reflection on 31st class

Today was the last day of our Math class, all in all I have learnt that math is not always about solving problems but basically building on thinking skills. I realised that even the word problem sum was an oxymoron and it should be called word problem. We revised on procedural, conceptual and conventional terms.
We looked at assessment - procedure and conceptual which can be tested with pencil and paper test and method which which is tested by oral test or interview.
I learn that there are array situations and rate situations.
There are 3 types of counting - counting all, skip counting and using 5 or 7 timestable using the hort park as an example.
There are 2 types of units like SI units and imperial units. I understood that for younger children when we use non standard measurment we should ask as how much does this weight instead of what is the weight as the children will be introduced to weight as mass in primary school so it will be good not to confuse them.
I learnt that if we are teaching time to younger children that we should relate the time to an everyday event so that they learnt the concept of time.
When we teach measurement to younger children we use the term "about" as it is not used with standard measurement.

The answer for the MRT activity is 16 steps x 4 sections x 13.5cm(height of a step) = 864cm

Reflection on 26th class

Today we learnt in depth about solving fractions sums and frankly I could understand some of it, which was a incredible discovery to me. I learnt about Bloom Taxonomy.
I understood that there are 3 levels of difficulty in primary school Math - A - application, C - comprehension and level 1 is K - knowledge level. KCA.
I learnt that when we are trying to teach the children we should not do the right and wrong face as this is an external artificial signal which the children will get used to and will be lost if they do not see the signal especially during exam time, we should coach them to learn the signals internally. We should question them even when they are right or wrong so that, that will stimulate them to think and reason out why they did the sum the way they did it.
I learnt about George Pick's theorum and we had a practice with learning how to calculate with dots.
I actually went back and gave a few of the sums that we had done to my two girls who are 11 and 9, and was impressed that they were able to do the sums and I was impressed that for the first time I could understand how they solved it.
Thank you Dr Yeap!

Reflection on 25 class

Yesterday, we learnt how to fold our papers differently and how we can figure out fractions easily instead of how we were taught last time. I felt that if I was taught like this I would have attained distinction for my Math. As it made alot of sense how Dr Yeap had done the sum in such a short while rather than the long way. I guess that is why it is important to be a teacher who understands the best method to teach and understand which is the best method the child can easily adapt and learn.
I learnt that things like money and kilograms are called continuous quantity and things like marbles and monsters are called discreet quantity.
I realised that to make lessons more interesting I must include variations like part part whole and change problem sums so that the children are challenged with different types of problems sums. Zoltan Dienes has stressed that variation is important and not repetition.
Frankly fractions seemed alot simpler yesterday the way Dr Yeap had explained it than when I learnt it back in school.

Reflection on 24 Aug 08

Today Ms Peggy took our class, she was very enthuasiastic. She showed us three videos about Lesson studies. I found that instead of attending PDs when others come into our classroom and observe us and give us constructive feedback is a good way to improve on our teaching as we listen to see other people's point of view and perspective which can improve us.
The PCF teacher I found tried to teach more and less, her lessons were good as it was open ended but I personally felt she could have interacted more with the children on what they did with the their own paper plates. The second time round she was more aware of seating the children in a circle which was a good practice as everyone could view the teacher easily.
I particularly liked the Japanese video where the teacher is observed by a group of seniors and given feedback, they pointed out things like you shouldnt have given the answer to the children but allowed the children to come up and give the answer so that we will find out how they solve the problems, which is what Dr Yeap has been talking about, giving the children the decision making power, let them solve their own problems with our facilitation of course.

I learnt that inquiry method is like mathematical investigation with multiple solutions, divergent methods with different answers which actually gives us an insight into the children's thinking and enables us to learn their order of thinking. Which will be a good step as we would know how to plan for that child so that we can scaffold that child.

Reflection on 23 Aug 08 class

Today I realised that mathematics is about generalising. There are three questions I should answer before I embark on planning the curriculum for the children.
1) what is it I want them to learn?
2) what if they cannot? (intervention)
3) what if they already know it (differentiated tasks) (scaffolding)

The dice game in lesson 7, was intriguing, I was amazed how Primary 1 students could think in different ways. And that was the key point Dr Yeap was trying to put across, how can we teach our children to think and look at problems in different ways, let them do the problem solving themselves. The ability to make decisions which is a life long skill.

In lesson 8, I learnt that there are three types of understandings
1) procedural understanding
2) meaning behind procedure - conceptual which is written by Richard Skemp - relational understanding and instrumental understanding
3) conventional understanding
These are the understanding the children must learn with our facilitiation
We must teach children and not teach Math, Math is used only as a tool. Allow children to correct themselves.

In Lessson 9
I learnt that in the big umbrella of developing thinking skills and problem solving there are 5 elements
1) visualisation
2)generalising
3) metacognition (managing information)
4) communicating ideas
5) developing number sense

In these two days we have learnt about what to teach and in the next three days we will learn how to teach, I am looking forward to learning Math in a fun way!

Reflection on 22 Aug 08 Class

I always had a hard time comprehending Math as I never did well in it in school. Yesterday's class really gave me a different perspective in learning Math. Dr Yeap made it interesting with using so many tools, taking them out from his bag non-stop. I must honestly say that I was lost some times especially in the finding out different ways of finding the answers in the last lesson. But I was in agreement with providing children with the same types of items to count and sort so that they do not get confused and see the properties clearly. As I think we do overlook this vital point when we bring materials to children to sort or count. I liked the card trick as well and I am keen to try it out with my children at home. I hope that being in Dr Yeap's class will bring back my love for Math and decrease my phobia as even when I looked at the quiz questions I'm freaking out.

EDU330 Elementary Mathematics - Assignment 1

Assignment 1 – Precourse reading – Chapters 1 and 2.

Chapter 1

I have learnt that before we start to teach Mathematics we should observe our children first, like how do they learn mathematics and how I can teach it so that they are able to understand the concept. I as a teacher should impart teaching of mathematics by concentrating on the thinking and reasoning (www.nctm.org). I realise that The Assessment Standard clearly shows the importance of including assessment with instruction and points to the importance of how assessment assists in implementing change. I learnt that there are six principles of Principles and Standards for School Mathematics – equity, curriculum, teaching, learning, assessment and technology.

The equity principle state that all students should be given equal opportunity to learn under high expectations.

The curriculum principle state that the importance of mathematics should be inculcated as a whole principle in the classroom instruction.

The Teaching principle state that teachers must understand how they teach, how the children learn and choose methods that children will be able to improve on their learning in Mathematics.

The learning principle state that Mathematics should be learnt with understanding and build the ability to think and reason.

The Assessment principle state there should be ongoing assessment which will ensure that children are able to interact which will encourage students learning.

The Technology principle states that technology strives to teach children to reason and solve problems which increase exploration and different ways of representing ideas.

I learnt that there are five content standards and number and operations is given the most importance from pre-K to grade 5. I learnt that there are five process standards which are problem solving, reasoning and proof, communication, connections and representation.

I realised that different countries have different standards and methods to teaching mathematics.  We often forget that teaching is a cultural activity and should observe our children on how they learn and adjust the teaching for the children so that they understand and apply the concepts easily. Usually text based and drilling methods do not help as it does not assist or develop the children to think and apply the skills at higher order thinking.  It is noted in this text that text books influence the way teachers teach and do not allow the flexibility of allowing the teacher to cater to the individual needs and understanding of the children.

What I basically understand from Chapter 1 is that there are standards and text to follow in teaching the Mathematics subject, but as a teacher we should inculcate a love to pass on to the students and be able to make a change to suit the learning abilities of the children we teach. As I feel that we as teachers should instill a love for the subject so that the child is able to problem solve and think and reflect rather than just focus on how to solve the text book problem as understanding and applying Mathematics is a life long skill.

Chapter 2

I understand that doing Mathematics does not only mean solving a problem but to see how this problem can be solved in different ways. I realised that even young children should be given the opportunity of exploring the sciences of Mathematics. The terms that we use in the classroom to teach Mathematics plays a part in our execution of our lesson, like understanding, making sense of a problem instead of listen, memorize and drill. It is very important as a teacher how we set the scene for teaching Mathematics. 

We should teach Mathematics thorough inquiry, we should encourage, entice and inculcate a sense of curiosity and enthusiasm as they strive to solve the problems. Students should never be put down or told that they are doing it wrongly but given support so that they are able to problem solve and be encouraged to try again to use other techniques to solve problems. This will encourage the students to try again instead of shying away from trying and being ridiculed and saying that you are not smart enough to solve this problem.

How can we include technology to ease the task of solving problems? Some problems can be solved by the use of calculators.

I understood that there can be different methods that you can break up a problem sum to understand it better like drawing diagrams, using models or pictures to create a clearer picture for the student to understand the problem.

The theories come into play in Mathematics as well, like constructivist and sociocultural theory where we learn from each other and our need to observe the child so that we can scaffold the child to the next level (ZPD).  There is a connection between theory and practice – the relational knowledge.

I personally thought that learning Mathematics was always learning how to solve the sums according to the text book. But from this textbook I realise that teaching and learning Mathematics is a social and interactive experience. The students should be given multiple opportunities to reflect, make mistakes take these as learning opportunities, not as failures and how they can work together as a team to solve these problems. How these problems can be simplified and broken down using models. And how it is utmost important for the teacher to create an environment for the students to explore and learn at their own developmental capabilities.

I like to share my personal classroom experience in relation to what I have read in Chapters 1 and 2. Recently we had our National Day Celebration. To create a social and math experience, as I was cutting the cake to give to the children to design our Singapore Flag I asked the one of children “how many pieces do I need to cut”? He started to count the number of peers and the teachers in the classroom; he was able to count the ten of us in the room. There was one child who was not present for that day and I asked him who are we missing and he was able to name the child that was absent. I asked him so we have ten of us, how many pieces of cake do I need to cut and he showed his ten fingers and said ten. He is three years old. He was able to display one to one correspondence as he was able to count the number of peers and teachers and relate it to the number of pieces of cake that is needed for each person to have one piece of cake. I find that as we inculcate such mathematical experiences through social experiences the children will be open to learning math as it will be a fun and practical way of learning math from young.