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When I was a grad student, I taught a Calculus I course during the summer. Somehow I came across Robert Moore and I ended up reading his book which I connected with. Rather than being a great student, I learned slowly but deeply—a lot of experimentation because I do not have a good memory.

I tried that summer course using the Moore Method and it was semi-successful. Most of the students I could see were willing to try to cooperate. Now in high school it seems the Moore Method can morph into a project-orientated program using Desmos to experiment and create effectively "products" for the real-world. One difference (and also the problem) between college and high school seems to be this mandated passing of the state test.

Do you think with the advent of Desmos/GeoGebra, the Moore Method is more accessible to high school?

But of course this requires teachers to be well-versed in programming with Desmos.

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  • $\begingroup$ Just as an FYI: R L Moore was notoriously racist (even for his time), and there are a lot of modern mathematicians who get kind of touchy around the "Moore Method". I believe that the preferred description is "inquiry based learning" (which is not quite the same thing, but is close). I am not saying this to admonish you, but only to make you aware of something which might earn you a scolding from others (I have been very nastily scolded on this in the past---I would prefer to save you that experience). $\endgroup$
    – Xander Henderson
    Jan 15 at 13:19

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It seems like there are several questions here. I'll try to untangle them and address each one individually.

Do online graphing/visualization tools like Desmos and GeoGebra make projects more accessible?

Yeah, I would say so. There's a quick feedback loop, and it can kind of feel like a video game where your joystick is a mathematical expression. These tools can make projects fast & fun.

Can you teach a math class on the basis of projects only, as opposed to more traditional exercises?

Not really. Sure, projects can be useful for pulling a lot of skills together to do something cool and exciting. That's valuable. But the thing is, students need to acquire the component skills first. Most student's can't learn component skills on the fly in the context of a bigger project -- they need plenty of practice on each particular skill, where lots of scaffolding is provided at the beginning and then gradually removed.

For example, let's say you want to do a project where students sketch an image by graphing a bunch of straight lines in Desmos. Obviously, going into the project, students are going to need to know how to represent points in the coordinate plane and find the equation of the line between two points. They should also know how to manually create the graph of a given linear equation (otherwise they're not going to understand what Desmos is actually doing for them, and they won't be able to debug their equations if they run into issues). They'll need to be comfortable different formats of equations of lines, including $x=\textrm{constant},$ $y=\textrm{constant},$ $y=mx + b,$ $y-h = m(x-k).$

There are tons of component skills here and you can't teach this all in the context of the project. Each of those component skills has to be built up beforehand. And it takes plenty of time and practice to build them up. Most students are going to need a worked example and a handful of practice problems (with feedback) on each separate case of each component skill (separate cases involving positive numbers, negative numbers, fractions, decimals, etc.). If they don't get this practice, then they're going to be totally overwhelmed by the project, spend a ton of time working unproductively, and ultimately learn little to nothing from it.

Can you run a successful high school class using the Moore Method?

Regardless of the tools at your disposal (Desmos, GeoGebra, etc.), a successful implementation of the Moore Method will require extremely motivated students who really enjoy intense, effortful thinking about math and are bright enough to construct a subject from the ground up with minimal guidance. Needless to say, this is typically a tiny proportion of students, which becomes vanishingly small as you climb down the ladder from graduate --> undergraduate --> high school --> middle school --> elementary school math courses.

Personally, I spent several years teaching at a highly advanced, opt-in math program where students entered in 6th grade (generally starting at prealgebra), took AP Calculus BC in 8th grade (with many students earning 5's), and studied undergraduate math during high school. I worked with something like 100 students across that program but can count on a single hand those students who I think would have been able to succeed with something like the Moore Method. Even in the highest courses within that program, which filtered down to the most motivated and capable students, I would estimate that the proportion capable of succeeding with the Moore Method was something like 10% -- and this an incredibly optimistically biased subsample, within an already incredibly optimistically biased sample.

So while I suppose I can't claim that it's impossible in theory for a Moore Method course to be successful at the high school level, I think the likelihood of having a group of students for which the Moore Method could work (leaving students not only with a decent grade in the class, but also the ability to solve actual problems that are standard for the subject, and not just the simplest cases) is so vanishingly small as to be effectively impossible in practice.

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  • $\begingroup$ Just one comment I'll make (and this goes into people's different deep fundamental beliefs about school and education) is that Thomas Edison did not understand the deep physics behind the creation of the light bulb, but still built something great (though it seems not the first first light bulb). However, then you might say well that's the difference between engineering and science/math/physics. You don't need to understand all the ins-and-outs; it just needs to work. People are good at different things, and so I think we should start earlier in school when we start to play to their strengths. $\endgroup$ Jan 6 at 19:38
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    $\begingroup$ @MatthewAlbano are you suggesting that aspiring engineers should not be required to learn how to do algebra by hand now that we have computers? $\endgroup$ Jan 6 at 21:59
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    $\begingroup$ "You don't need to understand all the ins-and-outs; it just needs to work." Yeah, the bicycle gear just needs to work and, perhaps, the first bicycle gear teeth were designed by trial end error or just by letting the chain slowly eat its way to the right shape. But knowing a bit of theory helps a lot if you try to experiment with non-standard designs (like elliptic gears). So, true, you can get away with lack of understanding now and then, but you can go much farther if you have some :-) $\endgroup$
    – fedja
    Jan 7 at 3:57
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    $\begingroup$ @fedja yeah, I'm with you on that. Been seeing a lot of those "anyone can do X" statements recently, many of which go as far as "anyone can do X without having to learn X." Part of the issue seems to stem from a simplistic view of what programming is, e.g. that building a basic website in Wix is a representative task. So while it's true nowadays that "anyone can create a basic website without knowing how to code" it's a far cry from "anyone can build cutting-edge technology", especially "anyone can build cutting-edge technology without knowing how to code". As you say, indeed we will see :-) $\endgroup$ Jan 7 at 4:43
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    $\begingroup$ I've forgotten the attribution for something like "Weeks of experimentation can save an hour in the library" :) :) $\endgroup$ Jan 7 at 22:19

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