Making Connections through Promoting Mathematical Thinking. Lim-Teo Suat Khoh, MME, NIE Mathematics Teachers Conference 2 June 2011. Overview. Mathematical Thinking and Connections in the Singapore Mathematics Curriculum Connections within mathematics strands Connections across strands
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Promoting Mathematical Thinking
Lim-Teo Suat Khoh, MME, NIE
Mathematics Teachers Conference
2 June 2011
Do these sound familiar?
Do these sound familiar?
Where are the connections between topics within or across strands?
Connections within Strand A person does mathematics when he/she engages in such thinking processes.
A Kite is made up of two isosceles triangles with equal bases
Symmetry properties of isosceles triangles
Line of symmetry is the perpendicular bisector of the base and is the angle bisector of the third (unequal) angle.
Properties of kites
Diagonals are perpendicular, one of the diagonals is the angle bisector of two angles and it also bisects other diagonal perpendicularly
Constructing a kite and its diagonal
From a diagonal, constructing a kite and symmetry diagonal
Construction of perpendicular bisector of line segment
Construction of angle bisector
A square is a rhombus because it satisfies all the properties which define a rhombus.
Set of Real Numbers
Expansion of the concept of numbers: from counting numbers, to fractions, to negative numbers and irrationals.
Need for negative numbers !
Moral of Xuan’s story – even primary children can understand concept of negative numbers
If I choose to add 2 and 3 by writing 2 as 6/3 and 3 as 12/4 and use the rule for adding fractions would the answer be correct?
ax2 + bx + c:
y2 + (2x + 3)2 = 10
2x + y = 1
e-x(2e-x + 1) = 15
Piaget, Bruner, Dienes, Gagne, Skemp, Marton
Average rates of change
Intuitive understanding of tangent as instantaneous rates of change
Connections across strands A person does mathematics when he/she engages in such thinking processes.
Connections to Reality A person does mathematics when he/she engages in such thinking processes.
Connections are the essence of mathematical structures
Connections enhance learning (better and deeper learning)