What Is Research?

February 23, 2009

Doing it oneself versus spoonfeeding

In previous posts titled knowledge matters and intuition in research, I argued that building good intuition and skill for research requires a strong knowledge and experience base. In this post, I’m going to talk about a related theme, which is also one of my pet themes: my rant at the misconception that doing things on one’s own is important for success.

The belief that I’m attacking

It is believed in certain circles, particularly among academics, that doing things by oneself, working out details on one’s own, rather than looking them up or asking others, is a necessary step towards developing proper understanding and skills.

One guise that this belief takes is a skew of learning paradigms that go under names such as “experiential learning”, “inquiry-based learning”, “exploratory learning”, and the like. Of course, each of these learning paradigms is complex, and the paradigms differ from each other. Further, each paradigm is implemented in a variety of different ways. My limited experience with these paradigms indicates that there is a core belief common to the paradigms (I may be wrong here) which is that it is important for people to do things by themselves rather than have these things told to them by others. An extreme believer of this kind may consider with disdain the idea of simply following or reading what others, but a more moderate and mainstream stance might be that working things out for oneself, rather than following what others have done, is generally preferable, and following others is a kind of imperfect substitute that we nonetheless often need to accept because of constraints of time.

Another closely related theme is the fact that exploratory and inquiry-based methods focus more on skills and approaches rather than knowledge. This might be related to the general view of knowledge as something inferior, or less important, than skill, attitude, and approach. Which is why, in certain circles, the person who “is smart” and “thinks sharply” is considered inferior to the person who merely “knows a lot”. This page, for instance, talks about how inquiry-based learning differs from the traditional knowledge-based approach to learning because it focuses more on “information-processing skills” and “problem-solving skills”. (Note: I discovered the page via a Google search a few months back, and am not certain about how mainstream its descriptions are). (Also note: I’ve discussed more about this later in the post, where I point out other sides of this issue).

Closely related to the theme of exploration and skills-more-than-knowledge is the theme of minimal guidance. In this view, guidance from others should be minimal, and students should discover things their own way. There are many who argue both for and against such positions. For instance, a paper (Kirschner, Sweller, and Clark) that I discovered via Wikipedia argues why minimally guided instruction does not work. Nonetheless, there seems to be a general treatment of exploration, self-discovery, and skills-over-knowledge as “feel-good” things.

Partial truth to the importance of exploration

As an in-the-wings researcher (I am currently pursuing a doctoral degree in mathematics) I definitely understand the importance of exploration. I have personally done a lot of exploration, much of it to fill minor knowledge gaps or raise interesting but not-too-deep questions. And some of my exploration has led to interesting and difficult questions. For instance, I came up with a notion of extensible automorphism for groups and made a conjecture that every extensible automorphism is inner. The original motivation behind the conjecture was a direction of exploration that turned out to have little to do with the partial resolution that I have achieved on the problem. (With ideas and guidance from many others including Isaacs, Ramanan, Alperin, and Glauberman, I’ve proved that for finite groups, any finite-extensible automorphism is class-preserving, and any extensible automorphism sends subgroups to conjugate subgroups). And I’ve also had ideas that have led to other questions (most of which were easy to solve, while some are still unsolved) and others that have led to structures that might just be of use.

In other words, I’m no stranger to exploration in a mathematical context. Nor is my exploratory attitude strictly restricted to group theory. I take a strongly exploratory attitude to many of the things I learn, including things that are probably of little research relevance to me. Nor am I singularly unique in this respect. Most successful researchers and learners that I’ve had the opportunity to interact with are seasoned explorers. While different people have different exploration styles, there are few who resist the very idea of exploration. Frankly, there would be little research or innovation (whether academic or commercial) if people didn’t have an exploratory mindset.

So I’m all for encouraging exploration. So what am I really against? The idea that, in general, people are better off trying to figure things out for themselves rather than refer to existing solutions or existing approaches. Most of the exploration that I’ve talked about here isn’t exploration undertaken because of ignorance of existing methods — it is exploration that builds upon a fairly comprehensive knowledge and understanding of existing approaches. What I’m questioning is the wisdom of the idea that by forcing people to work out and explore solutions to basic problems while depriving them of existing resources that solve those problems, we can impart problem-solving and information-processing skills that would otherwise be hard to come by.

Another partial truth: when deprivation helps

Depriving people of key bits of knowledge can help in certain cases. These are situations where certain mental connections need to be formed, and these connections are best formed when the person works through the problem himself or herself, and makes the key connection. In these cases, simply being told the connection may not provide enough shock value, insight value, richness or depth for the connection to be made firmly.

The typical example is the insight puzzle. By insight puzzle, I mean a puzzle whose solutions relies on a novel way of interpreting something that already exists. Here, simply telling the learner to “think out of the box” doesn’t help the learner solve the insight puzzle. However, if a situation where a similar insight is used is presented shortly before administering the puzzle, the learner has a high chance of solving the puzzle.

The research on insight puzzles reveals, however, that in order to maximize the chances of the learner getting it, the similar insight should be presented in a way that forces the learner to have the insight by himself/herself. In other words, the learner should be forced to “think through” the matter before seeing the problem. The classic example of this is a puzzle that involves a second use of the word “marry” — a clergyman or priest marrying a couple. One group of people were presented, before the puzzle, with a passage that involved a clergyman marrying couples. Very few people in this group got the solution. Another group of people were presented a similar passage, except that this passage changed the order of sentences so that the reader had to pause to confront the two meanings of “marry”. People in this second group scored better on the test because they had to reflect upon the problem.

There are a couple of points I’d like to note here. That depriving people of some key ingredients forces them to reflect and helps form better mental connections is true. But equally important is the fact that they are presented with enough of the other ingredients in a manner that the insight represents a small and feasible step. Secondly, such careful stimulation requires a lot of art, thought, and setup, and is a far cry from setting people “free to explore”.

When to think and when to look

Learners generally need to make a trade-off between “looking up” answers and “thinking about them”. How this trade-off is made depends on a number of factors, including the quality of insight that the looked-up answer provides, the quality of insight that learners derive from thinking about problems, the time at the learner’s disposal, the learner’s ultimate goals, and many others. In my experience, seasoned learners of a topic are best able to make these trade-offs themselves and determine when to look and when to struggle. Thus, even if deprivation is helpful, external deprivation (in the sense of not providing information about places where they can look up answers) does not usually make sense. There are two broad exceptions.

The first is for novice learners. Novice learners, when they see a new problem, rarely understand enough about their own level of knowledge to know how long they should try the problem, what kind of place to look up if any, and what the relative advantages of either approach are. By “novice learner” I do not mean to suggest a general description of a person. Everybody is a novice learner in a topic they pick up for the first time. It is true that some people are better in general as learners in certain broad areas — for instance, I’d be a better learner of mathematical subjects than most people, including mathematical subjects I have never dealt with. However, beyond a slight headstart, everybody goes through the “novice learner” phase for a new field.

For novice learners, helpful hints on what things they should try themselves, how long they should try those things, and how to judge and build intuition, are important. As such, I think that these hints need to be made much better in quality than they typically are. The hint to a learner should help the learner get an idea about the difficulty level in trying the problem, the importance of “knowing” the solution at the end, the relative importance of reflecting upon and understanding the problem, and whether there are some insights that can only be obtained by working through the problem (or, conversely, whether there are some insights that can only be obtained by looking at the solution). Here, the role of the problem-provider (who may be an instructor, coach, or a passive agent such as a textbook, monograph, or video lecture series) is to provide input that helps the learner decide rather than to take the decision-making reins.

A second powerful argument is for learners whose personality and circumstances require “external disciplining” and “external motivation”. The argument here is essentially a “time inconsistency” argument — the learner would ideally like to work through the problem himself or herself, but when it comes to actually doing the problem, the learner feels lazy, and may succumb to simply looking up the solution somewhere. (“Time inconsistency” is a technical term used in decision theory and behavioral economics). Forcing learners to actually do the problems by themselves, and disciplining them by not providing them easy access to solutions, helps them meet their long-term goals and overcome their short-term laziness.

I’m not sure how powerful the time inconsistency argument is. Prima facie evidence of it seems huge, particularly in schools and colleges, where students often choose to take heavy courseloads and somehow wade through a huge pile of homework, and yet rarely do extra work voluntarily on a smaller scale (such as starred homework problems, or challenging exercises) even when the load on them is low. This fits the theory that, in the long haul, these students want to push themselves, but in the short run, they are lazy.

I think the biggest argument against the time inconsistency justification for depriving people of solutions is the fact that the most clear cases of success (again in my experience) are people who are not time inconsistent. The best explorers are people who explore regardless of whether they’re forced to do so, and who, when presented with a new topic, try to develop a sufficiently strong grasp so that they can make their own decisions of how to balance looking up with trying on their own.

Yet another argument is that laziness works against all kinds of work, including the work of reading and following existing solutions. In general, what laziness does is to make people avoid learning things if it takes too much effort. Students who decide not to solve a particular problem by themselves often also don’t “look up” the solution. Thus, in the net, they never learn the solution. Thus, even in cases where trying a problem by oneself is superior to looking it up, looking it up may still be superior to the third alternative: never learning the solution.

A more careful look at what can be done

It seems to me that providing people information that helps them decide which problems to work with and how long to try before looking up is good in practically all circumstances. It’s even better if people are provided tools that help them reflect and consolidate insights from existing problems, and if these insights are strengthened through cross-referencing from later problems. Since not every teaching resource does this, and since exploration at the cutting edge is by definition into unknown and poorly understood material, it is also important to teach learners the subject-specific skills that help them make these decisions better.

Of course, the specifics vary from subject to subject, and there is no good general-purpose learner for everything. But simply making learners and teachers aware of the importance of such skills may have a positive impact on how quickly the learners pick such skills.

Another look at exploratory learning

In the beginning, I talked about what seems to be a core premise of exploratory learning — that learners do things best when they explore by themselves. Strictly speaking, this isn’t treated as a canonical rule by pioneers of exploratory learning. In fact, I suspect that the successful executions of exploratory learning succeed precisely because they identity the things where learners investing their time through exploration yields the most benefit.

For instance, the implementation of inquiry-based learning (IBL) in some undergraduate math classes at the University of Chicago results in a far from laissez faire attitude towards student exploring things. The IBL courses seem, in fact, to be a lot more structured and rigid than non-IBL courses. Students are given a sheet of the theorems, axioms and definitions of the course, and they need to prove all the theorems. This does fit in partly with the “deprivation” idea — that students have to prove the theorems by themselves, even though proofs already exist. On the other hand, it is far from letting students explore freely.

It seems to me that while IBL as implemented in this fashion may be very successful in getting people to understand and critique the nature and structure of mathematical proofs, it is unlikely to offer significant advantages in terms of the ability to do novel exploration. That’s because, as my experience suggests, creative and new exploration usually requires immersion in a huge amount of knowledge, and this particular implementation of IBL trades off a lot of knowledge for a more thorough understanding of less knowledge.

Spoonfeeding, ego, and confidence issues

Yet another argument for letting people solve problems by themselves is that it boots their “confidence” in the subject, making them more emotionally inclined to learn. On the other hand, spoonfeeding and telling them solutions makes them feel like dumb creatures being force-fed.

In this view, telling solutions to people deprives them of the “pleasure” of working through problems by themselves, a permanent deprivation.

I think there may be some truth to this view, but it is very limited. First, the total number of problems to try is so huge that depriving people of the “pleasure” of figuring out a few for themselves has practically no effect on the number of problems they can try. Of course, part of the challenge is to make this huge stream of problems readily available to people who want to try them, without overwhelming them. Second, the “anti-spoonfeeding” argument elevates an issue of acquiring subject-matter skills to an issue of pleasing learners emotionally.

Most importantly, though, it goes against the grain of teaching people humility. Part of being a good learner is being a humble learner, and part of that involves being able to read and follow what others have done, and to realize that most of that is stuff one couldn’t have done oneself, or that would have taken a long time to do oneself. Such humility is accompanied by pride at the fact that one’s knowledge is built on the efforts of the many who came before. To use a quote attributed to Newton, “If I have seen so much, it is because I stand on the shoulder of giants.”

Of course, a learner cannot acquire such humility if he or she never attempts to solve a problem alone, but a learner cannot acquire it if he or she simply tries to solve problems rather than ask others or use references to learn solutions. It’s good for learners to try a lot of simpler problems that they get, and thus boost confidence in their learning, but it is also important that for hard problems, learners absorb the solutions of others and make them their own.

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2 Comments »

  1. I would like to cite your blog as a source in a college essay, what is your name so I know who I should give credit to? Thank you!

    Comment by Joshua Barton — September 22, 2010 @ 10:34 pm

  2. Dear Joshua,

    My name is Vipul Naik.

    I don’t know if this blog post would be considered a respectable source to cite for a college essay, but I’ll let you be the judge of that.

    Comment by vipulnaik — September 22, 2010 @ 10:38 pm


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