## Saturday, 3 September 2011

### Lesson Relections

Monday 22 August 2011
This evening we were reintroduced to how numbers are used in different ways.
1.     Cardinal numbers
2.     Ordinal numbers
3.     Nominal numbers
4.     Numbers used in measurement
5.     Numbers used in proportion
I feel that the ten frame is a good tool to help very young children visualize amounts and numbers.
I realize that it is very important for teachers to help their students visualize and see patterns in order to help them understand concepts and do mathematics better.
Pre-requisites to counting- Children must be able to:
1.     Classify
2.     Rote count
3.     Understand one-to-one correspondence

Tuesday 23 August 2011
Games, games and more games. If only my Math lessons were just like today’s lesson, I would probably have done much better!
Patterns are everywhere! The ability to look for and see patterns is an important skill every child should acquire.  All patterns have rules and terms that are either repeating or growing.
According to MOE’s website, mathematics should be a vehicle for children to develop logical thinking; to become independent learners and to be able to correct one’s own mistakes and make appropriate decisions. This is similar to Jerome Bruner’s theory on Constructivism.  Bruner's theory emphasizes the significance of categorization in learning. "To perceive is to categorize, to conceptualize is to categorize, to learn is to form categories, to make decisions is to categorize." Interpreting information and experiences by similarities and differences is a key concept. I am so happy that MOE has adopted the CPA approach to teach young students tackle math.

Mathematics is:
- Generalization
- Communicating ideas
- Visualization
- Dealing with information
- Developing number sense

Wednesday 24 August 2011
Lesson Study- How important is it in Professional Development?
This evening, we were asked to observe two case studies and were tasked to identify factors of good math teaching and learning. I learned that it is important to give opportunities for differentiated learning so that the advanced learners are challenged and will not get bored; on the other hand, the average of slower learners work at their pace of understanding.
We, as a group concluded that a good lesson comprises of these aspects:
1.     Physical infrastructure- how the children were seated.
2.     Children’s involvement
3.     Teacher’s ability to ask appropriate open-ended questions
4.     Classroom management
5.     Use of manipulatives and charts so as to scaffold slower learners.
Mathematical investigations should be divergent in nature. It should allow for exploration and experiment and it should also communicate the process and result.

Thursday 25 August 2011

I didn’t think that I would enjoy doing fraction problems. However, by using concrete experiences and pictorial cues (folding and cutting paper), I managed to solve them! And not by the methods taught to me when I was in school eons ago!
This evening, Dr Yeap again emphasized how important experiences are to young children when doing Mathematics. It is a must for them to look at the concrete before abstract application. Teachers of mathematics should engage young children in thought-processes, so as to understand the sums and justify the rationale behind a solution they have found. The correct answer is not always important but whether the child is able to communicate his ideas or method.

Friday 26 August 2011

I am guilty of giving children “artificial stimulus”, which is a signal to tell children of my approval or disapproval to their answers. Instead, I should be d be eliciting answers from the children by asking them questions to prod them to think logically through a problem and get them to communicate their solutions.

# Pick's Theorem

George Pick’s simple geometry theorem allows us to find the area of any polygon that is embedded on a lattice or grid. It is especially useful for concave polygons, for which the usual textbook area formulas do not work.
Pick's Theorem works wonderfully on a geoboard, where students can design wild polygons with rubber bands stretched over the nailheads.
Pick's Theorem simply has us count up the number of points on the boundary of the polygon (where the rubber band touches a nailhead) and divide this number in half. Then add the number of points in the interior of the polygon (inside and not touching the rubber band) and subtract 1. We can write the formula like this: Area = B/2 + I - 1. For the polygon to the left, there are 16 boundary points and one interior point, so the area is 8/2 + 1 - 1 = 8 square units.

Wednesday 31 August 2011

The book “How Big is a Foot” by Rolf Myller was a refreshing way to start a Math lesson.  At the school where I work, we have been using stories to promote the connection between mathematics and children’s literature. All children love listening to stories and what better way to bring across a concept to them!

The highlight of tonight’s lesson was going down to the MRT station to solve yet another fun Math problem. Taking the classroom outside breaks the monotony of the lesson and showed us that “Math Is Everywhere!” Here is my solution:

There were a total of 62 steps.
Each step is about 14.8 cm in height.
62 X 14.8cm Answer = 917.6 cm

I must admit that I have enjoyed this module thoroughly and am certainly looking at Mathematics through New Eyes!

## Thursday, 18 August 2011

### Mathematics with New Eyes

Elsie Lim Swee Peng
BSC 05- EDU 330- Elementary Math

Chapter Reflections
Chapter One
As I read chapter one, I couldn’t help reflecting how I learnt Math when I was young child.  My earliest recollection was being flashed cards with the 1 to 10 by my mother and through Rote Counting. Making sense of the numerals only came a lot later. Pre-math skills of sorting, patterning, grouping was never purposefully taught. It was through play with older siblings that such skills were acquired.
Having taught pre-school for more than 10 years, I understand and fully support the importance of having children learn Math concepts through play and activities. In the “Principals and Standards for School Mathematics”, under “teaching principals”, I totally agree that it is pertinent that as teachers, we understand fully how children learn mathematics, and select instructional tasks and strategies that will enhance learning.

Math through Play
When children are engaged in play, they tend to solve problems that are challenging but not totally beyond their capacities. As children play, challenges will surface and this often will result in problem solving.  I advocate play is an important and powerful tool to enhance learning. In addition, children who play together tend to grapple with the same problem, they often come up with different ideas or approaches, discuss various strategies, and learn from one another. These aspects of play can promote thinking and learning in mathematics as well as in other areas. Teachers can enhance children's learning of mathematics when they ask questions that provoke questions, extensions, and development of new understandings.

The Five Process Standards
Teachers need to fully understand and the five process standard in order to teach math well. I strongly believe that “mathematics should be connected to the real world and to other disciplines” so that children can relate to and learn to make connections to their daily lives.
Here is an example of a child (3 years 7 months old) thinking and trying to make connections. The children were asked by the teacher to help put away the few pieces of floor puzzles left on the floor. There were three children and four puzzles left to be put away.
Teacher: “Quickly, let’s each put one piece of puzzle away in the box and we are done.”
Child: “But Ms Michelle, there are four puzzles left and only three of us here?”
Teacher: O yes you are right, then I will put one away too, and then we are done!

Chapter Two
“Mathematics is more than completing sets of exercises or mimicking processes the teacher explains. Doing mathematics means generating strategies for solving problems, applying those approaches, seeing if they lead to solutions, and checking to see if your answers make sense. Doing mathematics in the classrooms should closely model the act of doing mathematics in the real world.”
When I was in school about 20 years ago, I like many others, learnt to do math through many worksheets and workbooks. Remembering formulas and times-tables and regurgitating it. I was not asked to make connections to our daily lives. Doing Math for me became a chore. When I struggled at understanding certain concepts, I was not given concrete examples or manipulatives to help me understand but instead given more worksheets to practice! Now, my daughter who is in Primary One this year is given hands on experiences with counters and other manipulatives to help her understand concepts that may be abstract to her. Games are also played in class to help the children understand and grasp certain concepts better. I am really happy that MOE has reviewed their curriculum and am hopeful that my daughter will enjoy her Math lessons more than I ever did in school.

Implications for Teaching Mathematics
- Build Knowledge from prior knowledge
- Provide opportunities to talk about Math
- Build in opportunities for reflective thought
- Encourage multiple approaches
- Treat errors as opportunities for learning
-Scaffold new content
- Honour diversity
This segment in this chapter is empowering. To me it is not only relevant to teaching Math but also other subjects as well.
In spite of my lack of good experiences and poor results in Math, I am looking forward to approaching Mathematics with “New Eyes”.  Reading this book has given me hope that even though I did not score well in Math, I can be a good Math teacher and will try my very best to make Math come alive for the children that I teach using the new ideas, attitudes and skills I will learn in this module.