Despite popular notion, mathematics is more than just about numbers. Due in part to the stereotyped images in mainstream media, when people think about math, they usually think about numerals—recognizing them, counting them, adding, subtracting, multiplying or dividing them. However, math is as complex as it is versatile, as one can infer from its use in various fields such as engineering, programming, robotics, chemistry, physics, statistics, and business and finance, just to name a few. On a more practical note, math is used to understand in a variety of ways in our communities, from how quickly a city can become infected by a new strain of virus given the city’s population and the speed at which the virus multiples, or the probability of a town getting affected by a volcanic eruption along with estimated death tolls using statistics and probability, or how profit can grow and plummet, or how an entire stock market can crash overnight.
Even in everyday life, math plays a role. From telling the time to driving to doing the grocery, to counting the calories in a dessert to consider a healthier diet, eye-balling measurements or following a recipe when cooking, purchasing that item on sale, or deciding whether to pay off your mortgage or save up for your child’s college fund, whether implicitly or explicitly, math is there.
Given its role and importance in the individual and collective existence of mankind, from the beginning of civilization up to our modern times, it comes as no surprise that math is as challenging to learn as it is to teach. And one of its more challenging areas is heuristics.
Heuristics in Singapore Math
A heuristic (or a heuristic technique)—a term that comes from a Greek word meaning “to find” or “to discover”—refers to any approach to problem-solving using a practical method that is not guaranteed to be perfect but is nevertheless sufficient in reaching a satisfactory solution. To put it simply, it is a mental shortcut that takes higher order thinking skills and one’s personal experiences into account in decision-making and problem-solving. It focuses on enabling a person to solve a problem by discovering or learning something by himself rather than by following a predetermined set of rules or codes such as a formula or routine steps.
In mathematics, heuristics are useful in solving simple and complex non-routine problems. As mathematics education keeps evolving to keep up with the developments of our changing times, educational content has evolved too and has become more challenging. While in the past many parents spent time memorising terms and concepts, practicing drills using sets of formulas, today’s students are expected to not only understand and master concepts but to have strong thinking and problem-solving skills to solve complex math questions as well.
To Singaporean parents, especially those of primary school children, the term heuristics is no longer a stranger. This is because the Singapore Math framework created by the Ministry of Education (MOE) has problem solving at its core, with all math-related skills such as calculation, spatial visualization, estimation, analysis, and forming connections directed towards the big picture: becoming masters at problem solving.
Image from Haig Girls’ School
However, many students in Primary 5 and Primary 6 find heuristics especially challenging, with some even losing marks on this area during assessments. This is probably because earlier math education is pretty straightforward, particularly problem sums in Primary 4 where approaches and solutions to problems are more obvious. In Primary 5 and 6, problem solving calls for more complex and higher-order thinking that goes beyond knowledge of facts and concepts. This is where heuristics become highly useful, as most children at this age begin to discover that (mathematical) problems don’t always have one perfect solution, and that in fact, one can arrive at a workable solution by using different approaches. And as they realize that word problems can be solved in several ways using different heuristics or using a combination of heuristics, they begin to see the complexity of word problems. Here they learn that one can look at a problem from different angles, and in doing so, one is bound to come up with different solutions. This insight that mathematical problems are not clear-cut or black-and-white conundrums that require a single perfect solution serves as their introduction to real-life problem solving, as problems in real life are not always clear-cut and requires us to come up with different strategies in order to solve.
Heuristics tuition options
As a parent, it is always important to know and assess your child’s learning strengths and gaps first before diving right into tuition. Knowing where his current math skills are—whether it is at beginner, intermediate, or advanced level—would make it easier for you to find a suitable tuition option. To help you make informed decisions about choosing the right heuristics tuition for your child, we have come up with a list of Singapore heuristics tuition options that you can look into.
1. Maths Heuristics
• Website: http://mathsheuristics.com/
• Address: 195A Thomson Road, Goldhill Centre, Singapore 307634; with two other centres at Kovan and Tampines
• Contact: (+65) 6255 5941 (Main); (+65) 8333 6240 (WhatsApp)
A Total Learning Experience—this is what mathsHeuristics™ promises students. Maths Heuristics touts itself as the “first organization in Singapore to offer five integrated platforms as a turnkey learning solution,” offering individualized tuition in hopes of making any student a math whiz. To bridge the gap when it comes to maths heuristics education, mathsHeuristics™ designed its own syllabus and conducted classes that delivered its own mathsHeuristics™ programme.
As part of it services, mathsHeuristicsTM provides a range of programmes for students, parents and educators. For the Primary level, they offer classes that span one term and comprise 8 to 10 lessons, depending on level (Primary 3 – 6), with weekly classes designed to reinforce basic skills, concepts and build the foundations laid in the primary school, with the introduction of heuristics techniques for tackling challenging maths problems. Each lesson lasts 1½ hours (Primary 3, 4, and 5) or 2 hours (Primary 6). Class sizes are kept small (10 students maximum) to ensure every student gets the attention he needs.
2. Aspire Hub Education
• Website: https://www.aspirehub.com/
• Address: Blk 122 Bukit Merah Lane 1, #01-54/56/58, Singapore 150122
• Contact: 6377 7318 / 6377 7320
Established in 2001, Aspire Hub Education focuses on assisting students to achieve their academic goals. Their coaches help provide informative sessions to help students meet academic challenges ahead.
Aspire Hub Education’s heuristics workshop exposes students to the use of the various heuristic skills to solve routine and non-routine world problems. In addition, it helps to build students’ confidence and be more flexible in their approaches to solving mathematical word problems. This workshop incorporates not only mathematical knowledge and skills but also essential thinking skills like Classifying, Comparing, Sequencing, Analyzing Parts & Whole, Identifying Patterns & Relationships, Induction, Deduction and Spatial Visualization.
3. SG Math Tutor
• Website: http://www.sgmathtutor.com/
• Address: 60 Marine Drive, Singapore 440060
• Contact: +65 9665 2893 (Main and WhatsApp)
What SG Math Tutor promises is for every parent to get the best for his or her child, even in finding the best possible tutor—someone who not only has the right credentials to deliver results and provide the best instruction, but someone who is able to inspire and ignite your child's love for learning.
SG Math Tutor offers instruction of heuristic techniques, such as the popular technique Model Drawing and its subcategories Before-After Concept, Constant Total, Constant Difference and Working Backwards. SG Math Tutor believes in math learning by mastering heuristics, not just topics.
4. Polymath Learning Centre
• Address: 433 Clementi Ave. 3 #01-262, Singapore 120433
• Contact: +65 9022 3314 / +65 6909 5768
Polymath Learning Centre is a provider of premium PSLE math tuition via classroom setups that use e-Learning platforms and iMacs with the instruction of educators with experience in teaching the MOE syllabus. Their own developed proprietary system allows diagnosis of the strengths and weaknesses of students, and provides customised worksheets that tailor to their students’ abilities.
Polymaths’s heuristics tuition is given by teachers trained in teaching heuristic mathematics and are well-versed in different approaches to solving every type of math problem.
• Website: https://www.imath.sg/
iMath is the only tuition provider listed here that offers live, one-to-one online tuition services to help your child learn and master heuristics. From our fully-equipped virtual classrooms that provides your child with tuition access anytime, anywhere, or simply at the comfort of your own home; to our curated pool of highly-qualified tutors that have years of experience not only in teaching students but in training teachers as well; to our on-demand homework help that allows your child to simply post heuristics questions or any math-related questions on our Community Wall and get accurate answers (or to help answer questions from other students) from our nurturing and supportive community of math experts and enthusiasts, parents, and students; to our interactive online classes that allows your child to learn at his pace through recordable lessons that he can play anytime he needs to go back to a topic; down to our schedule tracking that gives you the peace of mind of not having to track tuition classes schedules. All these—plus the convenience of not having to spend hours driving or travelling to a tuition centre—are just some of iMath’s services that you can avail at affordable tuition rates—just $15 for every session. Visit the iMath website or download the iMath app today to learn more.
This article was written by Louise O. Lopez