## Tuesday, May 18, 2010

### SingaporeMath in Action

Based on teacher education program in Singapore, about 90 Filipino educators made up the first class of Singapore Math in Action. Slides from four sessions are available here. The next Singapore Math in Action is scheduled for 24-25 September 2010.

For participants of the first class, these are the readings that you should complete to deepen your learning:

Read http://en.wikipedia.org/wiki/Jerome_Bruner also for Bruner. There is a link to　Spiral Curriculum
Read http://www.skemp.org.uk/ for Skemp`s idea on understanding. This is his website and the paper on relational and instrumental understanding is found under the section titled Papers.
Read http://www.zoltandienes.com/ for Dienes` six-stage theory. And try to locate some reading, books or on-line, about perceptual and mathematical variability.

For participants who want to have a documentation of their learning beyond the certificate each has received, you are invited to submit something that you have tried out in your own classrooms based on Singapore Math in Action that you have attended. Details are in the e-mail sent to all participants of the course.

Questions posted at the seminar are found at www.askbanhar.blogspot.com

This session is on mathematical problem solving.

This session is on all things related to fractions.

## Monday, May 10, 2010

### Ateneo de Manila Summer Institute

This is the third year I have been here to teach the summer institute. This year I am teaching the middle school program where the teachers are teaching Grades 4 to 7. We began after a brief opening ceremony.

In the opening session, I tried to discuss Bruner's enactive, iconic and symbolic representations using division of whole numbers by fractions and long division algorithms. The teachers asked questions related to teaching of division of fractions by fractions, multiplication of decimals and operations involving negative integers. We ended the day with a game of 'either one or three'- in a game where two players take turn to remove exactly one or three paper clips from apile of clips and the winner is the person who remove the last clip(s) - what is the winning strategy?

What if the rule is changes to wither 'one or two'?

We begin Day Two with Dienes' Theory of Variation ... but not before I pose the class the Fido Problem. Tell you more later.

## Saturday, May 1, 2010

### Problem-Based Approach

The open-ended approach common in the Japanese mathematics classroom uses a single problem in a mathematics lesson. In training teachers at Bina Bangsa School - a family of schools in Indonesia that uses the Singapore curriculum - I introduced the idea of teaching new concepts, doing drill-and-practice as well as getting students to apply what they learn using a well-selected or well-crafted problem. Other than workshops and lectures, teachers also get to see such problem-based lessons - there was one on learning area (primary three) and one applying Pythagoras theorem to find distance bewteen points (secondary two). Teachers saw examples, they worked through afew such problems, I modelled a few of such lessons with them and one with students,they worked with other colleagues to design one such lesson which hopefully they will try out and see how studenys respond to the lesson).

In designing such lesson, teachers select a problem and solve the problem themselves to understand the processes and challenges involved, as well as to see the mathematics in the problem. They decide if the problem can be used to introduce a topic or to provide drills-and-practice or to provide opportunities for students to apply what they have learnt.

They also considered how students will solve the problem and how to use the solutions to help students construct knowledge.