Katha 2014: Understanding Math: CPA and Mental Computations of SG

Minutes of the Workshop transcribed. Speaker Ms. Pauline Mangulabnan

KATHA 2014: Day 3:

Understanding Math: CPA and Mental Computations of SG

Ms. Pauline Mangulabnan

De La Salle University Manila

July 26, 2014

Minutes of the Workshop

1. Introduction. The speaker started with the review of the past lectures. The aim of the lecture was to identify CPA in Math and what are the principles of Singaporean Math. One is to boost the self-esteem of the students in Math and be able to hone their mathematical skills. In the Philippines, math skills do not reflect high self-esteem. In Singapore on the other hand and other East Asian countries, math skills are important.

2. Singapore Math. According to Dinyal, the success of the SG curriculum is on the following: 1) intended curriculum, where the SG Ministry of Education studied the curriculum thoroughly. This paves way to the sayings such as “It’s okay for them to count with their hands” and “Self-esteem is a double-edged sword.” The intended curriculum has a differentiated approach but not different in content. It is carefully sequenced in terms of the range of topics in a spiral curriculum. Textbooks reflect multi-step problem sets using the CPA approach. 2) Implemented Curriculum. This is the centralized system in grades 1 to 4, where the students should be exposed to such system for at most five years. There is also the worksheet culture where teachers reinvent the curriculum. 3) Attained Curriculum. This is where the benchmarking of grades is included: In grade 4 for example, in Singapore it should be 71%, Hong Kong 67%, Japan 62% and China 50%. There is a large amount of time to be devoted to doing Math, at least 20% of the curriculum. Philippines has the highest time allotment for Math, but then it is not in the length of time but how we make use of the time given.

3. SG Math. There should be a right attitude for Math and an emphasis on visual thinking. SG problems can be simple and non-routine, where real world problems that are not well-defined must be included, open-ended and complex in nature. The focus on critical thinking is essential because it emphasizes mental computations, ensures conceptual understanding and de-emphasizes procedural memorization. CPA basically means Concrete-Prictorial-Abstract according to Jerome Brune’s Theory of Representation. The speaker added that “Teaching for learning is not a waste of time.”

4. How does Math start. Math starts in creation, communication, and use of intuition. In early kindergarten, introduction to word problems using nursery rhymes, games and fairy tales may be used. Concepts of absence and presence, syllables in lines, drawing scenarios with money in quantity and valuing what you have in life skills may also be used in this approach. The speaker also said “Don’t go straight to ABC’s, to XYZ; make use of pictures first especially in algebra.” Games like Piko may be utilized to create critical thinking problems. The speaker added that “Mathematics is a subject not to be memorized but to be understood.”

5. Number Bonds. Number bonds are one concept applied in Singapore Math also called as the Math family. Mental computation without memorization relies on concepts rather than in formula. Issues were raised that this kind of approach is not found in textbooks. The speaker clarified that they still have the same competencies but different approaches. The teachers have to identify which part of the curriculum can be applied. Reactions from the participants also included the “discovery approach”, but there may be time constraints with the number of competencies used; therefore it should be arranged in such a way that it can be accommodated. Another question was raised on if the children are then thinking critically, what would be its consequence. The consequence would be way beyond the teachers’ expectation, the speaker said. Concerns were also raised and included that elementary teachers are generalists. They could be assigned to different subjects almost every year, which may mean that there would be a loss of expertise, but the speaker perceived it as a new learning for them to apply this kind of approach.