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.