Hi Sunny
Please elaborate more on UTM.
Is it a more effective method as compared to other Heuristics?
Is model drawing or Guess and Check a waste of time?
Will the child be confused if he/she is taught a different method from schools?
Concerned parents
Hi Sunny,
Good Afternoon Sir,
As the name of your blog suggests, there is no better way to learn more about UTM than from the guru himself.
As compared to Model Drawing, UTM lacks the visual impact which enables a student to see Maths,so to speak.
In what way is UTM a more effective method than MD?
Could you help to illustrate with some examples?
Is UTM within MOE Maths syllabus?
Interested parents
From the desk of Sunny Tan ... ...
UTM RESEARCH BACKGROUD
The Unit Transfer Method is a fundamentally sound approach with research based on Teacher Work Series publication. Unit Transfer Method uses ratio with tabulation to help child to effectively analyze and solve challenging mathematical problems. This simple, logical yet powerful problem-solving technique is an alternative to the model approach and the algebraic framework approach.
MOE SYLLABUS
Reference to MOE forum replies “Different Approaches taught for Mathematical Techniques” dated 12th Feb 2007, Ms Ho Peng, Director, Curriculum Planning and Development.
“Other than the model drawing approach, pupils are also taught different problem solving methods. They are encouraged to try different approaches and have the flexibility to choose the method that works best for them in solving the problems’
“In the marking of PSLE mathematics, pupils are not restricted to the use of any one particular method. All mathematically correct solutions are acceptable”
In the replies above, the Ministry of Education will accept any mathematically correct method in the PSLE. In fact, the reply mentioned that pupils need a wider repertoire of approaches to work with more challenging problems.
The UTM is very effective in solving problems involving the Before and After Concept, which is one of the heuristics stipulated in the MOE curriculum.
PROBLEM SOLVING HEURISTICS
MOE has recommended 11 problem solving heuristics in primary level. Every heuristics plays a role in problem solving. The common misconception in many parents is that many are trying to search for the “holy Grail” or the most “superior” problem solving methods for their child.
Many parents have always raised these concerns during my seminar, “Is guess and check or model drawing a waste of time?” To answer these concerns, we have to ask ourselves "What is heuristics?"
Heuristics are methods that helps in problem solving. Heuristics does not guarantee a solution.
When approaching the problem, the child first understands the problem, chooses the method and carry out the plan. If it doesn’t work, the method should be discarded and a new method should be choose to solve the problem. However, many pupils or even us will “stubbornly” continue to usie the initial method even it doesn’t work!
UTM VERSUS MODEL APPROACH
As mentioned, many parents are guilty of searching for the “Holy Grail” or the most “Superior” problem solving method. We all know in fact, they never or will never exist.
Different children have different learning style - right and left brain dominant learners.
The left brain learners are strong in logical and analytical thinking while the right brain learner seeks to determine the spatial/visual relationships of all the parts.
The question of which is more superior method is therefore very subjective. Therefore, we cannot answer on behalf of our child. What is important as parents, we should equip the child with different approaches so that they have the flexibility to choose the method that works best for them in solving the problems.
The fundamental concept of the model approach and UTM utilizes ratio. Model drawing is visual or UTM uses tabulation. The combination of Model Approach and Unit Transfer Method utilize the left and the right brain- an integrated "whole" brain approach to maximize the untapped potential of the child.
VISUAL PROCESSING TECHNIQUE
“Do you know Guess and Check can be solved just by using 3 steps?”
“Do you know there are other ways to draw model other than horizontal bar?
By changing the orientation of the model, the answers is staring in front of them!
These are some of the topics that will be covered in the Parents’ Seminar.
Thursday, February 26
Using UTM for this question?
Hi Sunny
Using UTM for this question?
Mr Lim spent $1496 on some comics and dictionaries altogether. The number of comics bought to the number of dictionaries bought was in the ratio of 3 : 2. A dictionary cost $4 more than a comic. The total cost of the comics was 20% more than the total cost of the dictionaries. Find the cost of a dictionary.
February 24, 2009 1:53 PM
From the desk of Sunny Tan ... ...
The concept used for this question is propotion concept. The solution is as follows:
Using UTM for this question?
Mr Lim spent $1496 on some comics and dictionaries altogether. The number of comics bought to the number of dictionaries bought was in the ratio of 3 : 2. A dictionary cost $4 more than a comic. The total cost of the comics was 20% more than the total cost of the dictionaries. Find the cost of a dictionary.
February 24, 2009 1:53 PM
From the desk of Sunny Tan ... ...
The concept used for this question is propotion concept. The solution is as follows:
Tuesday, February 24
Can these problems be solved by UTM? - Mrs Sui
Q1) In Hall A, 30% of the 800 people were men. In Hall B 40% of the 400 people were women and children. After some of the people in both hall had switched hall, 25% of the people in Hall A and 75% of those in hall B were men. How many people were there in Hall B after the change?
Q2)During a warehouse book sale, Sally spent 62.5% of her money on 24 books and 18 pens. She also spent 25% of her remaining money on 18 files. Each pen costs 8/9 as much as the price of one book. The file costs $7.80 less than a book. Find the total cost of one book and one pen.
Question posted by Mrs Sui, UTM book reader
Tues, 24th Feb 2009
From the desk of Sunny Tan ... ...
Q1)This concept is covered in UTM book, Chapter 1.2 –Before and After (Total unchanged)
with Chapter 5 – Two variables concept.
i) The total number of men in Hall A and Hall B remain unchanged before and after the transfer.
ii) The total number of women and children in Hall A and Hall B remain unchanged before and after the transfer.
iii) The total number of people in Hall A and Hall B remain unchanged before and after the transfer.
2) The UTM concept to solve this question is covered in Chapter 6 - Proportion Concept.
Q2)During a warehouse book sale, Sally spent 62.5% of her money on 24 books and 18 pens. She also spent 25% of her remaining money on 18 files. Each pen costs 8/9 as much as the price of one book. The file costs $7.80 less than a book. Find the total cost of one book and one pen.
Question posted by Mrs Sui, UTM book reader
Tues, 24th Feb 2009
From the desk of Sunny Tan ... ...
Q1)This concept is covered in UTM book, Chapter 1.2 –Before and After (Total unchanged)
with Chapter 5 – Two variables concept.
i) The total number of men in Hall A and Hall B remain unchanged before and after the transfer.
ii) The total number of women and children in Hall A and Hall B remain unchanged before and after the transfer.
iii) The total number of people in Hall A and Hall B remain unchanged before and after the transfer.
2) The UTM concept to solve this question is covered in Chapter 6 - Proportion Concept.
Friday, February 20
Club A and Club B - Mrs Tan
Hi Sunny,
My son has school worksheet today and he faces difficulty in solving the question below using the Unit Transfer Method.
Club A and Club B had a total of 270 members. Club A had 80% as many members as Club B. During a recruitment exercise, more people joined both Clubs and for every 3 members who joined Club A, one member joined Club B. Given that the ratio of the number of members in Club A to Club B in the end was 2:1, find the number of members in each club in the end.
Question posted by Mrs Tan, Parent
Thurs, 19th Feb 2009
From the desk of Sunny Tan ... ...
My son has school worksheet today and he faces difficulty in solving the question below using the Unit Transfer Method.
Club A and Club B had a total of 270 members. Club A had 80% as many members as Club B. During a recruitment exercise, more people joined both Clubs and for every 3 members who joined Club A, one member joined Club B. Given that the ratio of the number of members in Club A to Club B in the end was 2:1, find the number of members in each club in the end.
Question posted by Mrs Tan, Parent
Thurs, 19th Feb 2009
From the desk of Sunny Tan ... ...
Saturday, February 7
UTM book, chapter 1.1, question 7 - Mdm Chong
With reference to the UTM book, chapter 1.1, question 7:
A concert hall has 600 seats. 10% of the seats are VIP seats while the rest are normal seats. How many VIP seats must be added so that the number of VIP seats will increase to 20%?
Please advise what is wrong with the following reasoning:
Question posted by Mdm Chong M.K, UTM Book reader
Fri, 6th Feb 2009
From the desk of Sunny Tan ... ...
A concert hall has 600 seats. 10% of the seats are VIP seats while the rest are normal seats. How many VIP seats must be added so that the number of VIP seats will increase to 20%?
Please advise what is wrong with the following reasoning:
Question posted by Mdm Chong M.K, UTM Book reader
Fri, 6th Feb 2009
From the desk of Sunny Tan ... ...
Confusion Alert:
The 540 normal seats in the Before and After scenario remains unchanged. However, the percentage of the normal seats changes from 90% in the Before to 80% in the After scenario.
It is important to highlight to the students that percentage is relative to the total sum.
The number of the quantity being unchanged does not imply that the percentage of quantity being unchanged.
It is important to highlight to the students that percentage is relative to the total sum.
The number of the quantity being unchanged does not imply that the percentage of quantity being unchanged.
Therefore, in the Unit Transfer Method, students are encouraged to convert fraction, decimal, ratio, whole number, and percentage into units as follow:
Friday, February 6
About Unit Transfer Method
Heuristics in Primary Maths Syllabus
Heuristics is a specialised mathematical problem-solving concept. Mastering it facilitates efficiency in solving regular as well as challenging mathematical problems. The Ministry of Education in Singapore has incorporated 11 Problem-Solving Heuristics into all primary-level mathematical syllabus.
Challenges in Learning Heuristics
Instead of containing the 11 Problem-Solving Heuristics neatly into specific chapters though, they have been integrated into the regular curriculum. This not only makes it difficult for students to pick up Heuristics skills, but can also make mathematics confusing for some students. For us parents, it is difficult for us to put aside the regular-syllabus mathematical concepts we were brought up on to re-learn Heuristics, much less teach our own children this new concept.
Take Algebraic Equations, for instance. Primary-level Mathematics Papers these days include questions from the topic even though the topic has never been, and is still not, taught at primary level. Parents, being familiar with the topic, will attempt to teach their children to solve the question using Algebraic Equations, which will only further confuse their children. According to current primary-level mathematical syllabus, Heuristics should be used instead.
Overcoming the Challenges
These and other challenges were what I observed first hand during my years as a mathematics teacher, and what provided me the impetus for my post-graduate studies, mathsHeuristics™ programmes and now this series of books. Indicative of the effectiveness of my methodology, it helped a P6 girl from CHIJ to improve her Mathematics grade from 52% in the First Semestral Assessment to 99% in the Preliminary Examination, to achieve A* in the 2008 PSLE – all within just 20 weeks!
About this Series
This series of books is a culmination of my systematic thinking, supported by professional instructional writing and editing, to facilitate understanding and mastery of Heuristics. Through it, I have neatly packaged Heuristics into logical topics (Series of books) and sub-topics (Chapters within each book). For each sub-topic, I offer many examples, showing how the sub-topic may be applied, and then explaining the application in easy-to-follow steps and visualisations without skipping a beat.
This particular book in the series deals specifically with Unit Transfer Method, the use of ratio to effectively analyse and solve challenging mathematical problems. This simple, logical yet powerful problem-solving technique is an alternative to the model approach and the algebraic framework approach.
The entire series of four books provides a complete and comprehensive guide to Heuristics.
While each book introduces parents to a few Heuristics topics, it gives students the opportunity to see how the specific Heuristics work as well as get in some practice. For students enrolled in mathsHeuristics programmes, each book serves as a great companion, while keeping parents well-informed of what their children are learning.
Sunny Tan,
Author
Heuristics is a specialised mathematical problem-solving concept. Mastering it facilitates efficiency in solving regular as well as challenging mathematical problems. The Ministry of Education in Singapore has incorporated 11 Problem-Solving Heuristics into all primary-level mathematical syllabus.
Challenges in Learning Heuristics
Instead of containing the 11 Problem-Solving Heuristics neatly into specific chapters though, they have been integrated into the regular curriculum. This not only makes it difficult for students to pick up Heuristics skills, but can also make mathematics confusing for some students. For us parents, it is difficult for us to put aside the regular-syllabus mathematical concepts we were brought up on to re-learn Heuristics, much less teach our own children this new concept.
Take Algebraic Equations, for instance. Primary-level Mathematics Papers these days include questions from the topic even though the topic has never been, and is still not, taught at primary level. Parents, being familiar with the topic, will attempt to teach their children to solve the question using Algebraic Equations, which will only further confuse their children. According to current primary-level mathematical syllabus, Heuristics should be used instead.
Overcoming the Challenges
These and other challenges were what I observed first hand during my years as a mathematics teacher, and what provided me the impetus for my post-graduate studies, mathsHeuristics™ programmes and now this series of books. Indicative of the effectiveness of my methodology, it helped a P6 girl from CHIJ to improve her Mathematics grade from 52% in the First Semestral Assessment to 99% in the Preliminary Examination, to achieve A* in the 2008 PSLE – all within just 20 weeks!
About this Series
This series of books is a culmination of my systematic thinking, supported by professional instructional writing and editing, to facilitate understanding and mastery of Heuristics. Through it, I have neatly packaged Heuristics into logical topics (Series of books) and sub-topics (Chapters within each book). For each sub-topic, I offer many examples, showing how the sub-topic may be applied, and then explaining the application in easy-to-follow steps and visualisations without skipping a beat.
This particular book in the series deals specifically with Unit Transfer Method, the use of ratio to effectively analyse and solve challenging mathematical problems. This simple, logical yet powerful problem-solving technique is an alternative to the model approach and the algebraic framework approach.
The entire series of four books provides a complete and comprehensive guide to Heuristics.
While each book introduces parents to a few Heuristics topics, it gives students the opportunity to see how the specific Heuristics work as well as get in some practice. For students enrolled in mathsHeuristics programmes, each book serves as a great companion, while keeping parents well-informed of what their children are learning.
Sunny Tan,
Author
Saturday, December 13
Glen and Ryan - Mrs Tan
Hi Sunny,
Need your help to solve the following.
Glen and Ryan had $403 altogether. After Glen used 1/4 of his money and Ryan used 1/3 of his money, Glen has twice as much money as Ryan. How much money did Ryan have at first?
Question posted by Mrs Tan, Parent
Fri, 12th Dec 2008
From the desk of Sunny Tan ... ...
click on picture for bigger view
Need your help to solve the following.
Glen and Ryan had $403 altogether. After Glen used 1/4 of his money and Ryan used 1/3 of his money, Glen has twice as much money as Ryan. How much money did Ryan have at first?
Question posted by Mrs Tan, Parent
Fri, 12th Dec 2008
From the desk of Sunny Tan ... ...
click on picture for bigger view
Friday, October 10
3 questions - Mr Shew
Dear Sunny,
Thanks for the extra mile for the consultation session.
Alden has the following questions to ask:
(a) A bill of $72 was paid with $10, $5 and $1 notes. If 13 notes were used for payments, how many notes of each kind were used?
(b) Vanessa and Bobby had some telephone cards. AfterBobby gave 4/9 of his cards to Vanessa, the ratio of the number of Bobby’s cards to the number of Vanessa’s cards became 10 : 17. What was the ratio of the number of Vanessa’s cards to the number of Bobby’s cards at first?
(c) 12 workers took 10 days to make 800 bowls. How many days 3 workers need to make 40 bowls?
Question posted by Mr Shew, Parent
Thurs, 9th Oct 2008
From the desk of Sunny Tan ... ...
click on picture for bigger view
Thanks for the extra mile for the consultation session.
Alden has the following questions to ask:
(a) A bill of $72 was paid with $10, $5 and $1 notes. If 13 notes were used for payments, how many notes of each kind were used?
(b) Vanessa and Bobby had some telephone cards. AfterBobby gave 4/9 of his cards to Vanessa, the ratio of the number of Bobby’s cards to the number of Vanessa’s cards became 10 : 17. What was the ratio of the number of Vanessa’s cards to the number of Bobby’s cards at first?
(c) 12 workers took 10 days to make 800 bowls. How many days 3 workers need to make 40 bowls?
Question posted by Mr Shew, Parent
Thurs, 9th Oct 2008
From the desk of Sunny Tan ... ...
click on picture for bigger view
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