Math Teaching Methodology

When universal education was first started in Singapore to provide an educated workforce for the labour market of the 1950’s and 60’s, education was seen as nothing more than the memorization and accumulation of facts and figures with no application of skills required to organize and integrate what was being taught. 

Such an education is understandable given that the labour of that time was considerably more menial and low-tech than what is required of PMETs nowadays.

However with the demands of the new knowledge-based economy, education has take on a new role and it is no longer considered enough to just know or memorize facts and accumulate information. 

The Singapore Ministry Of Education has recognized this and has moved towards giving education a new role and purpose. Education is now geared towards equipping the learner with a set of tools to be used together with the knowledge possessed to solve problems in new situations. This is also known as “Self-Directed Learning, Problem Comprehension, Knowledge Application and Heuristics”

Changes to the Primary School Math Education Landscape

When it comes to maths and science, the educational trend is clear - memorizing facts, formulas and concepts is no longer the key to acing the exams. Instead students are now required to think fast to solve unfamiliar, tricky and mind bending questions. 

As the primary school examinations in schools gear towards such new educational trends, many parents perceive the difficulty level of exams to be rising. Instead of recognizing that their child requires help in engaging his critical thinking skills and guidance in the application of the necessary problem solving skills, the parents, in the misguided notion that "more is always better" tries one or more of the following :

  1. Advancing the child’s academic knowledge by teaching them upper primary syllabus when they are still in lower primary. 
  2. Un-meaningful work on large quantities of assessment books and practice papers.
  3. Teaching the child to use Algebra in solving Problem Sums. 
Algebra is a particularly dangerous tool for a primary school child because children below 12 are better able to grasp and understand abstract mathematical concepts using visual methods. 

Algebra from a Primary school child’s point of view is simply an algorithm or formulae to memorize and apply. This is because, according to child education psychologists, they are still within the "Concrete Operational Stage of Cognitive Development" (Piaget Cognitive Model) which begins at the age of 7 and continues until the child is of 11 to 12 years of age. Thus, they have not yet developed the cognitive capability to understand the inner workings and abstract concepts of the algebra required in problem solving. Even if they have been trained to use algebra for certain types of questions, they lack fundamental understanding of the question's concept and thus would be unable to solve the question if the context of the particular question should be changed slightly. 

Using algebra as a crutch to help the child approach primary school maths problems would result in stunted problems solving skills and mathematical cognitive ability which would not serve them well as they progress further up the education system.

NickleBee Tutors shall now elaborate on how we will go about helping your primary school child through the ever changing education landscape.

Singapore Model Method & Heuristics

We will teach all our students on how to master and apply the "Singapore Model Method" to solving PSLE maths problem sum questions. NickleBee Tutors is of the belief that most if not all of the problem sums in the PSLE can be solved using the simple combination of understanding the context of the problem followed by application of the necessary procedural knowledge. 

The "Singapore Model Method" advocates the Concrete-Pictorial-Abstract approach as recommended by MOE for the development of mathematical concepts, skills and process. In this approach, students are provided with the necessary learning experience and meaningful contexts, using concrete manipulatives and pictorial representations to help them learn abstract mathematical concepts. 

We will also teach our students "Heuristics" which is a set of thinking tools or frameworks to solve unfamiliar and complex problems.

An example of heuristics would be “HOTS” or higher order thinking skills which is the ability to analyze (Break information into small pieces), synthesize (put separate information together in different forms) and evaluate (deduce and judge value of outcomes in a logical manner)

MOE has incorporated as many as 11 problem solving heuristics in the primary school level syllabus BUT heuristics itself is not explained clearly.

We at NickleBee tutors supplement our Mathematical Instruction with “Cognitive Conceptual Approach in Learning Mathematics” which was pioneered and developed by Mr Ammiel Wan (former Vice-Principle of Rosyth Primary, Author of the popular "thinking Math @ OnSponge" &  "GetMeThinking" math assessment books and currently Principal Consultant at Visible Math)

This Conceptual approach is designed based on research findings which showed that there are 2 components essential to solving mathematical problems. First is Conceptual Knowledge - the Facts, Concepts and Principles (or better known as "What" and "Why"). Second is Procedural Knowledge - such as Heuristics/Modelling which is used to recall and construct information while solving the problem (also referred to as "How"). Both Conceptual Knowledge and Procedural Knowledge are equally important in helping the child excel in problem solving. This Conceptual Approach is currently used by Catholic High, RCG and SCGS and other top schools to help their students tackle higher level PSLE maths questions. 

C3PO Math Problem Solving Approach

To complement the above-mentioned Heuristics and Model Approach, Mr Zhou uses the "C3PO Math Problem Solving Approach" as his teaching methodology.

The C3PO Math Problem Solving Approach was developed by Mr Zhou based on knowledge and experience gained from 10 years in the educational sector and elements of his approach are adapted from Mathematician George Poyla's influential Math Heuristics guidebook "How to Solve It" and Mr Ammiel Wan's ground-breaking "Cognitive Conceptual Approach in Learning Maths" (Mr Ammiel Wan is the author of the popular "thinking Math @ OnSponge" & "Get Me Thinking" Math Books and was formerly Vice-Principal of Rosyth Primary).

Mr Zhou recognized that most students view solving Problem Sums as merely a "Means to an End" where the final answer is the main focus and less thought is put into how the question is approached or the thought process that allows one to derive the answer. That will prove detrimental to the child's educational development as such an approach encourages rote learning and the blind application of algorithms and techniques without any proper understanding as to why such techniques are so used.

The C3PO approach on the other hand emphasizes development of Reasoning and Analytical Skills and the enhancement of thought processes based on Logic and Critical Thinking. This results in a Visual and Logic based method of Problem Solving that is both Rigorous yet Resilient.

C3PO is made of up :
  1. Comprehension  - Reading to understand the context of the question and how the words and numbers are woven together to form a coherent whole.
  2. Critical Thinking - Reasoning & Analytical Skills, Higher Order Thinking Skills (HOTS)
  3. Concepts - What is the concept or idea that will help you solve the question? Why do you use this concept in this particular question? The student must recognize that concepts can be applied across question of various contexts.
  4. Procedure - How you actually solve the question. Heuristics, Model Method, Unitary approach and any mathematically correct solution.
  5. Overview - Reflect on your thought process (meta-cognition). Check back on the viability of your procedures and accuracy of workings. Extend the problem by thinking briefly of any alternative solutions that could be used.

4 Step Problem Solving Approach

We teach a 4 step Problem Solving method invented by Mathematician George Polya and developed further by Head Mentor Mr Zhou. This will help students improve their problem solving not only in Maths but also in other subjects even as they journey through the education system.

His method consists to 4 steps and helps students : 

  • Step 1 (Understand the Problem) : Read and Understand the context of the question (Not as easy as it sounds!) Identify the Essential Data/Information and Key Concepts from the question that would help you in solving the question. 
  • Step 2 (Devise a Plan) : Determine the Method (e.g Model, Guess-and-check, Heuristics etc) that you would use to understand the Problem (i.e Procedural Knowledge). Arrange, Organize and Translate the Data and Key Concepts (from the 1st Step) into Models and/or other Visual/Pictorial/Tabular based representations so as to determine the relationship between the Data and Concepts and allow the structure of the word problem to be more evident.
  • Step 3 (Carry out the Plan) : Apply the method/solution that is the most elegant and logical for that particular question. Proper labeling of statements must be done and all workings have to be in a sequential and logical manner. 
  • Step 4 (Reflect on the Problem) : Check your solution by inserting the answer back into the problem to determine if it is reasonable. You'll be surprised how many children don't do this! Extend the problem by thinking briefly of any alternative solutions that could be used.