Calculators - again?

First the relevant part of Chris Goodalls post for context:

Many have had a trip down memory lane and compared the introduction of AI to the calculator in Maths.

In the case of AI, I think we are starting to see a similar pattern of adoption. Some have moved through the fear and need to hold on to the past (See Pic 2) and have moved to acceptance and are embracing and experimenting with ways to adapt methods of assessment. They are changing lanes.

In Maths we moved to calculator and non-calculator papers as a solution. I wonder if we will see something similar with artificial intelligence (See Pic 1).

My gut feeling is that although this works with the calculator, it wont work for long with AI, and maybe we’ll see a situation where the lanes will merge (See Pic 3).

Then my reply:

The funny thing is...

Let’s follow the comparison for a moment. Most people have become worse at performing simple calculations without the tool. There has definitely been a "learning loss" following the introduction of calculators in schools. Perhaps they are introduced too early in K-12? On the other hand, the calculator makes it possible to move on to "heavier" math sooner. But at what expense? Is heavier math easier to understand once you have practiced mathematical thinking more rigorously? Or does having the tool at hand make the concepts easier to grasp? There are likely both gains and losses.

Now, let’s pivot away from that comparison. Calculators can do simple math for us, but they truly shine when we perform math that would otherwise require vast manual labor or utilize mathematical principles a student might not yet understand. We take a shortcut, trusting that there is sound math behind it (after all, a calculator doesn't really produce "hallucinations" or failed approximations). That is the gift of the calculator. That is not the gift of GenAI.

The tasks we are suggesting GenAI should do for K-12 pupils are not insurmountable—unlike the complex functions of a calculator (♤). We are asking it to write or read. One would hope that we still cherish our students' ability to excel in these skills. As I see it, there is no "writing aspect," "reading aspect," or "internet search aspect" that is beyond a student's fundamental comprehension. We don't need GenAI to complete these specific tasks for us in the same way we need computational power.

When doing research or analyzing data at the university level, GenAI tools begin to reach a level where they can shine (partly by taking on the role of a calculator using Python). At this stage, tasks start to become insurmountable—as most statistical analysis would be. Most people who learn to perform statistical analysis don't learn the actual underlying math; they learn to use a tool (Stata, SAS, Python, R, or the like).

Ultimately, it comes down to what we are prioritizing: Efficiency? Learning? Building skills? Capacity? And at what loss? What is the cost-benefit ratio?

Yes—as teachers and schools, we must integrate the GenAI world into our didactic framework and recognize it as part of the digital landscape students already inhabit. But that does not mean we need a "strong" integration of GenAI as a productive tool. Perhaps rather the opposite. Students need to build that "math skill" and "math knowledge" (to return to the analogy) before they can afford to be "lazy" and use the "calculator" to become efficient. Only then can they truly understand what the "calculator" does, and properly evaluate and utilize its output.

♤ yes I know we also use a calculator for less arduous tasks - but that's not where it shines and that use is arguably detrimental considering the loss of cognitive capacity mentioned earlier.