Mathematics Mastery Approach in Primary and Secondary Schools

In a recent study, researchers compared mathematics ‘teaching methods’ in the United Kingdom to the Singaporean method. Similar educational researches in the US also found that students learn better when they participate in problem-solving.

Singaporean primary and secondary schools have successfully implemented a more hands-on approach to teaching specific contents in mathematics. The mastery approach to teaching and learning school mathematics focuses on problem-solving approaches.

Here is a real story of what a student goes through the schooling system in PNG – he recalls that Early Learning Years in Rural and Urban Schools.

Mathematics mastery approach concentrates on problem-solving

The finding in the report revealed that students taught using problem-solving mastery approach learn faster than their counterparts. And, the students of mathematics mastery strategy make an extra month of progress in a calendar year.

Another point worth reiterating is that student’s ability to do well in maths can be enhanced by tweaking it at a certain time. The report highlighted that the right enhancement at age 10 yields long term economic benefits for individual and the country.

Performances of students in mathematics in Papua New Guinea

Students performances in mathematics examinations at Grades 8, 10 and 12 have been below the average levels compared to other subjects. Several regional and national tests have also shown similar indications of students’ dismal performances in mathematics.

The traditional methods of teaching mathematics – chalk and talk, recalling numeracy facts, performing mental calculations, etc. – may have to take on a new twist.

Perhaps, the policymakers and education leaders should consider new researches and developments and act on them as a matter of urgency.

Mathematics skills, knowledge, understanding and application in the country is at a low level. Students have difficulty recalling mathematical facts, let alone use the facts to solve problems.

Innovative and practical mathematics in classrooms

The challenge today is to effectively address mathematics learning in PNG schools. It does not mean changing the whole structure and curriculum.

But, to adapt the best practices in mathematics teaching and classroom learning.

What is means is to look at innovative and practical ways of solving mathematics problems in classrooms. Teachers will have to be trained to use those teaching approaches when delivering lessons, There are practical activities and bests practices in Singapore and UK classrooms that maths teachers can replicate in PNG schools.

Mastery approaches to mathematics

There are two examples in this article. But first, if performances in mathematics in the country were to improve, there is a need to intervene in classroom teaching of maths.

The mathematics teachers must look at ways to create resources targeted at developing student’s problem-solving skills – ideally students between the ages of 9 and 16 years.

Mathematics mastery approach to teaching math in Singapore schools

A good example uses three wooden bars to find three consecutive numbers that add up to 42. Another example is to use three die to find the numbers that add up to 11.

Instead of rote learning as shown in methods one and two below. Mathematics mastery approach is problem-solving by doing.

Curriculum designers design specific lessons in fractions, ratios, algebra, trigonometry, area, volume, capacity, etc..

Furthermore, a report puts it this way:

Based on this Concrete Pictorial Abstract (CPA) approach to learning, the team also developed a “spiral curriculum”, where each topic is revisited in intervals at a more sophisticated level. A concept is represented initially by “concrete” materials, later by models (pictures) and then finally by the abstract notation (such as plus or equals signs). There is also a strong emphasis on modelling mathematical problems with visual aids – using coloured blocks to represent fractions or ratios, for example. (Singapore Times, 03/02/2020)

Teachers often solve the problem of finding three consecutive numbers that add up to 42 either by trial and error or by using algebra.

Method one: By trial and error – choose 3 numbers at random

Start at 10, 11, 13 (=34);
11, 12, 13, (=36);
12, 13, 14 (=39)
13, 14, 15 (=42)
Three numbers are 13, 14 and 15

Method 2: By using algebra to solve the problem

Let the first number be x, second number x + 1 and third number x + 2
x + x + 1 + x + 2 = 42
3x + 3 = 42
3x= 39

The three numbers are 13, 14 and 15

What does Mathematics Mastery approach mean?

This is not about a complete shift in teaching styles. This is about enhancement – creating ‘power lesson’ effective enough to enrich students ability on a daily basis.

The importance of helping students to learn faster and think for themselves is far superior to preparing students for examinations. There has to be a balance between building strong problem-solving skills and preparing students to achieve good grades.

Papua New Guinea can do what Singaporean schools have done. Giving students the best possible opportunity to improve apply mathematical reasoning to solve problems in real life.

Note: This is a recollection from a newspaper article that the writer read several years ago. It is a topic to stimulate discussions about the curriculum and development of mathematics teaching and learning materials.

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