## Saturday, March 31, 2012

### Question on Retention

Question - How do we help students retain what they have learned.

ATeacher in Hawaii

A good program arranges the topics in a certain way for various purposes. To help students retain, one of the ways is to arrange topics in such as a way that students have many opportunities to revisit a particular key concept or skill.

Let's use the example of equivalent fractions. After it is learned in Grade 3, the chapters that follow it are adding unlike fractions and subtracting unlike fractions (but limited to cases such as a third plus a sixth or three tenths subtract a fifth where it is necessary to rename only one of the fractions to make both like fractions). The two weeks or so of constant writing fractions as equivalent ones as students add unlike fractions help them consolidate the skill learned. It is critical that a new skill is well consolidated before students leave them behind.

The next grade level when student said such fractions but for cases where the sum exceeds 1, students get to review finding equivalent fractions. In grade five, when students are dividing say a half by three, one of the methods involves renaming one half as three sixths before proceeding to divide the three parts into three. Using this method, three fourths divided by three can be done straight away but to divide three fourths by two requires renaming three fourths as six eighths. The opportunity to review equivalent fraction in a different context enhance the retention of the skill of finding equivalent fractions.

Two principles discussed here - ample consolidation after a new skill is learned and review but not a mere repetition but done in other / more challenging contexts.

Singapore curriculum is arranged for this to happen. Good textbook authors arrange the topics for this to happen.

## Wednesday, March 7, 2012

### A Bunch of Questions

Question
How can Singapore Math be taught to children who are at different learning levels? Answer
We just completed a two-day professional development on how to do differentiated instruction using Singapore Math in White Plains with 60 teachers. For struggling learners the concrete experience before pictorial representation helps them. For advanced learners, tasks can be easily extended to engage them in higher-order thinking. Singapore Math is well-known for helping average learners reach high levels of achievement. The last piece of information is what emerges from TIMSS and PISA where many of our average learners are performing at Advanced level in TIMSS or Levels 5 and 6 at PISA.

Question
How does Singapore Math help children who have difficulty learning math?
The use of visuals helps. In Singapore Math we use the CPA (concrete-pictorial-abstract) Approach based on Jerome Bruner's work. Students are taught an abstract concept via concrete expreinecs and the use of pictorial representations.

Question
How does Singapore Math help children with more advanced math skills? Singapore Math is based on the idea of using mathematics as a vehicle for the development and improvement of a person's intellectual competencies. Students with advanced skills get to work with more complex problem that requires deeper thinking (this is in the program). They also get to develop skills such visualization and ability to see patterns.

Question
What training do teachers/school administrators need in order to introduce Singapore Math in their curriculum?