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What was covered last year
Equipping parents with strategies to
guide their children in Model Drawing
as a problem solving tool to help them
become better Math problem solvers.
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Objectives of Workshop
To learn the use of • POLYA Thinking Routine through
guiding questions to promote your child’s metacognition.
• games for better understanding of Math concepts.
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What is
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Problem Solving
Problem solving is finding a way
around a difficulty, around an obstacle
and attaining an aim which was not immediately attainable.
(George Polya, 1945, 1957, 1962)
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What to achieve in Mathematical Problem Solving
Beliefs Interest Appreciation Confidence Perseverance
Monitoring of one’s own thinking Self-regulation of learning
Numerical calculation Algebraic manipulation Spatial visualisation Data analysis Measurement Use of mathematical tools Estimation
Reasoning, communication and connections Applications and modelling Thinking skills and heuristics
Numerical Algebraic Geometric Statistical Probabilistic Analytical
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Metacognition
• refers to the process of thinking about thinking
(John Flavell, 1979)
• is an important element in planning and problem solving
(Alan Schoenfeld, 1987)
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Metacognitive Strategies
• asking questions • planning • monitoring • checking • revising • self-testing
(Chan Chun Ming Eric, 2014, NIE, Singapore)
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POLYA
Thinking
Routine
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POLYA Thinking Routine
Read
Think
Plan
Do
Check George Polya (Hungarian Mathematician 1887 – 1985)
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Objectives
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POLYA in MFPS
Used mainly in core subjects
Teachers demonstrate the use of
POLYA Thinking Routine during
Math lessons
“POLYA Thinking Routine” hand-out
can be found in pupils’ handbooks.
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What do you notice during the
interaction between the parent and
the child during the role-play?
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1) Read with Understanding
Have you read the question
thoroughly?
What are you given? (Underline
the key information & data)
What is the question type/topic?
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2) Think & Plan
What are you asked to find?
How can you make sense of the
information?
Have you solved a familiar
problem before?
What strategy should you use?
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3) Do
Have you presented your
model, equation and working
correctly and neatly?
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4) Check
Have you answered the question?
Does your answer make sense?
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How to check / What to check for?
Numbers found in question are
the same as numbers in
equation/working?
Answer in working transferred
correctly?
N T – NUMBER TRANSFER U – UNITS C – CALCULATIONS
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What do you notice during the
interaction between the parent and
the child during the role-play?
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Tips for Parents
Withhold showing the worked solutions
Question your child to probe his/her
thinking
Actively observe and listen to your
child
Think about how to help your child to
get unstuck from where he/she is stuck
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Math Games:
are tools used to reinforce Math concepts learnt.
act as a platform for non-threatening, self–directed learning and peer learning.
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Pupils are: easily engaged as they learn
through ‘play’. enthusiastic participants. forthcoming in their response. not fearful in making mistakes
in a forgiving environment.
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Numbers within 10 / 20 SNAP
TRIO MATCH COMPARE!
Number Bonds of 10
DRESS ME UP!
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Place Value within 20 BING0 - Basic
BINGO - Intermediate
Numbers to 100 FIND MY NEIGHBOURS
- 1 Less / 1 More - 10 Less / 10 More
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Objective of game:
To relate numerals to its corresponding
words
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You will need:
1 pack of number cards
1 pack of word cards
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Instructions
1) 2 players – each
takes 1 deck of
cards
2) Place the cards
faced down.
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Instructions
3) Both players flip over 1 card from his/her deck at the same time. 4) If the cards match, the first player to touch the cards and shout ‘Snap!’ keeps the cards.
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Instructions
5) The player with the most cards win.
This game can be played using number and
word cards from:
1 to 10
11 to 20
1 to 20
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Objective of game:
To relate pictures and numerals to their
corresponding words
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You will need:
1 pack of number cards
1 pack of word cards
1 pack of picture cards
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Instructions
1) Display all the cards in 3 separate sets
on the table, faced up.
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Instructions
2) Players are to from as many sets of 3
cards (picture, number, word) within
1 minute.
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Instructions
3) The player with the most cards after a minute wins. This game can be played using numbers, words and picture cards from: 1 to 10 11 to 20 1 to 20
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Objective of game:
To compare 2 sets of quantities using the words more / bigger
or less / smaller
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You will need:
2 packs of number cards
or
2 packs of word cards
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Instructions
1) Players takes 1 deck of cards each and
place the cards faced down.
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Instructions
2) Both players flip over 1 card from his/ her deck of cards at the same time.
2 Ways to play: 1) The player who has the card with more items in the picture gets to keep both cards. 2) (vice versa)
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Instructions
3) The player who has the most cards wins the game. This game can be played with number or picture cards from: 1 to 10 11 to 20 1 to 20
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Objective of game:
To form
number bonds of 10
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You will need:
1 pack of ‘T-Shirt’ number cards
1 pack of ‘Skirt’ number cards
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Instructions
1) Display all the ‘T-shirt’ and ‘Skirt’ number cards in 2 separate sets on the table.
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Instructions
2) Players are to match as many sets of ‘T-shirt’ and ‘Skirt number cards to from the number bonds of 10 within a minute. 3) The player with the most number of sets wins the game.
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Objective of game:
To familiarise with place value within 20
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BINGO
1. 2- 4 players
2. At least 48 counters
3. Cards (Sets A to D)
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Set A cards (6 sets)
Place value representations in pictures
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Set B cards (6 sets)
Place value representations in pictures and words
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Set C cards( 6 sets)
Place value representations in pictures and numbers
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Set D cards (6 sets)
Place value representations in words and numbers
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Bingo (Set A Cards: Basic)
1. Each player selects a BINGO card. 2. An adult calls out a number from 1 to 20.
Player A Player B
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Bingo (Set A Cards: Basic)
3. Player places a counter on the box that shows the correct representation of the number called out.
4. First player who fills up the entire card is the winner.
Player A Player B
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Bingo (Set B Cards: Intermediate)
1. Each player selects a BINGO card. 2. An adult calls out a number from 1 to 20.
Player A Player B
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Bingo (Set B Cards: Intermediate)
Player A Player B 3. Player places a counter each on the 2 boxes that
represents the number called out ; matching concrete to abstract representation of place value.
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Bingo (Set C Cards: Intermediate)
Player A Player B 3. Player places a counter each on the 2 boxes that
represents the number called out ; matching concrete to abstract representation of place value.
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Bingo (Set D Cards: Intermediate)
Player A Player B 3. Player places a counter each on the 2 boxes that represents
the number called out ; matching concrete to abstract representation of place value.
4. The first player who fills up the entire card wins.
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Objective of game:
To find 1 more / 1 less or 10 more / 10 less
within 100
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Find My Neighbour
1. 2- 4 players
2. 100 chart
3. Square frame
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100 chart
Square frame
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1. Player chooses a number and places the window of the square frame over the number.
88
10 less
10 more
1 less
1 more
Find My Neighbour
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2. Player says out the number that is 1 less / 1 more / 10 less / 10 more than the chosen number.
88
10 less
10 more
1 less
1 more
Find My Neighbour
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References
• Polya, G. (1945). How to Solve it Penguin Group: London, England
• Flavell, J.H. (1979). Metacognition & cognition monitoring: A new area of cognitive developmental inquiry (pp. 334, 906-911). American Psychologist
• Schoenfeld, A.H. (1987). What’s all the fuss about metacognition? In A.H.
Schoenfeld (Ed.), Cognitive Science in mathematics education (pp. 189 – 215). Hillsdae, NJ: Lawrence Eribaum.
• Chan, C.M.E. (2014). Assessment for Learning. Strategies to Enhance Primary Mathematics Learning (pp.17-18). Pearson Education.
• MOE Mathematics Syllabus (2007, 2013)
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