What rationale could anyone possibly have to teach this mindless nonsense to children, unless it was to prepare them for other standardized tests later in life, which are unanimously the product of mathematically impotent failed bureaucrats?
For example, consider this problem for geometric series: 1 + 2 + 4 + 8 + 16 + 32 + ... + 4096 = ?. This problem may look completely intractible and tedious without a calculator. But once you start adding: 1+2=3, 1+2+4=7, 1+2+4+8=15, 1+2+4+8=31, ..., even a child can spot the pattern. Now that they are amazed, they will be motivated to learn more about the cause of this pattern, etc, etc.
Would the problem work if the student started summing backwards from the last item? How many items would the student have to swap in that case?. For how many random combinations of items would the problem "work" (i.e. require exactly one change?)
On the other hand, in your example you're not just trying random things until something works. Noticing that 1 + 2 = 3, etc is more analytical than adding members at random and hoping that the person who created the problem thought of the same random pattern you thought about.
The dollars-and-cents addition problem mapped onto the "fun" toy store narrative is not mathematically interesting until assigned the type of analytical firepower outlined in OP's blog post. It is a deliberately obtuse trick question posed as a learning tool; children labelled "gifted" will figure it out and feel the dull satisfaction of killing another "problem", and those without that benefit will simply experience more fear and boredom.
"Smart" children are identified early. After that they are smart because everyone knows they are smart. It is very hard for a person who knows they are not smart to convince a society who knows they are not smart.
Dumb people are sometimes lucky and get something right. That doesn't make them smart. Smart people sometimes make mistakes. That doesn't re-label them as dumb. The important thing is the label you start with. Smart people will recognize the grammatical "mistake" in the previous sentence and understand that this post came from a dumb person.
That said, this problem isn't about mindlessly adding. It's about figuring out a way to systematically discover the answer. Most math challenge problems are designed with a method in mind; it's your job to figure that method out, and that's where the fun lies.
In fact, this question is more than „just sum things up“, as described pretty well by the person above your comment.
I am a scientist. When I see a problem I have never seen before, I start to analyze it using the tools I know. This helps me to learn more about the given problem and supports me finding a „clever“ Solution in the next iteration.
I am not opposing the idea that to do math, you must occasionally "get your hands dirty" as another commenter says; I am opposing the idea that it is useful to set this question in front of third graders in the form "find the solution and move onto another problem". As OP's article proved, there are many, many interesting implications that arise from this problem, and an investigation of those implications requires much more care, passion, and analysis than is implied by the form in which the problem is presented (as a solvable worksheet). For what it's worth: if you want to teach the lesson "sometimes you have to just start adding things up", just write that down in plain English and teach that. Put this question in a giant book of trick problems with an explanation of why each question is a trick, don't put this on a worksheet for of children who are required to attend class and then expect them to pick up on the subtleties of instruction after they write down the answer and get their grade back.
I am not a very smart mathematician; I am a middling intellect and have been my entire life. It was not until I was two years out of my engineering degree that I started investigating the world on my own and began to find out the true size and power of mathematics, and now it always angers me when I see the shallow imitations of real pedagogy and instruction passed off on the world's children as "useful math worksheets". My self-esteem and lifetime mathematical achievement were butchered by worksheets just like these.
[1] https://www.maa.org/external_archive/devlin/LockhartsLament....
This is a thinking problem that could be approached in a lot of different ways. It's really the opposite of a standardized test problem.
>unless it was to prepare them for other standardized tests later in life
yes, it teaches you how to understand standardized tests and to exploit them.
There's a somewhat popular TED talk on how kindergarteners frequently outcompete adults in the marshmallow challenge (tl;dr; build the tallest structure possible using assorted materials but a marshmallow must be on top) because, among other reasons, they're willing to just try out different approaches and fail fast rather than take a long time to think up of an approach that ultimately fails.
https://www.tanveernaseer.com/5-lessons-on-fostering-team-su...