“Much knowledge does not teach wisdom.”
Heraclitus (c. 540 – 480 B.C.)
Piaget (1968) coined the term figurative knowledge to refer to knowledge that can be gained without understanding and the term operative knowledge to refer to knowledge based on understanding. Another way of putting this is that figurative is knowledge about the static world (e.g., Paris is the capital of France) and operative knowledge is knowledge about the how and why – that is, the dynamic properties of things in the world and the ways in which they can be understood, manipulated or acted upon. The distinction between figurative and operative knowledge is vitally important.
We certainly do not need, nor are we able, to understand everything we know. Yet it is easy to assume that knowing and understanding somehow always go together. In fact, we can know a lot without understanding much – or any – of it. Knowledge, is necessary but not sufficient for understanding. To illustrate how easy it is to learn without requiring any understanding at all, try the following two quizzes:
Quiz #1: The Nonk
Alpha-woopies enter the dinglefog through the weezer and then pass through the chamber of doyobongos, the twinklebin and finally through the umpendoopster, the three major structures of the dinglefog. Alpha-woopies then womp onto the rooter, which is made up of two types of alpha-woopie receptors: qwonks and ponks. Ponks are most sensitive to fevons, while qwonks are sensitive to weekeens and deekeens. The greatest concentration of ponks is in the splunch. In the Nonk, qwonks and ponks turn alpha-woopie energy into impulses sent, via the fizzer, to the bozo organ where they are qaumilated first by the weezapop granulator and then by the yololator.
Please answer the following questions:
1. What are qwonks and ponks?
2. Where are ponks most highly concentrated?
3. In what order do alpha-woopies pass through the major structures of the dinglefog?
4. Where are impulses sent to the bozo organ quamilated?
Quiz #2: Our Pal The Eye
Light rays enter the eye through the cornea and then pass through the aqueous humor, the iris and finally through the lens, the three major structures of the eye. Light rays then project onto the retina which is made up of two types of photo receptors: rods and cones. Cones are most sensitive to colors, while rods are sensitive to light and dark. The greatest concentration of cones is in the fovea. Rods and cones turn light energy into nerve impulses sent, via the optic nerve, to the brain where they are processed first by the lateral geniculate nuclei and then by the occipital lobe
Please answer the following questions:
1. What are rods and cones?
2. Where are cones most highly concentrated?
3. In what order do light rays pass through the major structures of the eye?
4. Where are nerve impulses from the eye processed in the brain?
1. Qwonks and ponks are alpha-woopie receptors located in the rooter.
2. Ponks are most highly concentrated in the splunch.
3. Alpha-woopies enter the dinglefog through the weezer and then pass through the chamber of doyos, the twinklebin and finally through the umpendoopster.
4. Impulses sent to the bozo organ are quamilated first by the weezapop granulator and then by the yoyolator.
1. Rods and cones are photo-receptors, located in the retina.
2. Cones are most highly concentrated in the fovea.
3. Light rays enter the eye through the cornea and then pass through the aqueous humor, the iris and finally through the lens.
4. Nerve impulses sent to the brain are processed first by the lateral geniculate nuclei and then by the occipital lobe.
It is likely that you think you understood something after completing Quiz #2 because “Our Pal, the Eye” pertains to something real and familiar; however, that sense of understanding is illusory: note that you can answer each of the questions on both “The Eye” and “The Nonk” correctly without understanding anything at all! Further, even though Quiz #1 is utter gibberish, it should look familiar, not only because it an exact copy of the Quiz #2 (with only key nouns and verbs changed), but because both typify the kind of exercises that are relied on all too frequently in education; namely, learning exercises that put too much emphasis on increasing (and easily “evaluating”) learner knowledge (i.e., figurative knowledge) and not enough on learner understanding (i.e., operative knowledge).
From a self-mentoring persepctive, consider the following:
- We know far more than we understand
- It is far easier to gain knowledge than understanding
- Never confuse knowledge for understanding (often easier said than done…)
- When learning on your own or teaching others, bear in mind the above, and carefully reflect on what needs simply to be known and what needs to be understood – remember, an ounce of understanding is often worth a pound of knowledge
Refrence: Piaget, J. (1968). Genetic Epistemology. Columbia University Press: New York.