Assessment. Volume and Capacity

My thoughts.....

We discussed about assessment. I assumed that we need to assess the subject through paper tests. Another way of assessing is through oral testing. We can provide a math problem to children and ask to verbalize the different ways of solving these problems.

We can teach maths through storytelling too. I have taught children on the concept of ordering three objects according to size. I used the story, Goldilocks and the three bears to teach this concept. The book Goldilocks and the three bears, shows the different sizes of the bowls, chairs, bed and the bears are also in different sizes.

Measurement of the floor at the MRT station.

The measurement of the length of the steps is 14 cm. There were 4 sets of 16 steps. the working is as follows.

16 x 4 x 14 = 896 cm.

The length of a level of the station is about 896 cm.

Time is also a concept which Dr Yeap emphasized that it has no physical quantity. We should teach time regularly.

We created a container for 15 beans. Although small, the container could hold more than 15 beans. The size of the container which contains 15 means was very small.

I always feel that learning should be child initiated and teachers play the role as a facilitator. If children play an active role in their learning, they gain confidence.

Fractions and Geometry

My thoughts

Talking about fractions brought memories on how I learnt the topic. I remember how my math teacher taught me how to overturn a fraction when we divide two fractions. Drawing models also makes comprehension of topics easy.

Geometry was interesting.  I created some shapes with the lines. Some of my classmates made some interesting shapes. One of my fellow friends actually found a pattern between the dots and the area of the figure. I heard Dr Yeap’s instruction wrongly. I thought i could draw any shapes, so I drew a  circle. Then I realised that the lines should be straight and should be connected to the dots.

The homework proved to be interesting too. I derived some ways to create the shapes of a square and triangle.

Addition and Subtraction

My thoughts........

Lesson 14 was very fascinating. The number which I chose was 5 and 8. Dr Yeap instructed us to add the 2 numbers which totals to 13. Then we have to join the 2 numbers together which is 58. Lastly, subtract the 2 numbers together and the difference is 45. I was pretty surprised that Dr Yeap was able find out the difference without knowing my second number. Later of which the class discussed that we can get the difference by multiplying the first number by 9.

We also discussed about the different qualities if a word problem.

Continuous quantities----------can’t be represent them 1 by 1

discreet qualities-----------------can be represent 1 by 1

I also learnt that children should be exposed to different variations of the problem as they provide a challenge to these children. Instead of just sticking on to that problem, children should be given more opportunities to explore the same problem in different variations.  For the example, the numbers of the word problem can be changed.

I also learned that, it’s important to keep the materials for counting as constant, For example, we cannot count pencils and erasers together. It will be confusing for children.

Lesson Study

My thoughts.....

When Ms Peggy asked me about the lesson study, I thought it was in dept study of a math unit. It’s actually a study of a research idea in the classroom. I saw that a team of observers observe the teacher in a classroom. After which, officers have a post lesson conference with the teacher. They suggest ways to improve the lesson.  One of the ways is the classroom management of the teacher. In the first video, the children were seated in rows. Some children were restless and kept moving.  The second video showed a better seating arrangement of which children were seated in a semi circle. Children were more focused during lesson.  Providing each child opportunity to explore the concept for in this case, each child was given paper plates to explore more and less, enables children to understand concepts more.

I have learnt in this session about differentiating during a lesson. In a class, there are different types of learners. Some might be fast learners, some need more assistance during teaching.  Planning should be based on different needs of the children. Teachers can challenge the fast learner by using a bigger two digit numbers and assisting the children with smaller numbers.

I and my groupmates created structure by using cubes. We created 17 different structures.

All about Numbers.

My Thoughts....

Session 2 was all about numbers. When we played the picking up the stick game in the group, I wondered, why I was losing throughout the game? I realised that all this while, I was picking up a bad number. After knowing the pattern of bad numbers , I was able to play the game.

In the lecture, Dr Yeap pointed out that we need to ask these key questions to ourself while planning lessons.

1. What is it,I want them to learn?
2. What if they cannot?
3. What if they already know?

When I reflected upon these questions,I realised that a teacher should plan according to the level of children. Teachers usually plan a general plan for all children. Does a pair of shoes fit all sizes? It varies according to the sizes. Planning lessons are also similar.  Educators should differentiate the lesson according to the different levels of the children. The tasks should be made simpler for the low level child, and more advanced for the high level child.

During lecture, when Dr Yeap talked about the traditional style of divisions, It brought unpleasent memories on my Math experience. I painstakenly memorized the times table and did divisons. When I saw simpler method of division, I was quite impressed by the simple way of divison which is easier for children to comprehend.

I think there is a need to cultivate the idea of self correcting in the classroom. This is will allow children to explore the different methods and aid comprehension. Giving children concrete experiences of counting allows children to build the foundations and help themto prepare for the next level

I believe that Mathematics is all about the different process standards like making connections, looking for patterns, reasoning and problem solving and etc. These process skills prepare children for life.

Day 1

My Thoughts.....

I enjoyed the session on Mathematics yesterday. I realised that there are more than 1 method of solving. First of which I whould like to highlight would be the Name Problem. There were 3 unique solutions to the problem. Firstly Dr Yeap asked us to find the patterns in the numbers. I came up with 2 different ways of solving the problem. First of which was I divided the number 99 by the number of letters in my name ( there are seven letters in my name). I worked the division and the answer was 14 remainder 1. When I counted the letters, it stopped at the letter "H" in the middle (Rahimah). I also found a patter in the letter h in the middle. The numbers in the middle increased by 8 and then by 4 and then by 8 and 4. When i added the numbers, 99 was at the letter "h" which i worked out earlier.

I also learnt that there were diiferent types of numbers. Previously, I thought that all numbers same and they represent a particcular unit. Numbers are different in terms of ordinal, cardinal, nominal and measurment numbers. This lesson was an eye opener. It is also important for teachers to be aware of these terms. One example Dr Yeap provided was the race example, Children might be confused if teachers ask who will finish at the the third position. It is neccesary for teachers to be precise like which child is in the third place from the finishing line.

Another matter I would like to highlight would be of counting things/materials in the same set. Counting similar materials will ensure consistancy. Different materials do not match together. As a teacher, I have made this mistake before.

As a teacher, I felt that teaching number facts through ten frames was rather difficult for children as it involves both counters and ten frames. By using the ten frames, children is able to count through 1 to 1 correspondence. It was rather interesting to find out the different ways of additions like counting on and counting all and commutative property.One strategy which attracted me was the make 10 strategy.

The poker card spelling was also unique. I thought, it was a kind of magic. The first thing which crossed my mind was to arrange the cards in one line and find a possible solution. After a few tries, we were able to solve it as a group.

I noticed some patterns when i did the arrangement, the numbers form patterns when we placed them horizontally. Thus it becomes easy to answer when the number gets too big. I also realised that every pattern has a rule and a term. A mistake teachers make is not to stae the rule and term.

Can't wait for session 2....

Teaching Mathematics in the classrooms.

"Small minds discuss persons. Average minds discuss events. Great minds discuss ideas. Really great minds discuss mathematics."

                                                                                                                          ~ Unknown

                                                                                                           

Knowing Mathematics

In the world of mathematics, there are patterns in different concepts. Processes such as problem solving, reasoning, communication, making connections and communication enable children to find patterns in concepts.

Classroom designed for Mathematics.

In order to aid the knowledge of mathematics, we have to design an environment which facilitates the learning. Freedom to express ideas should be cultivated in the classroom. As I mentioned earlier, children should be given opportunity to explore and learn. Setting up a learning corner as an extension of learning allows children to explore ideas independently.

While attempting to try the problems in the book, I realize that there is more than one way of solving problems

We are very familiar with Jean Piaget’s theory building schemas which mean that children build on their knowledge through their prior knowledge of the subject. When I asked children to arrange containers according to their size, they arranged it accordingly from big to small. After which, I taught children to teach children according to the width of the containers, they build on their knowledge and arranged them from the broadest container to the narrowest container. Thus it’s essential to for teachers to take note of children’s prior knowledge of subject matter and plan accordingly.

Another theory that I will emphasize would be Vygotsky’s sociocultural theory. He emphasized on the zone of proximal development (ZPD). When an adult helps a student to learn, he will perform better. The area between unaided learning and aided learning is ZPD.  Another feature of sociocultural theory is semiotic mediation of which information is passed through social communication to a person. Opportunities like group discussions should be given for children to interact socially in the class as it increases the learning potential of children.

When planning for a math lesson, I realized that it’s necessary to create new knowledge from previous experiences. For example; children in the kindergarten level basically know how to count by ones. When they learn how to count by 2’s, they learn a new way to count.

 In preschool settings, children should learn concepts through trial and error. Through problem solving, children grasp maths concepts better.

Children comprehension of new concepts will increase if they relate to their prior knowledge.  Some concepts are interrelated like the concept of money and counting by 2’s , 5’s and 10’s. Once I was teaching my class about heavy and light objects. Children related to the prior knowledge, if a heavy person sat on the sea-saw, he will go down. They related this concept to the pan balance. The heavy side of the pan balance will go down. By relating, children gain more problem skills and will become optimistic towards learning.

Usage of Manipulative

Manipulative can be used to represent concepts. Recently I used a connecting cubes and asked children to pair up and compare within themselves, who has more/less. By using these physical objects, children are able to understand the concept.

Incorporating Technology in class.

Technology can be incorporated in class through computers, interactive learning or even simple calculator. In my school, we incorporate the interactive whiteboard in the classroom. The modelling of a concept is magnified in the whiteboard so learning would be clearer and more fun.

My thoughts....

I agree that children learn best if they build on their prior knowledge. Classroom should also pose as positive environment for learning maths. Teachers should not stick to one way of solving problems rather they should be open about different solutions. Positive environment promotes positive learners.

Mathematics in Modern Times

“The essence of mathematics is not to make simple things complicated, but to make complicated things simple.”

 ~S. Gudder

When Mathematics subject is mentioned, some of us shudder away. Why is this so? Is it due to the difficulty of the subject? When I ponder upon my own experience of learning Mathematics, I feel that I was not given enough exposure or support to comprehend the problem.

The National Council of Teachers of Mathematics (NCTM) has made some significant changes to the subject of Mathematics. By using the different research models from the various psychologists, the council has determined the best ways to educate children in the area of Mathematics.  They published a document which provides direction of this subject for the Kindergarten level to 12 grade. This document consists of six principles of teaching mathematics in school.

• Equity
• Curriculum
• Teaching
• Learning
• Assessment

Six Principles of Teaching Mathematics in School.

• Number Operations
• Algebra
• Geometry
• Measurement
• Data Analysis and Probability

The goals in these contents differ according to the levels of the grade. Planning these goals helps teachers to plan learning outcomes efficiently.

5 process standards.

In addition to content standards, there are 5 process standards. Through these processes, children assimilate and learn Mathematics.

Problem solving: Children use a variety of methods to solve problems. For example, I asked a child to find a container, which holds more water. The child picked up a few containers which he thinks will hold more and finally chose a container that holds more.

Reasoning and proof: Children should question themselves on how they arrived at the answer. This will allow children rationalize their answer. For example, I taught children from Kindergarten 1 class on more and less concept. Children were able to understand that 5 birds is more than 2 birds. I asked children, “Why is it more?”.  They said they are many birds in the picture. “How many more?”  There were 3 more birds in the picture.

Communication : Children were able to solve problems if they discuss with a group. This will enhance learning and allow children to express more ideas. I asked children to form a group and form $2.50 with sample money. When I observed their interactions, I noticed that they could make 50 cents in a variety of ways.

Connections: Children can make connections in the subject of Mathematics.  For example, children can relate counting numbers in 10’s in the content of money. They can also relate their learning of money in real life situations, where children use money to purchase items from shops.

Representations: Manipulatives, graphs and other mathematical symbols can be used to represent mathematics data. For example, counters can be used to count numbers.

My thoughts...

Mathematics in this era must not be taught through traditional ways. Now Mathematics is implemented through unconventional ways. Through learning corners and technology children learn Mathematics in a modern way. Teachers should also have a positive attitude towards the subject and should constantly reflect the methods of teaching it.  

 

Introduction

Hi!!! I’m Rahimah Beevi from BSC05 cohort. I welcome the concept of using a blog as a reflection of the pre course reading as it is very new to me. I hope this experience will ignite my interest in sharing my knowledge of the field through the world wide web.