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Sounds like you are a very smart mathematician who knows how to write a 4th grader math question which isn’t just „sum things up“. In fact, this question is mo

by karxxm 5y ago

Sounds like you are a very smart mathematician who knows how to write a 4th grader math question which isn’t just „sum things up“. 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.

quacked 5y ago
This problem must be taken in the full context. This wasn't a free-form "explore the infinite bounds of mathematical expression" lesson, it was part of a worksheet. Worksheets are meant to be completed as proof of mathematical ability, and the relationship between one's ability to complete a worksheet and their intellectual potential is a poisonous lesson to teach to anyone. (Reference the past few pages of A Mathematician's Lament [1], or the whole thing if you have the time). 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.pdf https://www.maa.org/external_archive/devlin/LockhartsLament....

by karxxm 5y ago

quacked 5y ago

This problem must be taken in the full context. This wasn't a free-form "explore the infinite bounds of mathematical expression" lesson, it was part of a worksheet. Worksheets are meant to be completed as proof of mathematical ability, and the relationship between one's ability to complete a worksheet and their intellectual potential is a poisonous lesson to teach to anyone. (Reference the past few pages of A Mathematician's Lament [1], or the whole thing if you have the time). 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.pdf https://www.maa.org/external_archive/devlin/LockhartsLament....