Possible death of calculators in education?

[Vtile]

While I'm mr.average engineer and former average student. I can still understand the no CAS for that level of education. In the end, it is level where all the base of mathematical thinking is laid out. When you have CAS and use it for everything you outsource the very basics of mathematical thinking, since most if not all mathematics are eventually just applying the basic arithmetic’s and geometry. If you do not have those in your intuitive understanding (muscle memory/low level of consciousness) then you lack the ability to follow what more abstract mathematical construction (I purposely use this term) will work.
I sometimes find some basic things that I suddenly see in a whole new light, the last such thing is/were the fraction (seen on deltadays (JDN)) while I can mechanically use them they still did hide some finesses that I never thought of or/and teachers failed to point out (or I just slept on those classes). Another interesting personal finding were the realization of sin and cos as a complementary (which translated to my own language do not say anything if you are not familiar with Latin or some other language that contains lots of butchered Latin ie. English.) again while mechanically proficient, only after I stumbled to old Sin-Cos tables in about 80 years book it did strike to me what it means (well of course there had been much use of them between first learning and getting the stone out of my shoe so to speak. A small RPL script to convert between Cosϕ and Sinϕ did play a small role of reviving the interest of the subject). That is the calculators and computers gives nice opportunities of getting deeper understanding, but I can see how it have also hurt my understanding of the basics, at high school with algebraic calculator with its plug the problem in and solve didn’t necessary give insights of how the mathematical structures work (as an example such as operator sine).

The study books are often also pretty poor, unfortunately, they lack of the bigger scope, lack of reasoning (not proofs) why and where this particular tool is useful and the retrospection of the core basics needed in that mathematical tool. I can remember from elementary school or early high school the question some folks did ask, "I don’t need this or that while baying a milk from market", so why we must spend time learning this or that.

I also think that the importance of the basics will be on rise with ever growing digitalization and computerization. If you do not understand the basics and see how the mathematics work, then you never can program anything or need just blindly trust what some program tells you (if it can). in UoAS where I had opportunity to be a math student of one almost retired a bit old fashioned (you learn these or I make sure you do not graduate) PhD. I vividly can remember early trigonometry course where calculators were allowed (all makes and models, but the review were based on the capabilities of used calculator model), but exam were filled with simple plotting questions which were formed in a way that calculators overflowed and weren’t useful at all. Lesson learned, calculators aren’t always useful.

Everything in programming eventually returns to four basic operations addition, multiplication, division and subtraction. The computer and calculator is good slave, but a terrible master. That is something that is too often not put out in those public conversations I have seen in this subject (in regular media mostly). In that sense, I underline In my mind insightful and philosophical thought of that "Only those who can calculate shall use calculator", which is something similar I can recall from the early days of my school path. If the basics are outsourced in early on and as a wide the future generation lose big part of their freedom as form of being reliant in even basics for what a few CAS etc. provides. It is transition from creators and designers to blind users.

(Ps. Sorry of nonclarity. My do it all phone only shows two lines and one line must be written blindly :-\ PPS. Now edited with proper machine)

(05-21-2017 06:24 PM)Maximilian Hohmann Wrote:  Hello

(05-21-2017 01:24 PM)SlideRule Wrote:  This seems very normal to me.

To me as well. I am not a mathematician. For me mathematics is a kit of basic - quite sophisticated though - tools required to get other jobs done. A carpenter does not need to know how to solve Maxwell's equations in order to use an electrically powered circular saw (whose motor can be described with these equations). As long as I know which tools are best for which task I don't need to know how these tools are built.

Recently I talked to a former colleague of my father and friend of our family. Initially a mathematics teacher and later mathematician in the nuclear research environment. He has come to the conclusion that we should not torture our children/grandchildren at school with mathematics (the most hated subject for most of them) the way we do now. Teach them what is needed for life - fractions, percentages, some statistics - and leave the complicated stuff for the 2% who want to be physicists, mathematicians or other scientists which rely on an in-depth understanding of mathematics. Teach all the others languages or sociology instead if we want to have a future.

My son has just now been sitting his last exams (called Abitur in Germany) to finish secondary school. He was part of an experiment - which will end with his class - where students were using a CAS calculator (Ti nSpire in his case) throughout secondary education. The idea was to raise the overall level of mathematics education by leaving the routine tasks to the machine and letting the students do more abstract work. From what I see this experiment has been declared a failure and they will return to "traditional" mathematics teaching with pen an paper. So to say "the death of calculators in education" as the thread title goes, but not in terms of hardware.

Regards
Max