The traditional way of teaching at a college or university has always struck me as strange and artificial. The teacher summarizes sets of rules, illustrates the related concepts on the whiteboard, and students are expected to derive some form of understanding about the topic from this.
Contrast this to how a three year old learns how to play videos on an iPhone. No one tells her how the capacitive sensing array under the glass works or how the underlying operating system multitasks between gesture recognition and measurement of the gravity vector using onboard accelerometers. She simply moves and swipes, sometimes succeeding, sometimes failing at making the device work the way she wants. These hands-on, trial-and-error tests induce a change in how the child uses the phone. After a few months of learning like this, children are often more adept at using the phone than their parents are!
The child's inductive approach to learning is a stark contrast to the artificial deductive approach we experience so often in school. The inductive approach is more natural and typically leads to a deeper, more useful understanding.
I've recently improved my third-year electrical engineering course on sensing and measurement by augmenting the traditional deductive teaching methods with explicit inductive learning exercises. One goal of this course is to familiarize students with tools for analysis, simulation, visualization, and design. I wanted the students to be able to explore the models in a hands-on, self-directed way. It was critical that whatever tool I chose also explicitly confirmed the mathematical models the students saw in class and in their textbook.
I selected the system-level modeling tool MapleSim, from Maplesoft, to enable this inductive approach. It allows students to model a system, observe realistic behaviors, and generate equations that help explain those underlying behaviors.
To illustrate, let's take a very fundamental concept all EE students deal with -- op amps. It's important for students to tie in how an op amp modulates a signal or how it amplifies/attenuates a signal, and any simulation package used must be able to facilitate a clear understanding of this concept. In the traditional deductive teaching approach, the instructor would refer to a standard textbook like The Art of Electronics , and give students the golden rules of op amps and tell them how current goes into certain ports and not others, and why voltages should be of a certain value. The students are then asked to solve the circuits by hand. There's a lot of potential for error here. It's asking a lot of the students, especially if they haven't had any experience with electronics.
Alternatively, in the inductive (MapleSim) approach, students start by drawing the schematic, and then simulate it. Then they extract the underlying equations in the software, explore them using different scenarios, and analyze the equations to derive conclusions. The best part of this for students is that they can match it with what they are seeing in their textbooks, as the simulation process they go through is the same as in the textbook.
Traditional tools do have their place,