Session 6 Reflection (31st August 2011- Final session)

Session 6- 31^st August 2011

This was my final session with Dr Yeap. As we were discussing Lesson 22 with Dr Yeap, we learnt that it is important for children to understand the real-life meaning of the calculation done to get the answer. From the way they answer questions, we can infer their procedural knowledge, conceptual knowledge and whether do they know the right method to use. We also learnt of the various kinds of tests given to children.

1. Paper-pencil test

 2. Oral test

These are types of Assessment tasks given to children.

I like the real life math teaching moment with the Environment that Dr Yeap did with the class.  Math teaching should be done throughout the day, we can make use of the moment, make it a “math moment”!. Even when one is outdoors, we can use the environment to teach math such as the activity we did using the photo from Hort Park.  The class did Multiplication in Hort Park!!

“What are the ways children can count” ? Dr Yeap asked.

“Counting in two’s , 7 times table.. Etc…”?

“Will counting in two’s become an obstacle for them?”… Dr Yeap really made us think. “Do they have strategies to overcome weaknesses?” (These are assessing type of questions used I realized that Dr Yeap was encouraging us to think along these patterns...)

So, from this activity, I realized wow!!  We can really see how much a child knows. …I also enjoyed the other real –life environment activities like the Measurement of the top of the Bras –Brasah MRT staircase to the bottom.

My calculation is as follows:  62 steps x 15cm = 930

                                930 / 100= 9.3m 

Our group discussed the measurements we got and we also thought is it the exact distance from the top of the staircase to the bottom? What about the open space in between each set of steps… we didn’t count that.. We were wondering is it still accurate… hmnn…

As for the kidney bean activity,  we had to apply our pre- knowledge of volume & capacity  and newly found understanding of  volume and capacity that Dr Yeap briefed us on before the activity to the making of the container and whoa! !

I didn’t realize a small box would be able to hold so many many beans!! That activity was amazing….

Overall, I enjoyed my last- session and took note that as teachers Math can be taught when the moment is made teachable. Now I have a deeper understanding of what Math is and will apply the strategy and tasks learnt with my kids.

Math is looking for visualization, patterns, having number sense, metacognition & communication!!! Thanks Dr. Yeap J

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Session 5 Reflection (26th August 2011)

Session 5 – 26^th August 2011

This was session 5 with Dr Yeap.  We did some interesting activities and I was just thinking, kids these days really have to encounter tricky math problems! I struggle to do primary school math… ha-ha…! But overall, I enjoyed the sessions and discussing the questions and going through the activities with my fellow group mates. We learnt that there are assessment tasks types of questions given to kids. I learnt about Bloom’s taxonomy which describes cognitive processes and also describes the levels. And in math there are 3 levels of Bloom’s taxonomy used: 3 levels of 6 levels. When examiners set an assessment tasks, they set questions based on knowledge level, comprehension level (inferential) & Application levels.

Assessment task: Jerome Brumer- Repeated opportunity to encounter idea, without REPITITION. J

 In Singapore, they use the spiral approach where you get to encounter topics again and again but each time children will get to revisit the topic again at a higher level. Hopefully, they can master basic ideas and then they can proceed more into depth in the topic.

It was an interesting week and I managed to collect 4 pegs J



Our Peg- Graph!!



Session 4 Reflection ( 25th August 2011)

Session 4 -  25^th August 2011

Dr Yeap took us again. He’s a math magician!! I really liked the number game, the  2 digits one… wow ! I am so impressed he can really dissect and find patterns. Dr Yeap, its cool stuff that game!  You are a mind reader. And the saying communist teacher always makes me laugh hahah…  Mathematics curriculum explores to do things in different way, NO ONE WAY, we are not COMMUNIST  TEACHERS! I like that. :)

Also, I learnt that it is important to expose our students to different variations of the problem. And we were taught of 3 important people’s names ZOLTAN DIENES who is still alive and a century old. And yes I remember Mr Jerome  Brumer, the CPA approach guy and Mr Howard Gardner, the Multiple Intelligents guy!

And therefore, Math is not about repetition, children will learn well when given variant of the same idea!!

2 Digit Trick Game!

Session 3 Reflection (24th August 2011)

Session 3 – (24th August 2011)

This was our 3^rd session. Our guest lecturer Miss Peggy Foo took us for this session. She showed us a video of a teacher conducting a lesson with a group of kids. We observed and noted down areas where we could reflect on such as, seating arrangement, engagement/involvement, classroom management, manipulatives and use of materials, sequence of lesson, progression of lesson and whether was the lesson coherent? As I sat there observing this video, I thought of how important it is for ourselves as teachers to do this kind of reflection on our teaching. We could always get a colleague to video tape us and learn how to improve and what to change. It helps to hear people’s views and although nobody likes to be observed and discuss teaching styles, doing this will help the teacher grow and also her colleagues will benefit too and learn from it.

We also were taught and reminded to look for evidences of differentiated learning, which is important as not all students learn the same way.

The 2^nd video was Peggy’s video where it was her first time teaching K1’s.

We learnt a lot from her video and I guess she too. I must mention she was quite brave to show her video to the class. At the end of the video, we learnt that a teacher must act as a facilitator and observe the kids, listen for children’s reasoning, ask questions to lead children to THINK, ask questions, LOOKING/LISTENING and LEADING THEM! J

Last but not least, I really enjoyed the tangram activity which helps one to visualize!



Tangram -Can you VISUALIZE



Session 2 Reflection (23rd August 2011)

Session 2 ( 23^rd August 2011)

This was our 2^nd session with Dr Yeap.

Pick up sticks game

It was an interesting session where I enjoyed playing the pickup sticks game. I realized there is a pattern to it, an alternating pattern. There is a good number for either of the players and a bad number too. It was a good game. I learnt an interesting word which now is stuck in my mind SUBITIZE! I subitize , one look and I KNOW . J

It also made me reflect on my number sense which is not that great…LOL !!

This game is a good practice for counting. As a teacher, it lets our kids learn and decide. Kids can make decisions if a number is good for them and think how they can try and make it bad for the opponent. This game really dived into a good sense of counting!

Differentiated Learning

Dr Yeap also informed us that as teachers there must be differentiated instruction for children of different abilities.

Video Learning ( Dr Yeap Teaching)

Through this video ,I learnt there  was an interesting objective of this lesson.Can children add, can they see patterns, can they communicate mathematical patterns??? Having number sense is important and looking for patterns in one of the big sense.

Long Division Activity

I learnt the reasons of why we do long division in a certain way. It was a new way of thinking. This activity really reminded me of my math class when I was younger.

We not only need to know it is like that , it is important to explain the reasoning which Dr Yeap explained step by step to us, something that none of my math teachers in my entire life did. Thanks Dr Yeap!! J

Dr Yeap also reminded us we are not teaching Mathematics , but  we are teaching children. We use math as a tool and teach children how to correct themselves.

METACOGNITION- this manages our brains thinking.

I like this part of what Dr Yeap said, ‘Never teach children machine skills, teach children decision making, who cares about the calculation?’( any calculator can do that) we care about DECESION MAKING. That really sunk in..:)

I also like his point that the ability to remember is not a HUMAN STRENGTH.

Mathematics is not about MEMORIZATION!

I also like the point of anything with 10,000 hours if practice makes one a minor GENIUS!

I can make my list now … hahah

All in all on this session , I learnt that mathematics is developing thinking and metacognition skills, visualization, generalization , communication and number sense!!

Session 1 Reflection (22nd August 2011)

Session 1 ( 22^nd August 2011)



Name-Problem Activity



This was my first session in Dr Yeap’s class. It was an interesting introduction of our professors last name Ban Har which means a ‘thousand summers’ which I thought it was cool and has a nice meaning. And then it was time to problem-solve the Name- problem Activity!

Hahah… I did not know it will turn into a math activity. =)  because I so do not like doing math…..!! But I enjoyed the session because it helped  me to see Math in a different light. From this whole session, I experienced the 5 process standards through the activities which were designed to bring out problem solving skills, reasoning and proof, communication, connections and representation.

 (Name- Problem Activity)

This lesson helped me think of alternate methods and if there is more ways to solve this problem.  I noticed the more the class thought, the more methods the class found and they came up with 4 methods and communicated their views with the whole class. As I sat in class listening, I realized it is important to understand other people’s point of view even if we know the answer. In that way and applying it as a teacher, we need to know why our students think in a way, how they came to it, what do they understand and make out of it and how they connect it.

Uses Of Numbers

I learnt that it is important to explicitly teach young children that numbers are used differently and what are the various ways in which numbers can be used.

1.     Cardinal Numbers- Numbers to count

2.    *Ordinal numbers

3.    Position in space- no of letters

4.    Position  with respect to time

5.    Rote

6.    Nominal

7.    Measurement numbers

                    

An interesting thing I learnt in class was the common mistake teachers make because we are not careful when teaching ordinal numbers. When we teach ordinal numbers we tend to ask: `who is 3^rd in the race?’ Actually, anyone can be from the picture. We need to describe explicitly for young children.

e.g. At this point who is 3^rd from the finishing line ? We teachers should not mix up ordinal numbers in space and ordinal numbers in time.

More Uses of Numbers

There are also other uses of numbers which are odd and even, prime numbers, differences in numbers etc…

Teachers must understand the terms and observe children, as children are at different standards.

Some children do rote-counting, others have progressed to rationale counting or some might even say sequence of numbers correctly but don’t even know what the number represents and how it is used.

(Sound of a number Activity)

I found this activity interesting. Dr Yeap was talking about the sound of numbers- How many buttons are there in the can?

Questions class asked: Is it same size?

                                   : Is it same material?

It was good we asked this because we realized materials grouped according to size and same material is easier to count for young children. Dr Yeap mentioned it is a bad example if there is no grouping. Depending on a Unit you can count something. Some things can be counted and some cannot be counted. In the 2 cans there were same type of buttons and he emphasized to us you can only count things in the same set. (Good example)

He said that it is a good idea to use identical things or identical things which can be perceived as identical. It must be in same unit, same set.

When Counting:

 Teachers must also take note- children must be able to classify before they count!

            And that is why for meaningful counting there are 3 Pre-requisites

·         Ability to classify before counting

·         Ability to do rote counting in the correct sequence

·         Able to do 1 to 1 correspondence.

·         Appreciation the last number you utter represents the things in the group.

I found these points useful and definitely will come in handy as a Assessment tool.

Poker Cards Activity

 I really like this trick. I feel like a magician and was already imagining the    children’s reactions. I learnt there is a pattern to this trick and for a pattern question, rules must be stated. Patterns always have rules and terms!

Last but not least, I enjoyed this 1^st session and going through the 5 process experiences and agree that doing mathematics is not about getting to the destination it is a process and a vehicle and is to develop visualization and good thinking skills.



Poker Card Magic Trick!



Chapter 1 & 2 Reflections ( EDU 330)

Blog Entries Reflection (Elementary Mathematics)

Chapter 1:

Teaching Mathematics in the Era of the NCTM standards

As I read this chapter, I began to realize how meaningful and impactful the NCTM standards are. I looked at the Pre -K2 standards found in Appendix A and I remember during my time or Era in my preschool years, mathematics was route learned. There was no flexibility in expressing understanding. Those days were just one way, because it’s like that and it’s like that, no questions asked.

 Then, teachers were not really patient and I as a student was not really interested in this subject. I also didn’t have the motivation and persistence.

Furthermore, the teachers I had for math were also not really encouraging or dynamic. I enjoyed language subjects but didn’t really manage to cultivate the love or passion for math even up to my primary years of schooling and secondary school years too.

Reflecting on this chapter as a teacher and learner, I realized that the NCTM standards provide expectations that are more concrete and well-defined. I found the standards to be meaningful with ample reasoning given. The NCTM allows a child to make meaning and not just only know concepts but experience concepts. Knowing the WHY’S are important as it’s not just about knowing a certain formula. Therefore, when children inquire and desire to know why and how the problem is solved this way, it allows challenge and reasoning experiences into their mathematics learning. Also, as I pondered upon the five content standards I realized and agree that the five process standards direct the methods or processes of doing all mathematics learning and teaching.

5 Content standards

·         Numbers and Operations

·         Algebra

·         Geometry

·         Measurement

·         Data Analysis and Probability

5 Process Standards

·         Problem Solving

·         Reasoning and Proof

·         Communication

·         Connections

·         Representation

I also like the saying which I read from pg 4 of the book which says that, “we should teach in a way that reflects these process standards because it is one of the best definitions of what it means to teach according to the standards.”

As I read Appendix B, Two standards came across my mind.

1: Reflection on my teaching practice (Standard 7)

2. Reflection on Learning Environment (Standard 4)

I thought as an Educator it is important and good to check if meaningful teachings are taking place and whether a good learning environment is set up, one that cultivates active learning and also fosters respect towards each individual child needs and way of learning.

As I read about the data from NAEP, I realized that American students don’t really perform in math. There must be some factor that causes this and I believe mathematic passion has to be nurtured as well as cultivated and teaching has to be done meaningfully with proper goals. Instead of focusing to do everything I agree it is important to do a depth of study on each topic. It is more meaningful and therefore I like the idea of the Curriculum Focal points.

 In that way, students get to focus on a topic and have to put in their effort as well. This spurs more focused concentration and attention.

Chapter 2:

Exploring What it means to know and do mathematics!!

I agree with what I read in chapter two. To know and do Mathematics  means “generating strategies for solving problems , applying those approaches, seeing if they lead to solutions and checking to see if the answers make sense”. As said in the book, “Doing Mathematics in classrooms should closely model the act of doing mathematics in the real world”. (Pg 13) I believe, giving students concrete hands on experiences is essential. Creating a proper classroom environment for doing mathematics is strongly needed. Children must be comfortable in an environment where they can discuss ideas free of risks. Also as an educator, I believe that it is important to have a personal feel for doing Mathematics. Knowing the Science and Order of Math is very much vital as it helps us connect with our students’ predicament. We as educators have to remind ourselves how each unique child understands the problem and solves it. And when doing Math, using justification is also necessary as when we problem- solve, it helps determine if an answer is correct, because eventually when it comes to the real world there are truly no “answer books”.

Constructivist theory and Sociocultural theory.

Constructivist theory:

As I read about the constructivist theory, I begin to understand the figure 2.8 model better (pg 20) - We use the ideas we already have (blue dots) to construct a new, idea (red dot), developing in the process a network of connections between ideas. The more ideas used and the more connections made, the better we understand. This is where I think the 2 theories work hand in hand and they are quite similar. Pg 21 says, “…when considering classroom practices that maximize opportunities to construct ideas, or to provide tools to promote mediation, they are quite similar.”Ideas can be discussed in classroom interactions and that’s where we learn from each other and expound on more ideas. We can grow ideas together. To do this once again, the classroom culture and environment must be one that cultivates respect, sharing and a safe risk-free learning environment. And so, I agree with the points on pg 22

1.     Provide opportunities to talk about mathematics

2.    Build in opportunities for reflective thought.

3.    Encourage Multiple Approaches

4.    Treat errors as opportunities for learning.

5.    Scaffold new content

6.    Honor Diversity

What does it mean to understand Mathematics???

Pg 23- “ One way we can think about understanding is that it exists along a continuum from a relational understanding-knowing what to do and why- to an instrumental understanding- doing without understanding.

Relational Understanding and Instrumental Understanding

Pg 24 – Figure 2.11 says, understanding is a measure of the quality and quantity of connections that a new idea has with existing ideas. The greater the number of connections to a network of ideas, the better the understanding.”

And therefore I believe, relational understanding is very important as it provides reasoning and meaning to one’s work. It’s not just a “formula-basis” experience with math. Last but not least, I have learnt that to know and do math should be a purposeful and meaningful experience.