Chapter 2: Exploring What It Means to Know and Do Mathematics

Knowledge cannot be “poured into” a learner.

Students will tap onto their prior knowledge (represent by the blue dots) and try to connect/ develop relationship to the new idea (red dot) to build new knowledge, as shown in Figure 2.8 on page 20. As each student is unique with a different collection of prior knowledge and cultural experiences, teacher play a big responsibility to provide experiences to develop those missing blue dots and then connect to the new concept being learned.

There is a shift from traditional practice of teacher telling student one way to do the problem to cultivate a classroom culture where students feel free to voice out their ideas, approaches and strategies for doing mathematics.

Personally, I enjoyed doing mathematics as I enjoyed challenging myself to tough problems and the process of generating strategies by identifying pattern of regularity and logical order, with the aim of solving it. I learned multiplication through memorizing timetable, which is deemed as a weak construction and not connected to other knowledge. Therefore, understanding concepts and making connection is more useful than procedural knowledge.

I concur with the author that students can relate better if they can see the value of doing mathematics in the real world. There is no answer book in the real world, we have to find it, reason and justify that it is correct.

Chapter 1: Teaching Mathematics in the Era of the NCTM Standards

The 6 Principles and 5 Standards for School Mathematics (2000)
6 Principles 5 Standards
Equity Number and Operations
Curriculum Algebra
Teaching Geometry
Learning Measurement
Assessment Data Analysis and Probability
Technology

I am a strong believer that technology enhances the learning of mathematics, especially for young children who still love to play. I can vividly remember the days that I compete with my cousin on our speed in solving mathematics equations on Playstation software game, designed for various grade (Primary 1 to Primary 6). Through this activity, it boosts our morale to count mentally and motivate us to be fast and accurate in our solving.

Teachers’ teaching methodology will have a direct impact and influence students’ development for mathematics. I love the sentence “to respond to students’ challenges, uncertainties, and frustration you need to unlearn and relearn mathematical concepts.” The approach on how we used to learn mathematics for a certain topic from our teachers when we were young might not be the only method and only way to present it to children nowadays. Two decades ago teaching methodology that my teachers used on me, shaped the way I do mathematics but that does not necessary implied the same for this era learners. I can’t help but agree that what is familiar to you will become unfamiliar and vice versa, terminology/ expression that we are used to might be misleading to children, e.g reducing fraction. Hence, I am interested to know how we can employ innovative and conceptually sound methods for teaching fractions in Chapter 15.

Therefore, I totally agree that to become a teacher of mathematics, you not only need to equip
yourself with knowledge of mathematics content but also move away from procedure-focused to conceptual approach, so as to be able to explain the problem in different scenario and in a manner that young minds are able to visualize and understand. Teachers need to positive, think out of the box, be creative and engage students in interesting activities to develop them to be “math lovers”.

We need to move from traditional curricula to standards-based curricula! Teach students how to fish rather them feeding them with fishes. Help them acquire the skills to understand the concepts, focus on when computation might be needed or how that topic is related to other mathematics strands rather than focus on showing students how to do the computation.