Professional Development for Secondary Mathematics Teachers

At Meechai Pattana SchoolBuriram, Thailand

Yeap Ban HarMarshall Cavendish Institute

banhar.yeap@pathlight.org.sg

Slides are available at

www.banhar.blogspot.com

Outline of Workshop

Two Core Competencies in Secondary MathematicsLooking for Patterns and Relationships and Make GeneralizationVisualization

Bruner’s TheoryConcrete Pictorial Abstract

Problem-Based ApproachUsing one problem and asking students to solve the problems in different ways

Core Competencies in Mathematics Example from Thailand O-NET (Grade 9)

Figure 1 Figure 2 Figure 3 Figure 4

Figure 1 contains 1 triangle.Figure 2 contains 3 triangles.Figure 3 contains 6 triangles.Figure 4 contains 10 triangles.Which figure contains 55 triangles?

Look at the following figures.

Method 11, 3, 6, 10, 15, 21, 28, 36, 45, 55where you add 2, 3, 4, 5, 6 and so on to get the next term.

Method 2Using [2 x (2+1)] ÷ 2 or [n x (n+1)] ÷ 2

Method 31+2=31+2+3=61+2+3+4=101+2+3+4+5=15…1+2+3+4+5+6+7+8+9+10=55

Answer: Figure 10

Core Competencies in Mathematics Example from Singapore PSLE Mathematics (Grade 6)

1 + 2 + 3 + 4 + 5 + … + 95 + 96 + 97The first 97 whole numbers are added up.What is the ones digit in the total?

Answer: 3

48 pairs of 98 and49 which does notpair up.

The one digit in48 x 98 is 4.The ones digit in48 x 98 + 49 is 3.

Core Competencies in Mathematics Patterns & Relationships

Find the ones digit in the sum of 1 + 2 + 3 + … + 2010 + 2011

Find the ones digit in the product of 1 x 2 x 3 x … x 2010 x 2011

Find the ones digit in the product of 3 x 3 x 3 x … x 3 x 3

2011 threes

Core Competencies in Mathematics Patterns & Relationships

Find the ones digit in the product of 3 x 3 x 3 x … x 3 x 3

2011 threes

Number of 3s Product

1 3

2 9

3 27

4 81

5 243

6 729

7 2187

Core Competencies in Mathematics Patterns & Relationships

Number of 3s Product

1 3

2 9

3 27

4 81

5 243

6 729

7 2187

8 6561

9 19 683

The ones digit in 32008 is 1

The ones digit in 32011 is 7

Core Competencies in Mathematics Example from Holland

Core Competencies in Mathematics Example from Japan

Method 1Find angle ABE first using the parallel property.

Method 2Find angle AEC first using the parallel property.

Test Item from LAS which is a local assessment for Grade 8 (Mathayom 2).

This item requires the abilityto visualize. It is important todevelop the basic abilities tovisualize and observe patterns.

10 cm

8 cm

10 cm

4 cm

Core Competencies in Mathematics Area of Trapezium