An honest assessment of the current state of mathematics education exposes the need for improvement and reinvigoration. Despite the acknowledgment of the problem, and the billions of dollars that have been spent trying to tackle the problem, so far nothing has worked. At Mathable, we view the problem as a pedagogical issue. Traditional teaching methods involve some form of lecturing about conceptual issues, and then asking students to apply pat procedures to produce closed answers without explanations to a limited scope of problems. Students then become completely focused on these procedures, and often miss out on the conceptual underpinnings. They become fixated with temporarily matching algorithms to problem types and are unable to articulate anything about the models they are using.
In “Lockhart’s Lament” (Paul Lockhart’s famous 2002 rant on the state of mathematical education), he asks us to imagine a world where music is taught the same way as mathematics. In that world, music is taught without sound or instruments, using just written notes on pieces of paper. He then asks: if that were the case, would anyone actually like music?
Carrying the analogy further, what if we could teach mathematics the way we teach music? What if there was an instrument that students could learn to play and analogously use to ‘hear’ the music of mathematics? What if they could play with the concepts and models of mathematics before getting bogged down by calculations? Then, once the concepts, structures, and models were understood, the calculations would become more meaningful, simple, and understandable. There is such an instrument. It’s called Mathematica. And now there is an online learning system with content and learning management software that utilizes this instrument to help you teach students the music of mathematics. It’s called Mathable.
The Solution = You + Mathable
The instructor remains the essential part of the equation when engaging Mathable to teach mathematics. Mathable doesn’t replace instructors, but it changes their role from the presenter to the coach. Students go through the material and try examples written in Mathematica, and even create their own demonstrations. Eventually, they run into hurdles which become crucial “teaching moments.” Your responses to these teaching moments drive the courses forward and build your relationship with each student.