory.

What really got me is the importance of the teacher's role and how opportunities are essential for allowing the children to assess their prior knowledge to build on new knowledge- assimilation and accommodation.  I have a Math corner set up in my classroom. The children explored various materials provided there and have the opportunity to discuss and share ideas with one another. I think this is a great way for the children to take on new learning on top of the existing ones that they already acquired. This is what the blue dots and red dots are about. 
It is also interesting to learn how the two theories (constructivist and sociocultural) work together to enhance the children's learning process. I feel that the children should adopt active learning and the teacher must be present to facilitate and give the support needed throughout the process. 

Tools and materials should be used when an emerging idea is taught as children these days are visual learners. Figure 2.11 on page 24 showed a representation on how each tool aids the development of new concepts. "The more ways children are given to think about and test an emerging idea, they better chance they will correctly form and integrate it into a rich web of concepts and therefore develop a relational understanding." (p. 24)
Lastly, the use of technology-based tools are mentioned. It is important to keep our children aware of the technologies that are created to make learning more effective. However, is using the calculator advisable for pre schoolers and primary school kids? The text states that "it is important to  include calculators as a tool." (p.26)   I thought calculators are use mainly in secondary schools in Singapore. Will our young children use calculators to calculate once they discover the convenience and choose the easy way instead of doing mental calculations?

Basically chapter one is on the different standards on teaching Mathematics. There are 6 Principles, 5 content standards and 5 process standards. These made sense and as I was reading them, it made me reflected on the way I teach Mathematics from the day I started in Early Childhood field. I most enjoyed reading the section on listing and describing the characteristics, skills and the dispositions of becoming a Teacher of Mathematics (p. 9-10) There is a point that states that a positive attitude makes a lot of difference in the way a teacher teach Math. I feel about guilty as although I follow my lesson plans to teach Math and try to make learning Math as fun as possible, I don't feel so positive about Math as I don't like Math. Opps! Trying out the sums on Chapter 2 took me quite awhile as I was procastinating as long as i can to avoid those mind boggling sums! This chapter is rather short and straight forward so reading took a turn from dry (all those principles and standards) to interesting (teacher's attitude towards Math)