Bridging the Mathematics learning gap

The learning of Mathematics is so different from 20 years ago, that the MOE Mathematics curriculum now focuses on problem solving as its primary goal. In 2009, when the use of calculators were permitted during the PSLE Mathematics Paper Two, it became obvious that the learning of Mathematics does not just focus on computation skills any more.

Importance of Heuristics in Mathematics

Today, students no longer learn Mathematics by memorizing, rote-learning or drilling. How well the child learns Mathematics does not relate to “practice makes perfect”.

Instead, they must be able to connect, reason, model what they have learned in class and apply Heuristics to solve problems.

The teaching of Mathematics has shifted from white board learning to inquiry-based learning, whereby students discover facts, concepts and relationships by themselves.

Other than Problem Solving Skills, the following are also important thinking skills that the students must adopt:

    Observation
    Visualization
    Hand-eye co-ordination
    Analytical thinking
    Logical Reasoning
    Judgment
    Categorization
    Memory



The following is an illustration of how children can be trained with multiple thinking skills: 
Q: Which picture is correct?

                                                           


Thinking skills and processes involved in solving this problem:
a)    Correspondence skill
1.    What is the mass of a Monkey?               7 units
2.    What is the mass of a Chicken?              5 units

b)    Addition skill   
1.    What is the mass of a Monkey and a Chicken?    7 units + 5 units = 12 units
2. What is the mass of 2 Chickens?            5 units + 5 units = 10 units                                                                  
c) Judgment skill
1.    Is a Monkey and a Chicken heavier than 2 Chickens?
 If yes, then the answer is a tick.            Ans: 

Where is the learning gap in problem solving?
Students may understand certain concepts that have been taught, yet may still be
unable to do well in problem solving. In order to bridge this gap, students must apply
the following strategies when solving word problems:

Step 1 Understand the problem
    Students must comprehend the text and understand what is the question asking and what is required to solve the problem.

Step 2. Devise a plan
    Students must be able to identify the correct strategies to use in solving the problem. There are many problem solving Heuristics, and the Model method serves as a good tool to allow students to visualize a solution when solving the problem.

Step 3 Model and carry out the plan
    Students will draw a model, list a table or apply the correct heuristics to solve the problem.

Step 4 Reflection
    Students must reflect by substituting the answer into the problem to meet the conditions stated in the problem.



Quote: From a Facebook posting by Education Minister Mr. Heng: “a question requires a pupil to work through a few steps to get the final answer. And even if he doesn’t get the final answer, if he gets the first few parts right, he understands his materials and gets points for it.” Unquote.

Therefore, the focus is no longer about just getting the right answers but on the process of how the students derive at the correct answers.
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This article is contributed by Edison Innovative Pte. Ltd., the Master Franchisor for eiMaths. We are a Singapore-based Mathematics program focused on creative thinking and problem solving skills to identify and bridge your child’s learning gap in Mathematics. Visit us at www.eimaths.com.

4 Types of Heuristic Method in Maths

Traditional math places emphasis on the acquisition of knowledge. Heuristic method, on the other hand, places more importance on the manner of discovery on the part of the students. The difference of the two is the performance of the student. Heuristic method allows the kid to discover the lesson on his own. It's about the manner of acquiring the information. In the long run, the kid will be able to go about the problem to achieve the solution. He will be less dependent on prior knowledge. He will do away with memorization and fact tables. That is what traditional method failed to instill in kids - the ability to discern problems and issues independently.

4 Types of Heuristic Method in Maths

1. Representation

This is most suitable in word problems. Kids are used to equations. They tend to get lost in the problem when faced with too many words. That's where representation enters the picture. Kids do best when there is a visual representation. After reading the problem, make a list. Itemize the given numbers. It summarizes the information given and gives the kids a clearer picture of the whole problem. By singling out the numbers, kids will get to identify the pattern and they will be able to provide the needed answers systematically.

2. Making a calculated guess

It's the subsequent guessing and checking on the part of the kids. It'll help them narrow down their options. This is especially useful in problems with missing information. Instead of thinking of so many possibilities and wondering whether these will work or not, the kids get to narrow down their choices. Once his guess doesn't produce the intended effect then, he can try the next one. It helps the kids bring together a systematic list of possible choices and achieve the correct one in just a short period of time. It's all about patterns and sequences.

3. Going through a process

Kids learn best through experience and this type of heuristic maths method does just that. Kids will be asked to do the problems using actual objects. He can use balls or sticks to represent the items in the problem. This allows the kids to explore their options in an actual situation.

It's not all about the problems or words swimming in their heads. They can bring those concepts to the real world. What happens when you put this and this together? What happens when you put it this way instead of the other way around? They could try out their options. Find answers to their inquiries themselves. They get to understand the changes happening. What is the scenario before you added this to the pile? What happens after you placed it on the pile? By analyzing their actual objects, they could understand the before and after concepts.

4. Restating the problem

Not all kids think alike. Some can grasp the facts faster than the rest. By changing how the problems are presented, kids will achieve a certain level of understanding that is not present before. They can view the problem in a different perspective. Use items that they can recognize or tap into their interests. Once they started viewing it in a different perspective, they'll be able to know how to work it out. If the problem is too broad, breaking the problem down into simpler parts can help the kids understand better.

What do Children Learn in Maths Activity Class?

Children these days are taught many subjects for the purpose of high end learning right from the beginning of their school days. However, maths has a special purpose in every child’s life and while the subject can be quite demanding at times, it is extremely beneficial in the near future. A lot of preschools and kindergartens have introduced maths activity class due to the fact that it ensures learning and also gives a child the ability to think on a large scale. Due to the importance of this subject, teachers are always highly recommended to teach it with great care and dedication to the children.

Brain Enrichment

As far as the maths activity class is concerned, it allows children to think of all sorts of possibilities. The best part is the fact that they learn to use their brain for everything and the fact that they learn to properly utilize it is something that cannot be taught easily by another subject in general. This is amongst one of the most significant reasons for teaching mathematics to children in kindergarten as well as preschool. A child’s brain has a lot of imagination and creativity hidden in it and in order to bring that out adequately, the learning of maths is definitely required.

Out of the Box Thinking

Moreover, children get the ability to be able to think out of the box in maths activity class. This is due to the fact that maths is a vast and an extremely diverse subject that opens doors to a lot of new opportunities as well as concepts. While children learn all of these concepts, they also see how they can use these in real life. This is only if a teacher pays attention in teaching them about how to do it without making it entirely difficult for them.

Learning Numbers

Maths contains numbers and these are generally new for a child who has just started to learn maths in school. It does take a lot of time for children to get used to numbers but with the help of maths activity class, it has now become quite possible since this class is all about teaching children all there is about maths and how it can be understood. Sometimes children may understand it quickly, but the other times, it may take some time for them to get used to it in the process. However, the results are most definitely positive as the main reason for holding a class dedicated to this subject is to show children how important and fun it can be.

Time Management

Maths activity class also shows children the many ways through which they can manage time. Time management should be taught to children right from the beginning so that they do not have to face any difficulties during tests and important examinations in the long run. It is through time management that people get ahead in life and it can be taught very well with maths. Therefore, the purpose of holding this class is to also teach time management to children in a short period of time.

Is the Maths Activity Class worth it?

A lot of schools these days have introduced this class and the results have been tremendous as many children have learned a lot of things regarding maths. Many studies also show that the activity class for maths is also responsible for making children interested in mathematics right from the beginning, which is definitely a great thing as the subject becomes crucial in their lives later on. The activity class is held on a day to day basis in most schools in different parts of the world and has been made a proper part in the routine of all preschool and kindergarten students.