This area of study is commonly referred to as Computing Science or Scientific Computing. Many of my students go on to some of the Big Tech or Ivy League schools for a major in Engineering or the Sciences. In said fields students and professionals will be programming computers to solve their problems. These professionals may use a programming language such as Python, C++ or Java. More likely, they will use a mathematical programming environment such as MATLAB, Mathematica or SPSS. Alternatively, I try to expose my students to FLOSS (Free Linux Open Source Software) versions: Octave, SAGE or R respectively (we use Linux a lot).
These past couple of years I thought I'd replace the TI83/84 in my preCalculus classes. Since preCalculus is mostly a terminal course for Seniors (not Honors) in High School whereby a Graphing Calculator is not required (no Regents or AP), I thought this would be a great place to experiment. The classes took to this approach very well. These students even felt special and accomplished when they told their peers in other classes that they were coders! I did keep the coding to a minimum, however, using predefined functions in SAGE.
Early in the year (Sept), I did use pure Python coding for Sequences and Series as the List Data Structure, List Comprehensions and For Loops are very easy to introduce here. Later on (June), we were able to build on Sequence and Series when we got to Reimann Sums. Here's a playlist from that course.
Many schools nowadays have a 1-to-1 program where every student and teacher use some sort of compatible device provided by the school. Some schools, like mine, give out Graphing Calculators to everyone at the beginning of the year like a textbook. This way, everyone can use the same technology in class and at home. Some schools give out Tablets, unlike mine, whether it be an iPad or an Android, and use an app like Desmos or Geogrbra or even a TI Emulator. Don't forget, there's always a "App for that" or that "Droid does!"
Why not leverage the devices we already have? Most students and teachers have a Cell Phone or Tablet capable of coding with an online IDE, an app or a computing environment such as SAGE! As you can see from recent posts to this blog, the amount of python coding needed isn't much or hard to learn:
Of course, you could get a little carried away and teach a lot more (see the side panels of my blog for SAGE samples from all of the topics in preCalc and AB Calc).
I let my preCalculus students use SAGECELL in class and at home without a problem. I also let students use their own TI83/84 if they have one and prefer to use a Graphing Calculator at times as a mater of taste. I do not expose my AP Calculus students to any of this until after the AP Exam as they need to use a Graphing Calculator on the exam. Take a look at any playlist on my YouTube channel labeled "LAC" (Life After Calculus) for examples of what we do after the exam.
Using Python in SAGECELL or REPL or VPython in GlowScript very easy to use and teach. These environments are to python as Processing and OpenProcessing are to Java. So, I may use Java in Math class too!
I was one of the first to promote the use of Graphing Calculators back in the early 1990s. Everyone was resistant to change back then. If a particular technology were not required on a particular exam, I think more people would be receptive to change now. Why saddle our kids with outdated tech that costs about $100 per calculator when they already have a ton of tech in their pocket or backpack?