This seems to imagine that the only thing being taught/worth teaching on the mathematics curriculum is number sense.
Firstly, that's not the case. If you want students to answer a problem with any practical application (e.g. money/finance, statistics), or more complex problems where the point is to follow the logic, being able to use the calculator in your pocket is great.
A perfectly reasonable assigned problem might be: add the 7.1% sales tax to this ticket price, do you have enough cash?
And secondly, number sense is easier to teach without depending on particular algorithms.
This is the same complaint as people grumbling about "common core" math, or saying we should go back to the basics of just rote learning times tables and long division.
Students are learning about number sense by different routes now - routes that don't end up with most students blindly trying to follow a particular algorithm with no sense of what is actually happening.
I once taught in a physics curriculum that went a step beyond calculators. Students never had to do numerical calculations in the exams. For example, a question asking you to find a force, could have an answer like "F=ma where m=3 kg and a=2m/s". There were higher grades for showing insight into the physics that you could get by looking at the form of the symbolic equations you'd derived but would have trouble noticing if you'd substituted numbers early on.
I wish I had learned times tables properly as a kid though. I struggle with things like 6*7 on a near daily basis for my work and general life. Not really for number sense but for not having to shift my attention to a basic math problem while I'm working on something else.
I think you are misunderstanding me / underestimating students. The slide rule teaches in a very direct physical way how logarithms work and how they can be used. This is something that most people never learn, but is extremely valuable.
> This seems to imagine that the only thing being taught/worth teaching on the mathematics curriculum is number sense
First of all, number sense is extremely important. Probably the most important thing taught in primary/secondary math courses. But it is certainly not the only important thing.
Students can learn to use an electronic calculator in very little time. A person of average intelligence who understands the relevant math should be able to learn to use their calculator pretty much independently, and become fluent at it with a tiny bit of practice over a short time. There are very quickly diminishing returns to teaching “calculator skills”, because those are extremely shallow.
> And secondly, number sense is easier to teach without depending on particular algorithms.
I really have no idea which ‘particular algorithms’ you are talking about. Have you ever used a slide rule? It is a very flexible general-purpose tool.
> This is the same complaint as people grumbling about "common core" math, or saying we should go back to the basics of just rote learning times tables and long division.
No, it is precisely the opposite recommendation to those.
> A perfectly reasonable assigned problem might be: add the 7.1% sales tax to this ticket price, do you have enough cash?
This is a reasonable problem to teach students about for like 1 week at age ~10. If they learn how to do it using pen and paper, or a soroban, or mental arithmetic, or a slide rule, or a pile of loose pebbles, they’ll have no trouble accomplishing the same with a calculator. It is not a reasonable problem to spend 5 more years on. We are talking about exams for 15-year-olds.
> This is a reasonable problem to teach students about for like 1 week at age ~10.
I'm afraid you have a completely unrealistic expectation of the median student (which is reflected in your other comments as well). I have taught hundreds of students and I would think a handful of them could answer this at age 10.
This type of question first appears on the Khan Academy in Grade 7, i.e. targeted at 12-13 year-olds.
There is a significant body of prerequisite work in the earlier grades, some of which is limited by what is developmentally appropriate.
Students will need dedicated practice to recall this and most won't remember it after seeing it or mastering it on one occasion. It needs to be supported in the rest of the curriculum. You might be able to intensively teach it earlier, but it is hardly worth it, because they will completely forget when you intensively teach the next topic.
Many 15-year-olds will continue to struggle with this and, if they are well-supported, might be taught it as a step-by-step procedure in order to best score marks in the exam they need to. These students are unlikely to finish without a good concept of what they were doing - and might be more likely to pick it up as adults out of necessity.
«Add 7.1% sales tax to the $19.95 ticket» (or whatever) is a 1-step (or generously 2-step) arithmetic problem, of the kind most students in many parts in the world learn to understand conceptually at age 6–7 with no problem. It additionally involves multi-digit multiplication, of the type people typically learn by about age 9–10 (?).
If students have not practiced solving problems enough to handle combining these things until age 13, and many are still struggling with it at age 15 (with a calculator!), that’s a serious indictment of the entire education system.
Firstly, that's not the case. If you want students to answer a problem with any practical application (e.g. money/finance, statistics), or more complex problems where the point is to follow the logic, being able to use the calculator in your pocket is great.
A perfectly reasonable assigned problem might be: add the 7.1% sales tax to this ticket price, do you have enough cash?
And secondly, number sense is easier to teach without depending on particular algorithms.
This is the same complaint as people grumbling about "common core" math, or saying we should go back to the basics of just rote learning times tables and long division.
Students are learning about number sense by different routes now - routes that don't end up with most students blindly trying to follow a particular algorithm with no sense of what is actually happening.