1. Hawaii Public Schools
M o a n a l u a C o m p l ex A re a
Professional Development on Singapore Math
Dr. Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
www.facebook.com/MCISingapore
Marshall Cavendish Institute
www.mcinstitute.com.sg
3. www.banhar.blogspot.com
This seminar focuses on issues on pacing and differentiated
instruction. Assessment and teaching through problem solving are
secondary themes in this customized course.
This professional development is equivalent to MAP114
Differentiated Instruction in Primary Mathematics incorporating
Enrichment and Remediation in Primary Mathematics.
www.facebook.com/MCISingapore
5. “Upon separation from Malaysia in 1965, Singapore
was faced with … high levels of unemployment and
poverty. 70% of Singapore’s households lived in badly
overcrowded conditions, and a third of its people
squatted in slums on the city fringes. Unemployment
averaged 14%, GDP per capita was less than $2,700,
and half of the population was illiterate. “
10. Country
% of Low
Performers
% of High
Performers
Mean
Singapore
8.3
40.0
573
Vietnam
14.2
13.3
511
Thailand
49.7
2.6
427
Malaysia
51.8
1.3
421
Indonesia
75.7
0.3
375
OECD
23.1
12.6
494
| PISA 2012
11. Country
% of Low
Performers
% of High
Performers
Mean
Shanghai
3.8
55.4
613
Singapore
8.3
40.0
573
Hong Kong
8.5
33.7
561
South Korea
9.1
30.9
554
Japan
11.1
23.7
536
Finland
12.3
15.3
519
OECD
23.1
12.6
494
| PISA 2012
12. What is Essential in Mathematics Literacy
What should students be learning in mathematics and what are the
implications for classroom practices?
13. What is Essential in Mathematics Literacy
What should students be learning in mathematics and what are the
implications for classroom practices?
communication
metacognition
number sense
visualization
patterns
14. What is Essential in Mathematics Literacy
Let’s look at what international assessment (PISA) for 15-year-olds and
Smarter Balanced Assessment for Hawaii State test suggest.
25. What is Basics?
The state standards (in this case Common Core State Standards)
outline what the basics are. In the next three examples, the
standards suggest that (Kindergarten) knowing that 12 is 10 and 2 is
basic, (Grade 5) being able to add and subtract mixed numbers with
different denominators is basic and (High School Algebra) being able
to solve simple equations is basic.
29. Teaching for Meaning Making
Concrete Materials
Students are given
bags of 6 beans
each
Anchor Task
How many beans in
4 such bags?
Students Talking
Multiple Responses
Count all
Repeated addition
Multiplication
Board Writing
Student Journal
Meaning Making
4 x 6 is the same as 4 bags of
6 beans. Also linking new
materials (multiplication) to old
materials (addition).
30. Teaching for Meaning Making
How do I know if I
have taught in a
meaningful way?
• Link to previous
knowledge
• Link to a
concrete
scenario
• Students can
extend their
thinking.
32. Teaching for Meaning Making
Use of Textbooks
Suggest the kind of
anticipated
responses (add
another six, double,
associative
property and
subtraction
strategy)
As a reflection tool
for students at the
end of the
discussion (“Let’s see
how they do it.”)
39. advanced learners
4 allows advanced learners to use
doubling strategy (mental strategy).
The changes are not structural but
superficial to make the context
current (Christmas) and relevant
(rolls of films, seriously?)
4 and 24 allows advanced learners
to use 4 x 25 to do 4 x 24.
Another differentiated
strategy for advanced learners
is to ask students to pose
another word problem for 4 x
24
Struggling learners
may use repeated
addition.
Alternatively they
should be able to
figure out 4 x 4 and
20 x 4.
Use of concrete
materials helps
them.
struggling learners
40. Anchor Task
Make a play zoo using some animal
figurines. Talk about the animals. “There
are five ducks. Four ducks in the pond and
one not in the pond.” “Two big lions and
three small ones make five lions.” “Three
blue birds and four red ones make seven
birds.” Do the same with the animals on this
page.
Anticipated Responses
Expected
Find total by counting all.
Exceeded
Find total by counting on.
Find total using other sophisticated methods.
Find total suing number facts
For Struggling Learners
They may need to see how it is done
through teacher modeling or peer
modeling.
For Advanced Learners
Is there another way to find the total
number of ducks? Can you write it down?
Five parrots and four cats is …?
41. Differentiating for Struggling Learners
For Struggling Learners
351 is renamed as 300 + 30 + 21 before
the partial division is done. This helps
students who lack metacognition and cannot
manage switching between renaming and
dividing in the standard algorithm.
42. Differentiating for Struggling Learners
For Struggling Learners
Using childlike, informal
representation instead
of the long division
format.
