Shinglee Publishers Professional Development

d r y e a p b a n h a r

R E D E S I G N I N G T H E

S E C O N DA RY

M AT H E M AT I C S

C L A S S R O O M T h e P r o b l e m - S o l v i n g

A p p r o a c h

d r y e a p b a n h a r

S l i d e s a r e a v a i l a b l e a t

w w w . b a n h a r . l o g s p o t . c o m

• key findings from Japanese research on features of

effective mathematics lessons

• different types of lessons can be taught using a

problem-solving approach

• providing students with enriching learning

experiences that equip them with competencies

useful not just for mathematics but beyond

• three-part lesson format

w h a t

h ow

S I N G A P O R E M AT H E M AT I C S

C U R R I C U L U M

w w w . b a n h a r . b l o g s p o t . c o m

FOCUS ON

p r o b l e m s o l v i n g


p r o b l e m s o l v i n g

FOCUS ON

t h i n k i n g

S o u r c e : S i n g a p o r e E x a m i n a t i o n a n d A s s e s s m e n t B o a r d

Hong & Jeya Problem

S o u r c e : S i n g a p o r e E x a m i n a t i o n a n d A s s e s s m e n t B o a r d

Every minute Hong travelled 15 m more than Jeya.

Travel time = 240 15 = 16 min

Distance = 70 m x 16 = 700 m + 350 m + 70 m

= 1120 m

(a) Hong cycled 240 m more than Jeya.

(b) Jeya cycled 1120 m.

FOCUS ON

t h i n k i n g


Mathematics is “an excellent

vehicle for the development and

improvement of a person’s

intellectual competence”. Ministry of Education Singapore 2006

1992 Introduction of Problem-

Solving Curriculum

1997 Thinking Schools Learning Nation

1982 Introduction of Singapore mathematics

textbooks as they are known today. 2001 Introduction of textbooks published by

private publishers and approved by Ministry of Education.

2007 New editions of textbooks are

published with the introduction of the revised curriculum.

Mathematics is “an excellent

vehicle for the development and

improvement of a person’s

intellectual competence”. Ministry of Education Singapore 2006

2013 New editions of textbooks are

published with the revision of the curriculum.

Competencies

for the 21st

Century

w h a t

h ow

i n t r o d u c t i o n


S I N G A P O R E M AT H E M AT I C S

C U R R I C U L U M

Elements of Problem-Solving Classrooms


Elements of Problem-Solving Classrooms


Lesson Date:

x

y

x

2x

Anchor Tasks


Anchor Tasks


x

y

x

2x

Anchor Tasks


k e y q u e s t i o n


p o l i s h i n g p e b b l e s


c o l l e c t i v e a h a !


Extended

Engagement

with One

Task

Teach Less, Learn More


Extended

Engagement

with One

Task



a b

Extended

Engagement

with One

Task



a b

(a + b)2

Extended

Engagement

with One

Task



a b

(a + b)2

= b2 + …

Extended

Engagement

with One

Task



a b

(a + b)2

= b2 + a2 + …

Extended

Engagement

with One

Task



a b

(a + b)2

= b2 + a2 + ab + ab

= …

Extended

Engagement

with One

Task



effective mathematics lessons are based on an

anchor task



This is essentially teaching through problem solving.

effective mathematics lessons are based on an

anchor task



How does an anchor task benefit struggling learners?

How does an anchor task benefit advanced learners?

differentiated

instruction

guided practice

independent

practice

teacher models

teacher scaffolds

independent work

Lesson Structure

anchor task

guided practice

independent practice

Lesson Structure


anchor task

guided practice

independent practice

Instructional Model


model

scaffold

observe | independent work

i n s t r u c t i o n b e t w e e n d e s k s


s u m m i n g u p


b o a r d w r i t i n g


Lesson to develop concepts

Lesson to consolidate concepts

Lesson to apply concepts

Lesson Types


Anchor Task for Consolidation-Type Lessons


T h r e e T y p e s o f L e s s o n s

- D e v e l o p i n g c o n c e p t s

- C o n s o l i d a t i n g c o n c e p t s

- A p p l y i n g c o n c e p t s

T h r e e P a r t s t o A L e s s o n

- A n c h o r T a s k

- G u i d e d P r a c t i c e

- I n d e p e n d e n t P r a c t i c e

T h r e e I n s t r u c t i o n a l

P r a c t i c e

- M o d e l

- S c a f f o l d

- I n d e p e n d e n t

Shinglee Publishers Professional Development

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