May, 2023 | Yan's One Minute Math Blog

On May 23, 2023, @OrwellNGoode tweeted the rate question below, with the “teacher” marking the student’s answer of 20 minutes wrong, and showing why it’d be 15 minutes instead.

Who the heck takes 10 minutes to saw a board?

I’ve no idea what grade level this math question was being assigned to. Although questions on ratios and rates are formally introduced in grades 5–6 in most parts of the world, however, it’s not uncommon to spot these types of mathematical quickies in grades 1–4 Singapore math olympiad papers to trap the unwary.

Assuming that the word problem didn’t come from a bot or from ChatGPT, the teacher’s intuitive reasoning may be said to be ratio-nally sound but rationally incorrect in solving this pseudo-proportional math question.

Logically or mathematically speaking, few math teachers would disagree that the student was right and the teacher was wrong.

This arguably “badly worded” or “ill-posed” math question provides a fertile ground for a number of possible (valid or creative?) answers, probably much to the annoyance of most math teachers and editors, who often feel uncomfortable or jittery about questions with more than one possible answer.

Indeed, there is no shortage of supporters to defend a “15 minutes” answer. For example, since there is zero mention that the length of each board is of equal length (and we can’t assume it to be so), or as each sawing might take place in a different direction, the “logical” answer of 20 minutes can’t be taken as mathematical gospel truth.

That three pieces need two cuts or sawings is unanimous among problem solvers. The bone of contention is the assumed length of the second cut. Say, if the second cut was half as long as the first one, then it’d take half the time of the first cut, in which case the answer of 15 minutes would be practically plausible.

It looks like we’re only limited by our imagination or creativity to rationalize why the answer can’t in practice be 15 minutes or any other duration, by using a different (creative) reasoning from the flawed one provided by the “teacher.”

Like most artificial or impractical word problems in school math, this rate question debatably falls short of design thinking and is thus open to different interpretations or assumptions, which might also weaponize some “anti-woke” math educators to ban or censor these types of “confusing or tricky” math questions.

Ironically, this is why injecting a dose of realism or creativity to these oft-ill-posed or contrived math questions would help open up the minds of uncritical or unquestioning math educators.

Don’t just answer the questions, question the questions.

A grade 3 question with right answer marked wrong.

A grade 3 Singapore math question made some waves among netizens in yesterday’s local paper. https://bit.ly/3VOzpHP

Debatably, the root of the discussion centers around the “right” way to do multiplication.

Process v. Product

In Singapore, it’s not uncommon for elementary school teachers and tutors to witness a student’s incorrect method of solution to a word problem that produces the correct answer. This frustrating situation arises far too often than what many of them would want to admit.

Due to a shortage of time, most school teachers pay lip service to the method of solution, pretending not to see that the students’ workings fall short of what is expected of them. These time-starved civil servants would simply look at the children’s answers and conveniently mark them “correct.”

In some cases or circles, it’d not be surprising too that some teachers or tutors themselves are oblivious of the correct method or procedure to solve a (routine or nonroutine) math question.

Personally, I’d want to give these school teachers the benefit of the doubt that they’re merely “lazy” rather than because they’re conceptually blind to the mathematical stain on their students’ worksheets.

Getting students to master a math concept with understanding requires time and effort (and also patience and pain), and most stressed teachers can’t afford either one in the name of having to “rush to complete the syllabus.”

For example, students’ or parents’ parroting that “multiplication is repeated addition” gives teachers and tutors quasi-zero clues whether they’ve understood the multiplication concept or not.

With regard to this grade three routine question that made the headlines, writing the correct procedure, without the teacher explaining to the student why he or she went wrong, only solves half the problem.

Understandably, some parents would argue that teachers shouldn’t be too rigid or radical about their children’s half-baked solutions to avoid dampening their self-esteem. For mathematically puritan math educators, the process is more important than the product.

Procedural proficiency with little understanding of math concepts would only produce elementary school drill-and-kill math graduates—the whys are as important as the hows.

An early penalty is better than a later one when it comes to a child’s learning of basic mathematical concepts in their formative years, which must be accompanied by a teacher’s or tutor’s explanation of the incorrect solution.

And in this grade three routine multiplication question, order matters.

Yan's One Minute Math Blog

News & Views about Singapore Math

Monthly Archives: May 2023

The Pseudo-Proportional Problem

Right Answer, Wrong Method