Conceptual Learning and HOTS Testing

 I am in the unenviable situation of having to explain the heading of a blog post ... here I go.

To explain the first, I would go to Henry Bethe, son of Hans Bethe, physics Nobel Laureate. As Henry tells it, once when Richard, (“Uncle Dick” to Henry) visited his father at his house (when Henry had not reached double digit age), they may have shot the breeze for a while before the chief guest for the evening came. Richard told Henry that there are twice as many numbers as there are numbers! Totally stumped, Henry was.

So, Richard started a game with Henry – “Give me any number.” Henry did. Promptly Richard said, “Twice that number.” This went on a couple of more times and roles reversed. The child caught on to what Richard said at the beginning, that there can never be the greatest number. It need not be twice; it could have been any number of times! The concept of infinity and the teaching are conceptual!

On HOTS, it will not be quite so easy for me to explain, but I will try. The acronym “HOTS” expands to Higher Order Thinking Skills. CBSE says that skills beyond memorization and rote reproduction are to be tested. Per my understanding, context plays the primary role in this segment of testing.

In a course on design of steel structures, one of the questions was “What is a crane?” Besides being downright trivial and not worthy of a HOTS type of question, the response carries a heavy load of ambiguity – “A crane is a bird with long legs and a long beak.” Would the student get credit for it?

This can be taken to almost any level, but then this narrative might encroach upon specialist disciplines. Hence, I demur, but the point has been made.

Context defines the content. This is the characteristic of a HOTS question.

What is the level difference, if any, between conceptual learning and responding appropriately to a HOTS question?

In my humble opinion, conceptual learning must lead one deeper and deeper, but not down the rabbit hole! There is an element of judgement here.

Let us go again to Richard Feynman. He was asked by a colleague why Leptons have non-integer spin value whereas Bosons have integer spin value. Feynman said he would come back in two days. After two days, sure enough, Feynman’s colleague demanded an answer. That is when Feynman said – I paraphrase – “I have decided that I do not understand because I cannot explain the phenomena to a first year student.” Feynman was one of the great minds that tried to explain Quantum Electrodynamics, QED! That is conceptual understanding for college students just as Feynman’s reaching back to numbers to explain the concept of infinity to a pre-teenager.

Answers to HOTS questions, should they be at the higher level of comprehension – higher order and hence higher level of probing? The nametag says, yes. This is a misunderstanding.

One must still did deeper and perhaps ensnare heuristics along the way – a kind of cross-fertilization. Here I do need to give a specific example.

A lifeguard on a beach is looking at the water and finds a swimmer waving for help, perhaps water is deeper than the swimmer had reckoned. The lifeguard has to traverse sand and also swim through water to reach the distressed swimmer.

The quickest path is to shorten the length of the swim and make the traverse on the sand to something longer. Why? Running on the sand is faster than swimming in the sea.

This is precisely what a ray of light does as it changes the medium, say from air to glass! Light is faster in air than in glass, and our high school physics shows how to find this out. This is not a higher level of thinking, quite basic as it is. The process has diverged from the depths of concepts very early and has taken a nearby path. Heuristic has helped in the process. This is an example of HOTS learning.

I am sure people dedicated to teaching would find numerous such examples in their domain.

I conclude then, conceptual learning helps in answering HOTS question by taking the help of heuristics. It is for the teacher to inculcate this habit in the students, given the time.

Raghuram Ekambarm