Tag Archives: inductive reasoning

How I took my most effective notes in school

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The new Ron Joyce building, on the QEW towards Toronto, will house the MBA programme going forward. (B.Comm and PhD business students remain at main Hamilton campus).

The following post was in response to a Wall post by the McMaster University, Michael G. DeGroote School of Business Farcebook group on 19 August, 2010:

What’s the best way to take notes in class?

A) Good ol’ paper and pen
B) Laptop
C) iPad (or other tablet PC)
D) Sound / video recording
E) My brain absorbs everything I need

Since I didn’t seek permission to copy anyone else’s responses, my own response follows:

I found this entirely depends on whether an individual finds audio information easier to digest or visual. It took me until my MBA (McMaster 2003) to realize that my notes were virtually-useless compared to one listening of an audio recording of the day’s lectures later that evening. Even more so, minidisc recordings of my lectures helped me prepare during exam time, because by then, I had lost even more context to interpret written notes. I find myself reading and re-reading texts several times when trying to learn concepts.

One of the keys to making the most of my attention in class and study time before exams was reviewing the course content critically, a few hours after the course, making sure that I had not thought about the content for a few hours–like letting a steak rest after grilling it, before cutting into it–so that my mind wouldn’t feel overwhelmed or lose the “big picture” for the topics.  But just as important as the few hours’ rest was making sure to review the content–if not that night, then the next day, before adding more during the following lecture.  Just allowing my mind to have that rest and reviewing briefly but ensuring I fully understood the content not only drastically improved my performance on examinations, perhaps at least 20% (I never said I was a good student, had good study habits, or any self-discipline during undergrad), but also made preparing for the exams a vastly easier process since that review made it change from virtual re-learning ab initio to actual review before exam.

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When I began emphasizing higher order reasoning and focused on abstracting a general theory, characterizing then internalizing it (critical thinking), then arbitrarily applying the correct one in the correct way to a different situation (synthesis) during my later MBA and now my early PhD (Walden

2013) studies, I eventually combined audio and handwritten notes somewhat. Textbooks still remain quite difficult to learn from, for me. I realize that different people can be anywhere on this audio-visual spectrum, but when I tutor now, I always spend the time and effort to teach students not to look at a problem, recognize it as an _____ problem, and apply a technique, but rather by demonstrating a real-life case, the abstraction to a general case–especially noting any significant corollaries that are like curveballs in reasoning–and then allowing them to “test the waters” to determine the boundaries and characteristics of that generalized theory, to ask them to develop a parallel (but different) theory, showing any corollaries that correlate to the ones I demonstrated and synthesizing application informed by theory. One example of this is first demonstrating the derivation of a Demand curve in economics, interactively establishing what types of factors can shift demand, allowing the student to characterize (probe, test the boundaries) of the theory, and then allowing the student to derive the similar concept of the Supply curve and how and why it can shift.

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The Dark Ages

I should qualify that by noting that I found it quite disappointingly-uncommon to see well-developed critical thinking in most undergraduate students, and even fewer that had good enough understanding of a theory to synthesize application without prompting which theory to apply. This seems indicative of an educational system that teaches only lower-order reasoning, such as demonstrating how changes in, say, money supply, translates to a change in interest rate in various types of economies. This is similar to (drawing analogies is good because it requires the “draw-er” to abstract the essence of an example and find a different example whose essence corresponds well) reading the solution to a calculus problem in a textbook–it always makes sense and seems obvious–because it’s right! But come exam time, students have trouble identifying what a problem really is and even more so, selecting which technique to use to solve it.

Sure, it’s much more challenging, and sure our current, easier system has allowed our economies to grow significantly as more students complete higher education than during my parents’ less-forgiving, more demanding educational system, but at what cost? I have increasingly been helping students–up to third year–with skills as basic as “how to structure an essay” and even basic mathematics.

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Man Harnesses Fire

During my Bio/Biotech undergrad (Carleton, ’99), I was so focused on first-order reasoning–simply learning what factors or what effects without really internalizing and characterizing them through active listening/reading and critical thinking, that I often took “traditional” notes, but kept together in a five-subject coil notebook. When I began my MBA, this worsened into full-colour, colour-coded splendour, using all manner of gel pens. If I lost my pencil case, I would probably have to go to the local high school to ask at the lost and found.  I also recognized that I was a much better audio learner, and I realized if I recorded each lecture on Mini Disc, after letting my brain rest for a few hours, I could reinforce that day by listening to them before bed; preparing for exams became much easier because I knew the material so much better.  Whenever I tried learning a concept from textbooks, such as during undergrad when most of what I learned about any course was necessarily from textbook, I was constantly frustrated because no matter what strategy I tried, I would invariably end up 10 pages ahead of where I last knew, no clue what the pages in between were about, and not sure how I left myself get there.

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Your First Lightbulb Moment

During my MBA, I realized that the notes weren’t the key.  And at the time, I started having a lot of philosophical epiphanies about life that I began to write about, initially on the original Hullabaloo Message Board, although unfortunately, through various restarts (one complete reinstall in summer of 1999 lost a tremendous number of my most philosophical musings) most of those posts have disappeared.  I hope to commit them again, but when you lose a large amount of writing, the thought of writing it all down again feels like something is sucking the lifeforce out of you.  I still lead people through the thought process to their first real epiphany, usually something basic such as how we take what we think we know best for granted and stop critically testing it but just remember we know it from then on.  Consequently, the things we think we know best, we actually know the least.

That “ah hah!” feeling like a lightbulb just went off (went off = turned on) above your head is like becoming aware about being alive for the first time but in a new way.  If you’ve already realized that but have learned the value of triangulating better understanding by still learning other perspectives on something you already know, you can still have a lightbulb moment along with everyone else if you just stop acrimoniously insisting (in your mind) that you already know this and actually think it through, test it, along with everyone else.  You can “realize” it again, or in another way.

That’s how higher order thinking works.  It’s not knowing more facts about a topic.  It’s knowing more about the facts we already know.  Comparing thinking and reasoning to a game of chess, the lowest-order type of reasoning corresponds to memorizing a chessboard: you can explain there are 64 squares on it, alternating colours, and if you spend enough time, you could say what pieces you say where; if you recognize that there are some pieces that are the same and notice patterns like each player has two bishops, and each player’s two are never on the same-coloured square and you get the feeling they must be are a group that behaves similarly, that would be like 1.2-order reasoning.  You can score 100% on a chess exam that asks to show an example of a checkmate if you memorized a board right after some won (puns are good exercises for higher-order reasoning too, but more on that later).  When I was about 10 years old, I was in the library with my mother and sister–the Blossom Park library in South Ottawa, as I recall.  For some reason, I thought it would be impressive if I could show my classmates I memorized a lot of pi, so I got a book on it, sat there, and memorized (more on memorization techniques another time).  The next day I did wow the other nerds when I could recite 105 digits of it.  Most people would have been impressed if I could explain what pi was, what in our lives depends on it, or if I could directly use that information to show them how to draw a regular hexagon, but I couldn’t do that; I could just tell you the numbers (this is a good example I use to teach higher order thinking and basic math–remind me to explain next time!)

I realize that nobody has the attention span or patience to be reading and following me up to this point, so

But back to chess (I don’t have the patience or brains for chess in real life, by the way; I think I joined the chess club in high school only because other friends could play it and it let me avoid having to go outside in the cold Canadian winters)…

If you

. Our society emphasizes and reinforces the idea that “smart” means remembering more facts.  Exams that validate the importance of superficial recollection (questions asking for definitions, fill-in the blank, short-answer, or even math questions that resemble textbook samples) perpetuate society’s value of memorization and provide no incentive to understand better.

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If finding out that what think we know best, we know least was your first real lightbulb moment, here’s an opportunity to be rewarded with an equally-powerful second one.  But after I explain how, you’ve got to stop reading, close your eyes, and don’t take what I say as true.  Test it, think of cases that show it’s true; think of cases that might contradict it.  Watch a situation actually play out in your mind (the second lightbulb moment will be by a third, most likely accompanied by a “knowing” smile, if you keep thinking about it for a few more seconds after this one):

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Arrogance of Science, and Rubiks Cubes

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I have found that modern scientists have a certain arrogance that was not as evident in the past–a sense that “science has arrived,” and “we didn’t know better back then, but we got it right, now.” And it is this feeling that science cannot do wrong now, I believe, more than anything else, that is dangerous. The other day, I heard on CBC radio (Canadian Broadcasting Corporation is Canada’s public broadcaster, and might be compared to NPR, but it also comprises three radio streams and does broadcast content from alternative, contemporary, and classical music to talk radio) the other day that some scientists had begun to think that the greenhouse gases were out of control and that a viable solution would be to build an orbiting solar shield to counter global warming. That is precisely the kind of thinking that I find is absolutely irresponsible that happens across the pure, applied, and social sciences. We see it in medicine when a researcher makes the leap from “low blood levels of X result in Y,” to a drug that raises X and causes all sorts of complications with Z, W, and the other due to complex interactions that were difficult to anticipate given the rigid framework of quantitative methods. We see it in economics when we build increasingly accurate econometric models that are great for explaining what is causing economic crises and then try to operate these models in reverse to fix economies.

Some of the most famous and pivotal scientific developments of our time were once developed by Catholic priests and monks. Some of the most compelling mathematical and engineering developments have been made by devout Muslims in the earlier years of Islam. Yet now, the divide between science and religion has never been greater; indeed, the father of modern genetics can be considered a Catholic priest, Gregor Mendel, who studied heritability in pea plants. Having completed my own degree largely in molecular genetics (although I also extensively studied evolutionary and population genetics) before I had converted to Catholicism, people look at me in amazement and wonder how I can responsibly call myself a Catholic, knowing what I do as a scientist. Still more are shocked that I converted from no religion to Catholicism after completing my degree.

Before beginning my MBA in 2000, I was faced during my GMAT exam with a question pertaining to government funding of the arts, as part of my Analytical Writing Assessment. I cannot, of course, go further into detail about the question since I signed an agreement not to disclose test questions, but at the time I still held the belief that arts, such as literature and visual arts, should be maintained as hobbies, while artists supports their own–and society’s–needs through being a regular employed contriburing member of society. I now see the value of government funding of the arts. I now see the value of what could not be achieved without this freedom. I extend the same belief to science. With increasing funding coming from industry–with its associated expectations to do science that satisfies an intermediate- to short-term business goal–it is vital that the government maintain adequate funding–especially to the pure sciences–such that research without directly obvious commercial application or that runs afoul of current industry wisdom will still be carried out. University research must not be allowed to become an extension of a pharmaceutical R&D lab.

It is interesting how I arrived at that belief through inductive reasoning. I have recently become a huge fan of the Rubiks Cube, and subsequently, all of its larger cousins available commercially, ranging from the 2x2x2 Rubiks Cube to the 7x7x7 V-Cube 7. I have made many discoveries in pure inductive reasoning through it. I often found that traditional logic puzzles have a weakness where any critical thinker can “outsmart” the questions by thinking of exceptions and “what ifs.” Indeed, that might be the *responsibility* of a critical thinker. But reduced to coloured cubelets moving around, the Rubiks-type cube puzzles present to me a pure opportunity to study reasoning, much like Chess is to strategy.

I realize that there exist many algorithms to solve the cube, some of which involve no problem-solving or strategic skills whatsoever, and while I do not find much value in using these mindlessly following steps to solve the cubes, I do now encourage all beginning cubers to learn the simplest beginner methods–which reduce solving the basic 3x3x3 cube to six basic steps, recognizing a simple situation, and repeating a series of repeated moves–in order to be able to solve the cube well enough without thinking that the cuber can begin to focus on watching the behaviours of the cubelets. When I begin teaching someone to DJ or play the piano, for example, it is impossible to learn things like phrasing or articulating motifs while still trying to learn the technical skills; thus, beginners to musical instruments must focus on technique before interpretation. Likewise with cubing, a beginner set of algorithsms helps be able to solve the cube and focus entirely on studying the cubelet movements without being distracted by also thinking how to solve the cube.

But once someone is able to solve the cube in under roughly two minutes, I advise abandoning the beginner method for more intuitive ones. My favourite of these, the Jessica Fridrich method, eschews the initial first- and second-layer algorithms for a set of intiutive steps that complete the first two layers simultaneously.

When one progresses to the 4x4x4 cube (and higher order cubes), they will recognize immediately that the most common general solutions for them are to reduce the cube into a 3x3x3 and solve as usual–all centre cubelets are filled in and move as a single centre, and all edge cubelets between corners are paired and move as a single edge piece. There are issues that can arise in a 5×5 that could not exist in a 4×4 (a 5×5 has a 3×3 centre, whereas a 4×4 has only a 2×2 centre–in order to fill in 5×5 centres, it is necessary to fill in a 2×3 on one face, and a 1×3 on a separate face; then displace a 1×3 line of the 2×3, rotate the face, and return the displaced 1×3 in the empty 1×3 slot). This strategy had to be deveoped because the 4×4 only had two 1×2 slots for centres, whereas the 5×5 has three 1×3 slots.

When generalizing, therefore, is the pattern to fill in centres layer-by-layer, or to fill in two separate halves of a centre and join them? That is also not evident yet because the 5×5 does not have enough layers to abstract that information.

Moving onto the 6x6x6 cube (which has a 4×4 centre), it is readily apparent that the way to fill in centres is buiding two separate 2×4 segments and merging them because once a 3×4 block is created, attempts to displace and replace a1×4 block will disrupt the portion of the block between the middle of the cube and the second layer. Moving onto the 7×7, new challenges to the approach that worked so well for the 4×4, 5×5, and 6×6 come into view that could not exist because of the fewer layers in previous cubes.

But all other strategies and algorithms remain the same as lower-order cubes.

It is that elegance, beauty, and simplicity, the complexity, that I have come to appreciate from cubing. And the process of abstracting generalizations that apply to all (n-layer) cubes that I learned by developing strategies for solving (n-1)-, (n-2)-, and (n-3)-layer cubes, for example.

The same inductive reasoning do we strive for in qualitative research designs.