When should calculators be introduced to the curriculum?

chiro

I've already given my own response to that earlier in the thread, but in case you were wondering, my response was give them calculators when they understand the processes used on their calculators.

My later response though was targeted specifically at your response for programming, not for the calculator debate and I thought this would be crystal clear given that your response focused on programming.

All I'm saying is understanding programming, much like understanding mathematics is not about understanding a specific language or a bunch of largely un-connected specific examples like we have in the high school curriculum (right angled triangles, angle classifications for straight lines, etc).

Instead real understanding comes from knowing constructs like for example, doing a loop so many times to calculate a polynomial expression, or using an if statement to decide whether to use option a or optio b.

These kinds of things don't depend on languages in the absolute sense and if its taught this way, then the students will not be learning and we will continue the stupidity that is already happening in the classroom, where the students typically know the answers, but they really don't actually understand that much.

I don't have first hand experience of students being introduced to programming in schools on a classroom or school level, but I have helped a variety of people to learn programming of various backgrounds and ages, and I have seen that the learning difficulty shares similarities in mathematics where people often just do things without knowing until suddenly the lights go on and it makes sense.

In some of the above situations, people just read code (or reading symbols in mathematics) and they don't fully know what the code is even doing, so they fudge the code in some way to try and get what they are aiming for until it magically works.

This situation can be amplified when you use specific implementations and examples and if the course is structured bad enough, students can get away with going through the whole course by using a kind of superficial understanding to know what to fudge even if they have no clue why.

This is the gist of what I was trying to get at.

mathwonk

lurflurf:

"Who here can compute 357*79135=28251195 in less than 1.0 milliseconds?"

the teacher's problem is the kid who reads off 357*79135=2825119, and does not realize it is wrong even after much more than a millisecond.

moouers

If the teaching is done correctly, I don't think it matters too much when calculators are introduced. Basic four function calculators were introduced to me around the age of 9 or 10, scientific calculators in junior high, and graphing calculators in high school. If anything, having access to calculators at such a young age actually piqued my interest in mathematics ("How does it do that?!"). Calculators never really presented a hindrance to my learning anyway, due to the fact that none of my teachers, from algebra 1 to calculus 2, allowed the use of calculators of any sort during tests. The arithmetic was kept simple enough and the focus was put on the mathematical manipulations.

brimacki

Calculators should be allowed in courses after trig to speed things up. By the time students get to calculus they know when to rely on a calculator (arithmetic, trig functions that aren't based off 30 or 45 degrees, similar ideas...). A student shouldn't be held up on a multi-variable integration problem because they can't do longhand multiplication quickly. They still know how to do the multiplication, but it would just take a long time.