My Problem with Heuristics and Singapore Math

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Seth Godin published a blog post recently “For those unwilling to think deeply”, which made me think about the problem with Singapore Math and heuristics.

“You can just use the tool without understanding it, copy the leader without realizing where she’s going, follow instructions without questioning them.”


“More likely, you don’t want to expend the emotional labor to push through feeling dumb as you dig deep on your way to getting smart.”

If you think about it, Reasoning via First Principles – a mode of inquiry that goes back to Aristotle, but popularised by Elon Musk – is one that  pursues the foundations of a problem relentlessly; deconstructing one’s beliefs down to its fundamental roots before reasoning up.

“Arguing from first principles “takes a lot more mental energy,”

Most people Reason by Analogy – they do what they do because other people are doing it, says Elon Musk. This form of reasoning requires less effort.

Heuristics and Singapore Math

According to Wikipedia, the definition of heuristics is:

A heuristic technique (/hjᵿˈrɪstk/; Ancient Greek: εὑρίσκω, “find” or “discover”), often called simply a heuristic, is any approach to problem solving, learning, or discovery that employs a practical method not guaranteed to be optimal or perfect, but sufficient for the immediate goals. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of making a decision. Examples of this method include using a rule of thumb, an educated guess, an intuitive judgment, stereotyping, profiling, or common sense.

When I first heard about Heuristics in Singapore Math, it made me slightly uncomfortable.


How we Use Heuristics in Problem Solving (Math): Source: Marshall Cavendish Education

In particular, the second column “to make a calculated guess” felt like a tactic that we learnt when I was in school as “hack” for improving one’s score on standardized tests like the SATS.  By eliminating answers that are wrong, your probability of choosing the right answer increases.

However, if one understands Math concepts at the fundamental level, why should there be a need for an educated guesses – one should be able to work out the right answer in a logical manner.

In a society where over-tutoring is the norm, what if our students are not learning heuristics but are still stuck learning by rote? Do the benefits of heuristics  in making snap judgements diminish? Perhaps I am the one guilty of making snap judgements without really understanding what heuristics in Singapore Math involve. But my instincts lead me to this question:

By popularising heuristics as a mode of problem solving, are we as a nation encouraging lazy thinking or even worse, creating a systemic inhibitor of Critical Thinking?  

For those that are interested in finding out, Cambridge University, together with UK education technology company Macat are currently conducting what they hope will become the world’s largest survey on Critical Thinking.


Why Critical Thinking?

According to the World Economic Forum, Critical Thinking was one of the top 10 skills that employers are looking for.

Top 10 skills (Future of Jobs Report), WEF


Bloomberg’s 2016 Skills Gap

This is consistent with an annual Bloomberg survey on what recruiters are looking for in MBA students, and what they find hardest to find. Regardless of industry, Creative Problem Solving and Strategic Thinking – both elements of Critical Thinking were named as the hardest to find and the more desired.  Interestingly, entrepreneurship and quant skills were considered the least desired and the easiest to find.


Macat has broken Critical Thinking down into 6 elements:


How does that tie in with Computational Thinking?

Macat’s approach however is a humanities based one – they believe that using humanities and social studies is the best way to teach Critical Thinking.  What about Computational Thinking?  How does Computational Thinking fit into the picture I asked our friends at Macat?

Their response:

There is some overlap although computational thinking is essentially logical and can be programmed on that basis. We are only interested in pure critical thinking which by its nature does not necessarily produce a programmable outcome.

Before anyone makes any snap judgements about this response, let me again invite everyone in Singapore to participate in Macat’s study, whether you subscribe to their school of thought or not, there is value in seeing how Singaporeans, whether as individuals, students or employees stack up against our global peers.

As a reminder, an impressive list of participants have already signed up, including Dulwich, Eton, Marlborough, Stowe, Vodafone, WPP, Pearson, Ernst & Young, Nestle, Visa.  In fact, organisations like the BBC and Open University have over 1,000 participants taking part in the study. A total of 2,000 organisations and 300,000 participants are expected to take part.

It only takes 50 minutes to participate, it’s free, there is nothing to lose (unless of course your scores turn out to be lower than expected), and valuable insights about your organisation’s critical thinking capabilities versus a global benchmark to be gained.   It is an opportunity to take part in a seminal study – the world’s largest ever on Critical Thinking.

My only fear, however, is that even after 20 years, I will encounter the same the mindset that I faced as a 21 year old fresh-graduate from Cambridge University during my PSC interviews – i.e. the “our approach is better than theirs, hence we don’t need to take part in their study.”  You can read more about that on my personal website.


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