Katha 2014: Basics of Singapore Math

Minutes of the Workshop transcribed. Speaker Ms. Pauline Mangulabnan

KATHA 2014: Day 1:

Basics of Singapore Math

Ms. Pauline Mangulabnan

De La Salle University Manila

July 12, 2014

Minutes of the Workshop

1. Introduction. The speaker first asked why is Math called Mathematics to the teacher-participants. It is exactly a science which provides a systematic solution for a set of problems. It is essentially part of our everyday lives. How exactly? In China, math is used for trade (calculation), in Egypt the Egyptians made the pyramids using practical Math. Ancient civilizations used math all the time, while the Greeks and Romans formalized the theoretical Mathematics. Mathematics is basically a Greek word “Mathematikos” meaning learning and mental discipline. The speaker asked the participants what is math for them. One answer was that math is one subject that pervades life at any age, in any circumstance. Thus its value goes beyond the classroom and school.

2. It’s all about thinking. Why do young Filipinos have to learn Math as Math as a school subject? Therefore it must be learned very comprehensibly and with much depth, focusing on problem solving and critical thinking. It is recognized that Math is an excellent vehicle for the development and improvement of a country. Math offers the students the opportunities for creative work, moments of enlightenment and discovery.

3. K to 12 and Math. There are two goals of K to 12 for Math: critical thinking and problem solving. Students must 1) learn necessary math knowledge 2) effectively carry out math processes 3) understand concepts and connections and 4) transfer learning through performance.

4. 2 Approaches to Chief Problem. The speaker said that the teachers must retell the problem and ask the students how they understand the problem. Problem solving sets must be localized to what the students know. Instruction and Assessment should be in the same language used. In teaching, it is important to stimulate the student’s world and give him a view of the world that lies beyond his own. To teach math is to bring out the children’s desire to learn and to think, according to Toshiyuki Makata. The speaker also said to “teach the formula but teach it last.” She also asked how do teachers develop thinking/solving not by teaching them the formula but by showing them the patterns and coming up with formulas. Teaching mathematics is broadening one’s world. The speaker finally gave an activity to the teacher-participants.

Katha 2014: Teaching Geometry

Minutes of the Workshop transcribed. Speaker Mr. Robert Contreras

KATHA: DAY 5

Teaching Geometry

Mr. Robert Contreras

University of the Philippines Diliman

August 16, 2013

Minutes of the Workshop

 1. Introduction. Conceptual understanding in Geometry is essential for the students to understand and comprehend the subject better. There are necessary conditions on the different jargons and terms to be used in Geometry.

2. Geometry. The speaker said that Geometry is a tool for understanding and interacting with space. It also describes the world we live in and are axiomatic; that is it is rule-based.

2.1. Deductive System. This may be an analogy for a building where postulates are the base of the foundation of geometry.

2.2. Van Hiele Model. This model is learner-centered and is proposed in high school geometry in 1957 by teachers in Netherlands. It is a learning model with a holistic perception and develops a geometric thinking. It also refines the understanding of geometrical proofs.

There are three levels of the Van Hiele Model which are a validation of the CPA model: 1) Level 0 or Visualization. This is where the students perceive geometric shapes as total entities without attributes. This means that they are only aware of space as it is. 2) Level 1 or Analysis Model. This is where parts of the shape are already recognized by the students and they can discern characteristics of the shapes.  3) Level 2 or Abstraction. This is where figures are identified as having parts and are recognized by parts. Students can already discern the properties of the shapes and establish and analyze figures. Finally they can also subset classifications. 4) Level 3 or Deduction. This is the level where there is already the significance of deducing the figures to prove something and construct proofs based on the figures.  5) Level 4 or Rigor. This is where geometry is seen as an abstract form, i.e. in spherical geometry where parallel lines do not meet. Postulates are also recognized as usual functions of the body. These are the major characteristics of the Van Hiele Model, where it is sequential and in a reduction of level.

3. Implications to Teaching. This model entails mastery of polygons, grasping shapes as in CPA approach and the basis for each one. This can also be improved into shape teaching where teachers can create robots, counting how many are used, hopscotch, sorting cut out shapes and letting the students list the properties. The speaker illustrated different examples on how teachers can improve teaching Geometry through discovery games. He also provided samples on properties of shapes of everyday objects and property cards (What am I (shape)).