Daily Class Reflection

Session 4 – 25 August 2011

We are very used to getting approval for any little thing we do. Therefore as teachers we have trained our students to get approval from us. Now, the hit of today’s lesson for me is not to display any form of body language when students do some mistakes or achieve a correct answer. How to stop that???

I always felt that something is not finalised when Dr Yeap does not give any answers to the activities that we were engaged in during class. I was wondering why and I got my answer now. He is role modelling leaving the students to come up with their own decisions.  I feel that it could be sometimes difficult to leave kids without any form of approval. Alternatively, prompting students with questions and suggestions would make them think and reason out. Direct approval or disapproval could be avoided. I will have to try this out with my class before agreeing with this approach.

Classifying addition and subtraction into concepts of part – whole, change and comparison covers situations in which these skills are applied. I now have a better view of presenting the story sums to students. When students get to view it in these situations, better understanding takes place for the thinking process to be stimulated.

We explored fractions using materials to divide into equal parts. Fractions are not so difficult as I have always thought. Using concrete materials to see the parts made it very easy. Folding equal parts with a rectangle paper and further dividing it to smaller parts was interesting. Viewing different ways of folding equal parts was an eye-opener, especially four equal triangles in a rectangle.

Daily Class Reflection

Session 3 - 24 August 2011

This session conducted by Ms Peggy Foo is a reinforcement of how a lesson is planned and executed. After which, an evaluation is done to further improve the lesson.

There are two main points that I valued. The first one is regarding evaluating a lesson. Asking for other teachers’ input to further enhance the lesson is constructive. Discussions makes one view what went wrong and right and to make relevant changes to enhance the learning process.

Secondly, to be prepared for differentiation, which can be easily overlooked, thus causing problem with classroom management. Being a little more prepared is always useful.

Making structures with fixed number of unifix cubes was interesting. Working in a group was fun, especially when we two of us made the same structure and had to place them together to know that they are same. Interesting visualization!

Bring back the tangrams was useful. I asked my five year olds to form the shapes and it was interesting to observe kids flipping and turning the pieces and coming up with new shapes. It kept the kids engaged for quite a while. A lot of interaction in the form of thinking was taking place. When I attempted it by myself, there was times when I had to scratch my head. It made me wonder how the kids in my class were able to place back the larger version of the tangram in the form of puzzle(pic. below) quite easily after a few attempts.

It was a day to revisit and reflect on the way I plan lessons for my class. Useful reminders to include more ideas to keep kids thinking.

Daily Class Reflection

Session 2 - 23 August 2011

The video on the dice game brought awareness to how much we know about the materials we use in our daily teachings. I am aware that a normal dice has six sides and numbers or dots of 1 to 6 on each side. This game with the two dice made me learn that the total of the opposite side in a dice is 7. A simple game that can be played with the preschoolers, too.

During my primary school days (1970s), solving long divisions was like a nightmare. I can never get it correct, until I started explaining the steps, or rather memorise the steps. There was no understanding of tens and ones or any other skills. Not until I started teaching my own children did I get the understanding of how it should be done to make a child understand.

Jerome Bruner’s CPA approach well suits with the way children learn. In our childcare children are given concrete materials to explore. Then pictures are used and only when necessary abstract thinking is introduced. Not only for maths but also for any subject matter the CPA approach applies.

I enjoyed playing the sticks game in Lesson 6. Making a bad number brings in a lot of quick calculations to win the game. I played the game a few times with Elsie. We realised that proper calculation leads one to win the game. When children play it repeatedly, they will be able to comprehend the bad number concept. There is addition and subtraction involved in this game.

The five key points on generalization, visualization, communication, number sense and metacognition was experienced through the various activities that we did in class today. Via communication, students display their understanding and teachers assess the learning that has taken place.

Daily Class Reflection

Session 1 22 August 2011
In today's session all activity was interesting. The first activity was solving a problem with names. It was engaging and i was able to see a pattern in it. In doing math, there is always a pattern involved. It is a matter of seeing it. How do I get to see it? I feel that it prerequisites like multiples and counting in groups are necessary for observing patterns and it just does not appear in one look.  
I learned that ordinal numbers could be separated as numbers in space and time. Although we introduce this concept to children, there are always little things that get missed out and we end up making mistakes without realising that children are getting confused. The use of language plays a key role in relating concepts to learners regardless of experience.

Most names had the ninety-ninth place on the third letter of their names. I am very sure that in my name it is on the fifth letter, although there was a discussion involved and someone saw it at the third letter.
I was able to solve the problem of the cards and it's spelling using the cards. This was an exciting activity because after working it out, I had to check if I did it correctly. I felt like a child as I spelt out the numbers. A sense of achievement at the end.
I feel that this whole course is going to set me thinking if i have been teaching math to my studeents to make them think to solve problems in various ways rather than to get the correct answer.

EDU 330 Elementary Mathematics

Elementary & Middle School Mathematics

Reflection

Chapter 1 Teaching Mathematics in the Era of the NCTM Standards

In this chapter there is a lot of focus on the NCTM Standards, which may not be the standard used in Singapore. However, I read on to see what is there in for me as a teacher.

Under the heading Principles and Standards for School Mathematics, six principles are mentioned. Each principle emphasises the way Math should be taught. However, I find the Assessment Principle as an interesting and purposeful one. Assessments should be carried out to display students understanding and how and where they need assistance. It should not be to judge if the student is able to give the correct answer. The assessment should be for the process used by the student and the teacher and to evaluate if it works for both. In learning Math there is no one correct way. What works for a student may not work for another and the same for teachers. How I teach may differ from another teacher. I believe that being result oriented is not going to work for students in the long run of learning Math. It is a skill that needs practice and building on.

The Five Process Standards clearly states the way Maths is to be seen as a means to develop thinking and problem solving skills and not to be taken as a subject to study for getting a grade. It is entwined in everyday living. Though five, it is not seen as separate skill or concept but as a process to be utilised for teaching. Looking at different ways to solve a problem is enhancing thinking skill. In my class, I always ask children to think of different ways to display number values using their fingers and different arrangements of cubes. Children enjoy doing this on their own during free choice play.

The Reasoning and Proof standard is very interesting. It gives the chance for children to explain their process and be able to correct their own mistakes if any. It also gives opportunities for teachers to comprehend the way the thinking process is taking place in children.

Chapter 2 Exploring What it Means to Know and Do Mathematics

The first part of this chapter involved the reader to be engaged in working out some sums. It was fascinating to view the various ways in which it could be solved. No correct answers were given but the process in which the problems could be solved made my thinking process work in various ways too. The author said, “In the real world of problem solving outside the classroom, there are no teachers with answers and no answer books. Doing mathematics includes using justification as a means of determining id an answer is correct.” How do I apply this in the classroom where children are to be taught to pass exams which wants the correct answers? I am glad that I am working with the preschoolers who learn through play. I can and have applied this with them to show that there is no one correct way but many.

The Constructivist theory and the Sociocultural theory may seem like two different aspects stating two different process of learning. However, in the learning process both have to be applied to enhance the learning journey. Connecting prior learning to new ones need the assistance of others most of the time. What exactly is prior knowledge was once also new knowledge. Thus, though two by name these two theories have to be connected to enhance growth. I do not think that any one of these theory can work by itself. As a teacher I have to know the prior knowledge of my students to provide them with challenges to bring them to the next level. I have to be the scaffold for my children to act on their prior knowledge to connect to new knowledge.

In teaching mathematics, it is important to accept that “concepts and connections develop over time”. What the child do not comprehend today may be seen to be applied by the child after some time. Engaging in related tasks and constant practice make students see connections. In mathematics practice is something that has to be constant. To engage children various means of practice is necessary. This will make children see the connections and be able to relate.

These two chapters in this book has shown various aspects of teaching and learning mathematics not only for the students but also for the teachers.

Intro

Hi

I'm Vasandy S Narayanayar from BSc05. First time I've created a blog, so am exploring to learn more about it. You may call me Vasandy. Looking forward to the class too.