The Tinkering Thinker

Recently, I helped to give two workshops at Universidad del Turabo in Puerto Rico on the use of personal instrumentation (e.g. Digilent’s Analog Discovery, National Instruments myDAQ and their version of Analog Discovery 2, Analog Devices ADALM 1000 …) in the teaching of circuits and electronics. In attendance were great people from all of the engineering schools on the island. They were really engaged and asked wonderful questions, even though several were uncomfortable working exclusively in English.

One of the best questions I was asked has helped me to formulate what is, I hope, a very productive way of framing the discussion of how best to educate engineers. I was trying to make the case for Experiment Centric Pedagogy (ECP), for which the guiding hypothesis is that students and instructors are more motivated and engaged and engineering education works best in a learning environment where experimentation plays a central role. This is in contrast to  the traditional STEM classroom: the lecture hall, occasionally augmented with separate labs provided as expensive limited access facilities permit.

Engineers must tinker with ideas but, unfortunately, modern technology is so complex that tinkering has generally become too difficult. (There is an excellent article on the early days of the Mobile Studio Project in the Sept 24, 2007 issue of EETimes on this topic.) Those of us old enough to have developed our interests in electronics and electrical phenomena in the 1950’s were lucky enough to work mostly with discrete components (tubes!) which allowed for a lot of tinkering and shocks and burns.

The question raised at the Turabo workshop had to do with Thinking vs Tinkering. Traditional, lecture-based instruction requires students and instructors to think their way through a subject and the questioner was concerned that student tinkering may just be a trial and error effort to find an approach that involves little or no thinking. I certainly agree that I have, for example, seen students randomly make a bunch of attempts with a spreadsheet to solve a problem without really learning what they did and why it worked. The best scenario is that they know how to repeat what they did in the same way that the work their way through a video game. However, in spite of what often happens, tinkering and thinking are not exclusive activities.

Let’s look at tinkering a little differently and ask the following questions: Can we get a tinkerer to think or can we get a thinker to tinker and which is better? That is, should our students be Thinking Tinkerers or Tinkering Thinkers? From the title of this posting, it should be obvious what I think. It is also what nearly everyone I know says (so far anyway) when I ask them to choose. Whether or not we recognize that we are asking our students to apply the scientific method, we all work hard to get our students to predict what is going to happen (hypothesis) before they do an experiment (testing). Again, what we see too often is students cranking through a task list without stopping to think about what they are doing and why. That is why thinking comes first and we have the Tinkering Thinker.

Voltage Divider Circuit (Wikipedia) & Breadboard Version ( 

An example of ECP: One of the most ubiquitous and useful circuits is the voltage divider, which I will use to show an example of ECP in action. The goal of ECP is to think our way through the process of understanding how a particular circuit works by tinkering with it both experimentally and using simulation. The process could be shown as a flow chart, but I would rather keep it more informal than that.

  1. What is a voltage divider? Look it up on Wikipedia or in a textbook. The former approach seems like the most common these days. It is also very often possible to find good videos on topics like this. I have done a bunch on the voltage divider … more on that at the end of this example.
    1. From available information, find the circuit Diagram and what it looks like when it is built? The two figures above show examples of each.
    2. What is the formula that characterizes its operation? A common question because the first thing needed is how is it analyzed or how do we use it?  In the Wikipedia, the relationship between the output and input voltages is given as  V_\mathrm{out} = \frac{R_2}{R_1+R_2} \cdot V_\mathrm{in}
  2. Build one and see what it does? Before doing any analysis, build one and try it.
    1. It has to be built correctly and data collected correctly, so some basic experimental skills are necessary. Build the circuit … connect the sinusoidal voltage source (aka function generator) … measure accurately both the input and output voltages. It is almost always necessary to measure both.
    2. How do measurements compare with the ideal formula? Are there any data features that do not agree with formula? Is the formula general enough? What happens when we add a load? What happens if it works well with 1kΩ resistors but not if it is made with 1MΩ resistors?
  3. Simulations do not show noise unless it is specifically added. Simulations are usually more ideal than experiments. Simulate it to see if there are any things left out in the ideal formula? This can be done with any version of the SPICE program. LT-Spice from Linear Systems, is a good choice because it is free.
    1. When this is done, it is seen that the simple divider seems OK. Maybe this verifies that simulation is being done properly in addition to showing us what the voltage divider does in an ideal world.
    2. Voltage dividers have no purpose unless we connect something to them to read the output voltage. Does adding a load affect its operation? It should be observed that loading does make the divider work differently, just as it did experimentally, except without the noise.
  4. Go back to the basic reference used and see how the formula is derived. What are the assumptions? Are any violated with loading?
    1. Basic analysis is based on Ohm’s Law and that the current in both resistors is the same (the resistors are in series). This is clearly not the case with a load, but, if the load resistance is 100 times R2, it will have no noticeable impact on the operation of the circuit.
    2. Analysis with load — eureka! Since adding the load resistor does not really make the analysis much more difficult (R2 is replaced by the parallel combination of R2 and the load resistor), a new formula can be derived that does a very good job of predicting the output voltage.
  5. Go back to the experiment and look at non-ideal characteristics that occur with different resistances, voltage levels, frequency, etc. Determine the limits for application of the ideal model. This and the preceding steps are addressed in a series of videos I made for my Electronic Instrumentation class. Watch the first three videos for the topics addressed here: 

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