Thursday, September 30, 2010

My Reflections

This math module was indeed an astonishing experience for me. I had never been taught by a male lecturer for all my early childhood modules. If I had Dr Yeap as my math teacher in my secondary school, I believe that I would fare better in math. He had made a difference by changing my impression of math. I had truly enjoyed myself throughout the course. 

Ever since I begin teaching, I never like teaching math in my classroom as I do not like the subject in the first place. But I never knew that math can be so much fun. The fun and interesting activities that Dr Yeap has taught us was indeed an eye opener for me. From the activities we did in class, provided me with lots of hands-on experience which enables me to truly understand the math concepts. With the knowledge I gained from this course, I am eager to create more fun and interesting math activities. I am also inspired to be a teacher who will bring enjoyment all my students. 

 Number of cookies: 1 ¾

Geometric Thinking

Through this exercise, I recalled some geometry concepts that I have learned back in secondary school. To get the interior angle of pentagon, one has to divide the shape into basic triangle. For pentagon, it can be separated into 3 basic triangles. Each triangle has the interior angle of 180°, so the total interior angle for the pentagon is 3 x 180° = 540°.

Similarly the same concept can be used to work out the interior angle of other polygons. Try finding the interior angles of the following polygons.
I realized that good spatial sense is needed. "Spatial sense includes the ability to mentally visualize objects and spatial relationship" (Van De Walle et al, 2009, p.400). Contrary to typical belief, spatial sense has proven to be more of a nurture skill rather than nature. According to Van de Walle (2009), "We are all capable of growing and developing in our ability to think and reason in geometric contexts." Research done by Solder & Wearne has shown that improvement in the geometric reasoning can be achieved by proper training since young. I believe in learning through exploration. Teachers should introduce the basic shapes such as circle, triangle, rectangle and square and provide exploration opportunities for children to "get to know" these shapes. 

Van Hiele's theory suggested the 5 levels of geometric thinking; ranging from level 0 to level 4 (Page 400). 

Visualization Level 0: Students can name and recognize shapes by their appearance, but cannot specifically identify properties of shapes. This level of geometric thinking can be observed in nursery children. I believe one of the most effective instructions of visualization is for children to manipulate with physical models.

Analysis Level 1: Students begin to identify properties of shapes and learn to use appropriate vocabulary related to properties, but do not make connections between different shapes and their properties. A simple instruction using analysis is to classify shapes according to their properties. 

Informal Deduction Level 2: Students are able to recognize relationships between and among properties of shapes and classes of shapes and are able to follow logical arguments using such properties. A suggested instruction using informal deduction can be using properties to define a shape. 

Deduction Level 3: Students can go beyond identifying characteristics of shapes and are able to construct proof. A secondary student should be at this level. 

Rigor Level 4: This is the highest level of Van Hiele's theory. Students who are at this level can work different geometric systems, where they can understand that there are properties within geometry. This group of students would most likely be in university.


Reflection on practice – Number Sense

I would say that number sense is for children to understand the relationship between numbers symbols and quantities. When I was young, I remember my mother teaching me numbers by asking me to count my fingers. This helps me in building up the basic foundation of numbers. Soon, I was able to count, recognize numbers write numbers and so on. I believe that it is essential for teachers to design high-quality number activities for children, so as to help sharpen their number sense.
Some common practice our pre-school setting:
  • The relationship of more, less, and same Van de Walle (2009) mentioned that "Children begin to develop relational ideas before they begin school. This activity will help children to build up a basic knowledge of more, less, and same. When given two sets, most children will know which set has more and which set has less. This will usually be the case of the quantity is obvious. On the other hand if the quantity in the sets is too big, children can be asked to count in order to determine the quantity.
  • Early counting Children can begin counting from the preschool level. In order for children to fully understand the concept of counting, they have to be able to count in sequence and perform one-to-one correspondence.
  • Numeral writing and recognition Once the child achieves the skill of counting, he/she can be taught how to write numerals. Interesting activities such as tracing in sand, using body movements to form numerals, finger painting and so on can be implemented in the classroom. This can help to enhance children's interest in learning math.
  • Estimation and measurement According to Van de Walle (2009), "One of the best ways for children to think of real quantities is to associate numbers with measures of things." I agree with this statement as this is a common instruction used by teachers. For instance, preschoolers can estimate the height of their friend using pencils. Children have to understand the concept of "about" in estimation. They would say that their friend is "about" 12 pencils tall.
  • Data collection and analysis I often use graphing activities in my nursery two classroom. Graphs make it easier for children to connect numbers to real quantities and to make comparisons between the numbers. A pictorial graph shows pictures of realistic things. It helps to attract children's attention.

Sequencing learning task for place value

What is an appropriate sequencing? My sequence for the 5 sequential learning tasks as per following:

Step 1: Place Value Chart
I choose to introduce the place value chart first as I believe that by breaking down a two digit number into the chart will allow children to see how the number came about. I believe this helps to build on the child's prior knowledge of place value.

Step 2: Tens and Ones Notations
Using the child's prior knowledge of the place value chart, children should be able to understand that a two digit number is made up of tens and ones. Most of us introduce numbers through route counting and children can easily count numbers 1 through 10. Using the example of bundling sticks, children learn to count by bundling the sticks into tens and ones.

Step 3: Expanded Notations
In expanded notations, children should be able to visualize and understand the tens and ones. Teachers can further enforce this knowledge by breaking up the tens and ones.

Step: 4 Numerals
Once the children fully understand how a numeral is derived, they can be taught to write the numeral.

Step 5: Numbers in Words
The last step will be to teach children how to spell the numbers. This should be taught when they are able to recognize the numeral.

Problem Solving

According to Van de Walle, J. (2009), "Most, if not all, important mathematics concepts and procedures can best be taught through problem solving." I believe that we learn best when we discover the answer for ourselves and by solving problems as it is then that we will become interested in the basis of the problem and the end results.

I agree with Van de Walle (2009), "Teachers must select quality task that allow students to learn the content by figuring out their own strategies and solution." Bearing this in mind my group planned an activity which requires children to problem solve and come out with a solution. This activity is designed for children between the ages of 5-6 year olds, which teaches the concept of counting money. Each child is given a total of $10 and was told to make purchases at DIASO ($2/ item shop). The task is to buy materials to make a gift for their parents. The objective of this activity is to get children involve in planning and counting money.

George Polya's four-step problem solving process acted as a guide to us in our activity.
  1. Understanding the problem: When given the task, children are to figure out the problem. In this case, the problem is to use the given sum of $10 to make purchases in order to construct a gift.
  2. Devising a plan: Children had to plan their purchases so that they get sufficient materials and avoid over-buying.
  3. Carrying out the plan: The plan is implemented at DIASO, where children get to shop for materials they need on their own.
  4. Looking Back: A reflection session is conducted at the end of the activity. So as to allow children to reflect back on the problem and see if their solution makes sense.

My learning in the first session

I dragged myself to class today knowing that it was math class. All this wile I had a phobia for math. I thought to myself "How am I going to survive this course?" When I arrived at the classroom door, I heard lots of laughter. Just a week ago I heard many classmates whining about this math course. I was surprise to see all the happy faces the moment I step into the class. After I sat in for awhile, I felt relieved. Dr Yeap's humor had eased my worries of his math class.

The video on the dice trick left me a deep impression. I was so amused to find out how Dr Yeap knew the covered numbers on the dice. I love playing with dice but it has never strike me to think of such an activity. This video also taught me that how a teacher should facilitate children in solving a problem. Instead of revealing the answer, Dr Yeap had facilitated the children by asking them questions and building on their understanding of the problem. I believe that the teacher's role is to facilitate learning. Learning may be facilitated by directing children's attention to objectives, posing questions, encouraging children to relate information to their prior knowledge, logical sequencing of content etc.


Saturday, September 25, 2010

Message to Dr.Yeap

Please assess my blog on 30th Sep.