There are so many online tools available for students to read, watch, learn and practice math that anyone can learn from anywhere. Unfortunately, I think the problems we face in mathematics education revolve around the fact that students simply don’t care about learning math. Those who are successful, typically follow rules and do as they are told, just as expected in a traditional math classroom. Those who are not, likely lost their curiosity for mathematics somewhere between grade 1 and 6. While these online tools are extremely innovative and personalized to the learner, those who could benefit from them the most will likely never utilize them.

Simply put, online tools such as Khan Academy are your best option if you are unwilling to move away from a traditional mathematics education, but still lack the real personalization students need in a face-to-face classroom.

In any case, one needs more than motivation to build a scaffold – a student needs practice and examples of building connections and discounting spurious connections. Eventually, with maturity of thought, the student will make his/her own hypotheses.

So, yes, mature self-motivated students with enough existing knowledge and skills to bridge and extrapolate is the goal but until then, external motivations, guided (personalised?) pathways, tricks and crutches are required to keep in the zone.

I respectfully disagree, at least in part. the Zone of Proximal Development is important, but education is more complex than that. Students are not necesarily motivated because they know they will actually be able to solve the problem.

A motivated student can build his or her own scaffolding. A motivated student who doesn’t know how to learn might also get frustrated. So some emphasis on learning how to learn is important.

http://turtleacademy.com/index.php

What is important for personalisation is the ZPD where a student has enough support and incentive to become independent and make their own connections. Before that can happen, it is up to the teacher (or virtual teacher) to teach students to make connections by example or open questioning.

Adaptive systems, therefore are trying to create that zone where students are comfortable to explore and challenged to widen their experience. If adaptive systems were perfect they might even induce flow given adequate rewards.

(When was dieting, detox and colonic irrigation ever part of the maths curriculum?)