i was sent a link today to this thing called the qama calculator, which basically, is an attempt to teach kids to depend less on the calculator and get better at mental algebra and calculations. and, to me, this is so fundamentally wrong that i want to cry. qama calculators are exactly what we don’t want to give to our students!
as i have explained several times in this blog, i myself am terribly bad with numbers and calculations. also, i don’t know of anyone who works with mathematics in daily basis, just as i do, that is any particularly better in mental calculus than any other person NOT doing maths at all. furthermore, being agile with number operations is of little to not help at all for them! surprised again? then take this: mathematics is not about numbers. really. mathematics is about relationships, patterns, rhythms, colors, shapes, proportions, behaviours, structures, you name it. numbers, although important, are nothing but the simplest and most primitive of all of the possible mathematical objects you might ever want to work (play?) with. as a professional you’ll probably analyze, explore and express ideas through maths, but any actual flow of numbers through all of those formulations, if any at all, is of little interest.
however, despite agreeing that numbers don’t have that much room in real/professional life, one might believe that they actually still have a pivotal role in education. that would justify a need to be agile in both manual and mental computations…?
first, i believe that in education numbers should be just one more member in a big family of mathematical objects like colors, graphs, shapes, movements or sounds (to name a few), and not especially more important than those. secondly, even when students would work with numbers, i believe that denying them the use of calculators not only has the negative philosphical impact if misleading them into believing that maths is about being good with numbers, but in practical terms it’s also a terrible waste of time and human potential. for these machines are really good at doing the mechanical/low level/stupid/algorithmical/repetitive part of any job that involves number manipulation, from which students should be free so they could spend their time doing the other non mechanical part of the job – the actual maths, such to speak. they could also use the time to internalize the real concepts, to build their own intuitions about them, to learn how to express those intuitions formally. even figuring out alternative constructions to describe the problem in question, and finding which of those alternatives resonates better with them. basically, the prohibition of calculators or projects like the qama calculator are, in fact, obsolete and represent a big blocker for teaching maths. it’s like attaching prison balls to the students!
still, some might argue that learning the algorithmic part of manual calculations is beneficial for understanding the underlying principles of, say, algebra. i think this is a misconception again. for example, all students learn that when doing a long multiplication they have to shift their partial muls by one column to the left prior to perform the final add. now, how many of them did ever naturally understand that 987 x 12 is exactly 9870 units bigger than 987 x 2…? not that many (or should i say, “zero”?). seems to me that getting them to memorize how to execute algorithms helps little on having them understand maths (in this case the distributive law).
so, since ideally we want a world where calculators (and computers, for the matter) are not seen as a thread to students, but as their friends, i cannot but feel that when there is an initiative that tries to help kids get better at manual or mental calculus is so a short in vision as thinking that training them in the art of ink & feathers calligraphy is of any use for becoming good at written expression/communication. instead, with those initiatives we are just putting even more obstacles in their path. and that’s when i think we are really doing it wrong.
so, to that qama calculator idea, i responde, “noooooooes!! please step aside! you are doing it wrong!”