Professional Development for Secondary Mathematics Teachers
At Meechai Pattana SchoolBuriram, Thailand
Yeap Ban HarMarshall Cavendish Institute
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
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