Sunday, September 4, 2011

The One at the MRT Staircase

But first, the answer to the height of the staircase at Bras Basah train station....

There were four flights of steps; with 14+16+16+16 steps.

Total no. of steps= 62

Height of one step= 14.8cm

The height of the staircase is about 62 x 14.8 = 917.6cm.

After converting to metre, the height is about 9 metres tall.

But may not be precise if I were to bring the measurement at the SI Unit office in France. So hence the use of "about" in the answer.

Assuming I did not have a ruler that day, how else can I measure the steps? Will it be possible to use my not-so-big feet? Perhaps my modest pair of Crocs helps. Use one side of the shoes and place against the side of step; mark where the height stops and then go back and use a ruler to measure that mark; multiply by the number of steps.

Part of tonight's lesson highlighted on the misconception of mass and weight- the difference of actual scientific terms and daily language use.
(Refer to discussion in textbook, Chapter 19, p.382).

To say, "my weight is 60kg" is not correct in science. That is known to be daily language. It should be "my mass is 60kg". Technically, our mass is the same but our weight change.
So other than the good news that I can be 100-neutons on the moon (i'm about 600-neutons on Earth), we delved into the question on whether to use or avoid introducing the concept of weight/mass in pre-school totally because students in P1 will be learning Mass. They will then have to change to the correct idea.

Dr Yeap pointed out that in pre-school, we can teach weight in statement like this:

"The book is as heavy as 3 cans of Lemon Tea.", "the bear weighs as much as 5 cubes".
Aside from Mass, the rest we can teach using non-standard units as usual.

Same goes for the concept of time.

The other night I asked Rushda, now in P1, what time it was. The clock in the car showed 22:20. She replied that it was "10:20". I asked how did she know it was "10"? She could not explain but I hope she will develop the understanding as she continues to learn concept of time till P4.

Dr Yeap concluded the night with a refresher course on the different types of graphs and the use of the diff types with the correct categories.

Many of us struggled in Mathematic due to the conventional methods we were taught. How lessons were presented were key for us students to grasp concepts. Although Math was painful to learn in school, I never hated it. I never hated the teachers/tutors who were screaming their heads off when I needed their extra coaching. Because now that I am an educator, I want to be sure that my young students get the best, positive and memorable Mathematic experience to gear them for more competent Mathematics.

EDU330 module is an eye-opening learning experience.
The math presented by Dr Yeap Ban Har was first magical, then it was mind-boggling. It just sets you thinking and thinking.

Thank you for the opportunity. Nevermind that I got a peg, that does not mean that I am giving up. This is a new beginning.


Friday, August 26, 2011

The One with Bloom's Taxanomy, Pick's Theorem and monster eyes

Today we did several lessons on the topic of Fraction.

I am trying to recall if my Math teachers in primary school ever used model drawing to explain fraction word problems. They did, but only at the beginning stage, where fraction was first introduced. When Dr Yeap does modelling of the story problem, we are able to "see" a better picture. Like what was shared by my other classmates, all that we were taught then were formulas - inferring denominators, using the LCM, turn over denominator over numerator when doing fraction division. It IS like that. I embraced it with no questions asked.

I never had problem with Math until Secondary Two. I joined the book-pickers club, picking up Math workbooks thrown to the floor. Well, we learned as we were taught then. Very procedural understanding.

But what Dr Yeap is trying to put across is that pictorial continues to help Math learners understand the conceptualization.

Dr Yeap demonstrated how Bruner's theory applies in the Spiral Curriculum.

In P2: deal with same denominator.
In P3: subtract different denominator
In P5: infer denominator

for children to learn, Bruner's style is, children "must have repeated opportunities" to explore concepts they have learned, and as they progress, newly-added ideas are given.

Different levels of Assessment Task

Bloom's Taxanomy described the different level of cognitive processes. Primary-levels Math are tested at the first three levels of Bloom's taxanomy: Knowledge, Comprehension and Application levels.

Then, we were presented with Pick's Theorem.

We were challenged to make as many squares as possible. When Dr Yeap told us that someone has managed to get more than 8, I knew this is another case of THINK OUT OF THE BOX. My brain enjoys being challenged, but it has its limitation. When it comes to Math, it has been programmed to think one-answer, although I tried very hard to push myself to the limit.

There is a theory shared in the link to Pick's Theorem. I do not understand it, but what I understood was Janica's discovery about the area of square. She's brilliant! As for me, I depended on Ain to simplify the explanation. Got a better picture afterwards. Thanks Ain.

Lastly, at the end of the day, we were given the nightly quiz. This time it is about monsters and eyes.
I did a layman's working as how I understood it: 2-eyed and 3 eyed monsters, how many monsters altogether when there are 19 eyes altogether?

2 + 3 = 5. (That's 2 monsters)
2+2+3+3 = 10 (4 monsters)
2+2+2+3+3+3 = 15 (6 monsters)

Add 15 eyes to 4 more of 2-eyed monsters, you get 19, and that gives you 8 monsters.
But when I was going through Rushda's Number Bonding homework the next day, I thought could this be it?

Dear God, please give my children the strength and ability to understand and make the learning of Mathematic a joyful journey for them.

Thursday, August 25, 2011

The One with Chicken Briyani

....for breaking of fast. I've been having sandwich for three nights. Repetition is not so good. So I decided to have Chicken Briyani. Good to have variations for dinner. :)

Nothing to do with Math at first. A dinner which I hoped would fuel my brain to think mathematically. But it didnt, however, I must say, my thinking process got better.

In tonight's class, Dr Yeap covered Lessons 14, 15 and 16.

Lesson 14 was a "Mind-Reading Game", which Primary-schoolers like Rushda would love.

This was one that you could identify pattern in the answers. Every answer turns out to be multiple of 9. How's that so? Does it matter what your second number is? Not really.

Again, Dr Yeap helped us see patterns when the numbers were explored. Making sense based on the numbers you have.

Rushda was able to conceptualize the "x (make 10) - x" , and she is able to "predict" my first digit. She has yet to establish multiple of 9.

Lesson 15: Subtraction with Renaming

Dr Yeap facilitated us in making connection with breaking down number, just like number bonds.

We then went one level up by creating problem sums.

The above is an example of Continuous Quantities (as in dollar and kilogram)

The above is an example of a change situation in a story problem.

The above is an example of a part-whole situation. This story problem used "Discrete Quantities".

Hence, i think it is best to introduce sums with Discrete Quantities for easier conceptualization.

Big Idea: In introducing subtraction word problems, start with CHANGES model, then PART-WHOLE model, then COMPARISON model.

Big Idea: In model drawing the word problem, the unknown can be on initial, on change or final.

Big Idea: "expose the children to VARIATIONS, not REPETITIONS".

(not only for food. Also for Math!)

Lesson 16: Fractions - parts and whole.

Intensity level was easy at first. In the above, the parts are named one-fourth, two-fourth, and so on. Dr Yeap, explained that the "fourth" here is a noun, just like cookies. One cookie, two cookies, etc.

Big Idea: Children are able to comprehend well if the language structure is given. Children are then able to understand, make connections.

Then intensity went one level up. A given rectangle- with 4 triangles. Are they equal? Yes, they are equal. Albeit visually, they are not identical. Prove it.

Concrete: Cut out the bottom triangle and further cut into half. If you place the cutouts on either triangles, they are equivalent. ("scary siah" - a response from my cousin who is in Sec 2).


Abstract: Calculating using the area of triangle. Honestly, I had that thought, but I was not sure how to present my idea, because no measurement was given. Amrita beat me to that. (There goes the peg)


Big Idea: Division has two meanings -
Grouping: 12 divide by 4. In 12, how many groups of 4 are there?

Sharing: 12 divide by 3. 12 is shared equally among 3.

Big Idea of the night: Jerome Bruner's CPA Approach- anything CAN be dealt at three levels: Concrete -> Pictorial -> Abstract.

Wednesday, August 24, 2011

The One with Peggy Foo

Live from....



with stand-in lecturer, Ms Peggy Foo. In today's lesson, we learned about Math for younger children.

Top 8 Big Ideas:

1. Case Study videos.
Peggy showed videos of Lesson Study. She posed 2 Case Studies, which were of a teacher teaching the concept of More and Less to a group of K2s. We were encouraged to watch the video and observe. We were asked to think of one strength and one area to improve for the lessons. At the third video, a lesson conducted by Peggy herself, we were tasked to critique on areas such as...

2. Teaching points
Case Study 2:
Research Theme: How can we help pupils to explore options.
(not seen in photo is: 9. attitude/dispositions)

I picked up lots of points shared by fellow classmates.
This was Rahima's observations of Peggy in terms of Classroom management.




3. "There is no perfect lesson"
Peggy humbly admitted that it was her first time teaching a group of kindergarteners, and as much as we want to, the lessons we have planned may not run smoothly. We are reminded to try our best to make spontaneous changes, to be observant and listen to the children . I thought Peggy did well in her video lesson. I would love to be a participant in her Math lessons. As a teacher, she was quite animated, encouraging and demonstrated positive Math towards the class.

Then I reflected on the lessons I did at school today and self-evaluate against the nine categories. If there are areas I could pay more attention to, it would be on...

4. Questioning techniques and differentiation. Peggy led us into a discussion and we talked alot about lesson delivery and delved into "open-ended/close-ended questions" I thought that was a  good reminder. Peggy explained how differentiation should be included to facilitate weaker and higher learners. Questioning techniques shoud include:
  • types of questions
  • numbers of questions
  • waiting time: give students ample time to answer and give their explanation
  • Teachers vs students: (i forgot what Peggy explained).
Can't help but to laugh now thinking of the reenactment Dr Yeap did of how traditional teachers taught division - "it's like that. You don't ask why. Naughty Girl".

5. Prior to her video, we had a brain-game with Unifix Cubes, involving problem-solving, cooperation and creativity skills.

The task: create as many unique structures with 5-unifix cubes.




The highest number of structures was 25. Then, we struck of the common ones, to find out the most unique. In this activity, we were challenged to figure out that 5 cubes will still be 5 cubes regardless of the different structures produced. In the video, Peggy introduced to children 3, 4 and 5 cubes.


6. Mathematical Investigation:
What we did was called Mathematical Investigation. It can be done at the beginning, middle or end of lesson. It can be integrated with Arts, Language, Science, etc.


7. Research Study
Peggy concluded with great info on: (slides will be uploaded on Dr Yeap's I-Teach K blog.


8. We have homework!!!! Yippee!!! We got these tangrams Visualization exercise. Brainstorm. Good luck, Raudha.



Hope to win some precious pegs tomorrow. Lol!! Upon leaving the class, Peggy asked us to describe how/what we thought of tonight's workshop in one word.

I wrote: "worthwhile".


Tuesday, August 23, 2011

The One with Spiral and Subitize

Today's lesson began with the Pick-Up Sticks game. Objective of the game was for two players to pick up either one or two sticks. Winner is the one who drew the sticks second last.

We predicted/ identified "bad numbers" based on the take-rule. Again, we were made to notice patterns. For example:

Take: Bad Number(s):
1,2. 3,6,9
1,2,3. 4

This has got something to do with odd and even numbers. I need to play again in order to explain.

Then, we played Spin-a- Number. Objective of the game is to make the biggest even number possible.

An example here would be: by looking at the four-digits numbers below now, you could re-position the digits to meet the objective rightaway. What made it more intriguing was the fact that numbers were revealed one at a time. This is an idea for a good betting game. Just kidding.

Dr Yeap showed a video (let's call it the "Magic Dice" video) of a group of students that was presented with "Magic Dice" that could tell the total sum of dots on the dice' hidden surfaces. So the children thought hard when Dr Yeap challenged the class to figure out how did he knows. We also thought hard. Here's what we found.

Loads of bite-sized yet enriching information given by Dr Yeap, which I will remember.

Spiral Curriculum: a curriculum used in Singapore math. It allows many opportunities to practice, but not through repetitions. Here, Spiral also means revisiting.

Big Ideas tonight from Dr Yeap include lots of terms and explanations. Great logical pointers.

"Either you have it or you don't." is not quite accurate, as Dr Yeap explained. 10000hrs of practices, is how much I need in order for me to be good in Math. So, Kumon is out of the picture for my P1 daughter.


Monday, August 22, 2011

The One with Magic Shows

Lesson 1
22 August

That number 1 in "Lesson 1", do you think it is a Cardinal, Ordinal or Nominal Number?
What about the "22" in the date?

These were some of the first few tricky questions at the very beginning of our lesson posed by our professor,

Dr Yeap Ban Har

 Tonight, Dr Yeap stimulated us with mind-boggling "magic" tricks. While still in awe (mouth-gaping and all) and wondering whether he is involved with withcraft, Dr Yeap had us brainstorm, count, look for patterns and find alternate methods. Ah, not withcraft. Just logical reasoning through patterns that can be found by numbers. I am overwhelmed by tonight's activities, so Im just going to list down Big Ideas I gathered from tonight's lessons.

1. Use of Numbers - as cardinal (to count no. of people, items. Quantity); ordinal (to indicate position either in respect to space eg: 1st on the left, 3rd from the right; or in respect to time (1st to reach the finishing line); Nominal No. (number to name item eg Bus 14); Measurement numbers; Number patterns: Rote counting or Rationale Counting.

2. Best to introduce counting sets of identical attributes, followed by not so identical.

3. The Four Prequisites to counting: able to sort/classify; rote-counting; one-to-one correspondence; ablility to utter the last no. as the answer.

4. Make-10 Strategy, Double 7.

5. 10-Frame is a good starter to develop reference to 5s and 10s. Through this, the child will develop understanding of conservation and visualization.

6. Games we played:
  • 99th Letter in B A N H A R
  • Cookies for Jun Jun, Lasene, and Siti.
  • Poker Cards Magic
  • Number Sense through T-shape grid

Tonight's contents helped us understand Chapter 8. Seems like my classmates are enjoying the class despite having to pause every act of the magic show to do some mental works. I like the fact that Dr Yeap did not put down any wrong answers. He constantly responded with "Let's Try".

"This is a free world" brings a smile to me.

Saturday, August 20, 2011

Big Ideas from Chapter 1 & 2

Reading chapter one of the textbook gave me the idea of the importance of "handling" math as a subject, delicately as you will towards young children. I had a better picture of how Mathematic advocators/believers wanted Mathematic to be introduced positively to students, even it was in the context of what the education board in U.S recommended through NCTM. Anywhere else, even in Singapore, it would be the same.

I would like to use this math-blog to list down "Top Ten Big Ideas" I gathered in every chapter of the book to summarise my understanding. The summary and my reflections would be intertwined.

The following are some Big Ideas I have identified from Chapter 1. The points encompass the evolution history of mathematics and its related facts.

1. Mathematics has been undergoing slow but steady changes in the last two decades.

  • inspired by "knowledge gained from research."
  • Two key factors were:
  • (1) professional leadership of the National Council of Teachers of Mathematics (NCTM),
  • (2) public and political pressure for change in mathematic education due to U.S students' performance in international studies.
Raudha: I believed that the "slow but steady changes" applies to Math in Singapore too. I hear alot from parents who have more than one child who are enrolled in the Singapore education system. One common comment from all of the parents is, "Math is getting tougher and tougher even at P1 level". Then, I thought it contradicted to what I saw during Primary School visits with my Kindergarten Two students. What I saw during the sit-in lesson was interesting. For one, it is different from how Math was taught during my time in primary one. Schools now have a projector in class known as Visualiser, to facilitate teachers' teaching. They were also using concrete materials to do counting. I was impressed! I thought, hey, no problem for my students. I bet they would easily feel at ease, especially with the use of materials, which we have been doing in K2 class.

Yes, indeed Math is taught in a more fun way now than before. But, the syllabus remains as a horror!

I can tell you now. My eldest daughter is in P1 this year.

2. NCTM advocated: "Learning mathematics is maximised when teachers focus on mathematical thinking and reasoning.(p.1).

Raudha: Focus. Not to get distracted. To add on to that, I believed that logistic prepartion prior to lesson is also key. At times, I see teachers delivering the lesson, with lack of materials. Had more focus been given BEFORE lesson, then yes, the learning of math can be maximised. Guilty me.

3. Principles and Standards for School Mathematic advocates coherence in building instructions both in curriculum and daily classroom instructions. (p.2)

4. Teaching Principle: The experience that teachers provide every day in the classroom determines what student learned about mathematic. (p.2).

Raudha:  Upon reflecting, I thought that yes, long-service teachers lack the creativity and enthusiasm when teaching Math. Hence, the  principles cited in the book: equity, teaching, learning, assessment  are great refreshers for teachers.

5. Teaching Principle: Teachers must first understand deeply the math they are teaching; secondly, understand how children learn maths. Thirdly,select instructional tasks and strategies that will enhance learning (p.2).

6. Learning Principle: Learning is enhanced in classroom when students are required to evaluate their own ideas and those of others (p.3).

7. Assessment Principle: Ongoing observation and student interaction encourages students to clarify their ideas.(p.3).

8. Make changes in my depth of understanding to best prepare for the instructional leader role. (p.9-10)

9. Research: teachers with positive attitude teach math in more successful ways" (p.10)

10. Best teachers improve their practice through the latest articles, newest books, most recent conference or enroling in professional development opportunities. (p.10)

Raudha: Im already feeling positive about this. Looking forward to Prof Yeap's classes next week. Will tell him that I saw him on Mendaki's SOS Matematik. And wonders if poor Math has got anything to do with ethnicity. Eg: Malay.

Chapter 2

Here are my Top Ten Big Ideas from Chapter 2.

But before that, here's my response to the question, "What it means to do and know mathematics?"
Answer: "To "do and know" Mathematics is, to be able to do (apply formula, problem solve) what you know (Math topics) through what you have been taught for Math ........."

Does not sound like a good answer to me. Let me try again. I read a fair bits from an article, Schoenfeld, A. H. (1994). What do we know about mathematics curricula? Journal of Mathematical Behavior, 13(1).

From what I understood of the writer's explanation was, a traditional view sees Math as content-based. Hence, to know and do Math means you are competent in answering addition, subtraction, multiplication, division, properties of shapes, volume, dst, algebra, trigonometry, etc. Whereas...
A learning theory would say Mathematic is about mathematical thinking process. It develops problem-solving, trial-and-errors, prediction, estimation, inferences skills - applicable in other situations.

Schoenfeld (1994) found that "the emerging view of mathematics learning differs significantly in perspective, scope, and detail from the traditional view" (p.4).
 It gave me some key ideas in helping me to answer the question.

1.The real glossary of Mathematics (other than plus, minus, times, divide, more/less, equal) as highlighted in Principles and Standards):
explore, investigate, conjecture, solve, justify, represent, formulate, discover, construct, verify, explain, predict, develop, describe, use.

These are higher-level thinking processes in contrast to drilling and memorizing.

2. Setting for doing math: the teacher's role is to create this spirit of inquiry, trust and expectation. Within that environment, students are invited to do mathematics.

3. Math use justification as a means of determining if an answer is correct.

Raudha: Yes, if we are talking about problem-solving in the outside world, we based on justification. At times, we are faced with a no wrong/right answers. We take themost logical answer then.

4. Constructivist theory (Jean Piaget): children are creators of their own learning. Constructing knowledge produce cognitive schemas which could be rearranged by our brain to assimilate or accomodate.

5. Socicultural theory (Lev Vygotsky): social interaction is essential for mediation. The nature of the community of learners is affected not only by culture the teacher creates, but also the broader social and historical culture culture of classmates, other than the learner's own ZPD.