The limits of ‘discovery learning’

“Discovery learning” is great, except when it’s ineffective, says Reform K12.

The discovery learning method is a way for teachers to allow the child to discover things for himself or herself, because when a child makes the discovery, the learning is much deeper and more likely to be remembered. That spark of “Eureka” or “I have found it!” is what kindles the true flame of learning.

Actually, we don’t disagree, it’s just we have a better proposal: Teach! Students will learn a lot more in less time.

Just so there’s no misunderstanding, we fully support the responsible use of guided discovery in the classroom. Master teachers have known this for years.

What we don’t support is the abandonment of direct instruction, especially for some key concepts and techniques which must be taught.

For example, in the University of Chicago’s Everyday Math program, they don’t recommend teaching children the long division algorithm, saying “let the children discover a division algorithm for themselves.” (The program also embraces calculator use starting with Kindergarten, so we bet we know which “algorithm” the kids would pick!)

We were fully grown before we understood completely how the long division algorithm works, so we’d place the chances at our discovering it in childhood, oh, at about zero.

Isaac Newton said, “If I have seen further, it is because I stood on the shoulders of giants.”

Good thing Newton didn’t have teachers enamored with the discovery learning method, or he would have been relegated to standing next to the aforementioned giants.

The California Curriculum Commission is urging the state ed board to not to buy K-8 science books that rely heavily on “hands-on” materials.

Thomas Adams, executive director of the curriculum commission, said critics are misrepresenting the panel’s views. He said commission members are trying to balance the need for a comprehensive science curriculum with the limited science background of many K-8 teachers. Twenty to 25 percent of hands-on instruction seemed like “the most reasonable amount of time for someone faced with the challenges of limited facilities and limited time,” he said.

Kimberly Swygert says too much lab work can become busy work. Smart teachers call it “hands on, brain off.”

About Joanne


  1. I’ve always preferred the prima donna version: “if have seen further than others, it’s because I’m surrounded by midgets”.

  2. At the University of Oregon, I successfully used discovery learning to teach graduate students the history of the Chinese language(s – but I’ll defer to the standard usage here). I gave them actual data from various time periods to analyze in lieu of telling them what was going on in the language during those periods. By the end of the course they were able to reconstruct the pronunciations of words from 3,000 years ago. However, this only worked because:

    (1) This was not pure discovery learning. Methods were imparted using direct instruction. Dumping data without methodological grounding would have been useless.

    (2) The students were a small, highly dedicated group of graduate students and one senior. The talent and work ethic of these students was truly amazing.

    Since then, I have used discovery learning from time to time with advanced students, but I mostly stick to direct instruction. Discovery learning is a useful tool, but it’s just one tool, and no one tool suits all.

  3. I wonder if the University of Chicago is gung-ho on admitting students who have learned their mathematics through discovery on their own. (Or have been calculator dependent since Kindergarten for everything from calculating their allowances, tips in restaurants and book books fees at whatever institutions of higher learning they may be able to enter…)

  4. Discovery learning is great, but incredibly impractical. I would rather teach my kids about the red burner being a bad thing to touch then having them make the ‘Eureka!’ discovery themselves. The same goes for the smell of gas in the house or sticking a screwdriver into a socket. I prefer to let them use existing technologies such as the wheel without requiring them to discover it themselves.

    Discovering something that everyone else knows is not that big a deal. Sounds like the teachers got tired of doing their job and decided to let the kids teach themselves.

  5. I have a PhD in genetics, so I took a lot of science courses in college. One of the most frustrating things that you could encounter was having the lab section get ahead of the lecture section, because you went into the lab trying to design an experiment when you had no idea what was going on. Lab work seems to work best when you have a grasp of the concepts being tested (ie you are taught the concepts and then test/implement them in the lab). When the science concepts being used in the experiments aren’t fully understood, it is not easy to understand how the data points fit with the theory. Once the theory is understood, though, students can look at the data and see how it does or does not follow the expected pattern. Even doing real research in the lab, you still try to read everything possible and discuss your ideas to get practical feedback on both the concepts and technical aspects of the experiment before beginning.

  6. Somehow I think Reform K12 is misrepresenting the University of Chicago’s Everyday Math program… I highly doubt they recommend not teaching long division,
    saying “let the children discover a division algorithm for themselves.” Utter nonsense. There is a lot of middle ground between forcing kids to rotely memorize algorithms
    and telling them nothing and having them flounder…
    For discovery learning to be effective… it must be GUIDED…
    I think the author misrepresents discovery learning when he implies that the students are left to their own devices unguided…

    I’ve mentioned this example before… I spent some time observing a charter elementary school in Boston… the teachers had a real innovative way of getting the kids to “discover” carrying and borrowing in addition and subtraction… they played this game (I don’t recall all the details) where the students had bronze, silver, and gold chips in 3 piles in front of them… 5 bronze = 1 silver, 5 silver = 1 gold… the rules were that they could not have more than 4 bronze or 4 silver at any one time…
    (obviously, you should recognize the connection to money here)… if a student had too many bronze, they had to trade up to silver (the equivalent of “carrying-over”)… if they needed 3 silver, and they only had 1, they had to convert one gold to 5 silver (the equivalent of “borrowing” in subtraction)…

    they played this game a number of times before the students ever were officially taught addition and subtraction with multidigit numbers….

    i got to see the process from beginning to end over a couple weeks, and was amazed by the results… the students really did have an intuiutive, gut understanding for addition and subtraction… far better than if they were told to memorize a given algorithm…

    the key was that the discovery learning was GUIDED.

  7. My son’s school uses Everyday Math and they seem to have taught him the long division algorithm somewhere along the way — and he actually understands the concept pretty well, too!

    The cited author says he/she was “fully grown before we understood completely how the long division algorithm works” — in which case, what was gained by not using a calculator? If it’s just rote computation without computation, then it hardly matters what form it takes. I suppose (A) perhaps the intention of using the phrase ‘understood *completely*’ is to suggest that he/she had partial understanding before.
    (B) Maybe what matters more than the method of computation is whether one understands the RESULT — what it means to divide one number by another, what a reasonable answer or approximation might be, etc. If you make a mistake
    in the long division (or with the calculator), then you can catch it.

  8. Independant George says:

    Don’t know much about the ‘Everyday Math Program’, but we did a combination of discovery learning & direct instruction in freshman calc when I was at Chicago. Got the basic rules down, then were told to prove various theorems using what we learned. With econ & science classes, it was a little different – the intro sequences were 80% direct/20%discovery, the upper-level classes were around 50/50. Always seemed the proper way to go.

    Calculators were generally allowed, but seldom used for anything other than basic calculations. Since we only got full credit if we showed all our work, calculator use could actually lower a grade.

    Of course, I always harbored suspicions about that Marine Biology class that featured a weeklong trip to Jamaica for “field research.”

  9. oops, when I typed:
    “If it’s just rote computation without computation…”
    above, I meant to say
    “If it’s just rote computation without comprehension…”
    which makes at least a little more sense.

  10. The Washington Post had an article on Virginia’s 2003 Teacher of the Year not long ago [Nov 6, p VA03] in which a reporter sat in on a classroom “Discovery Learning” lesson. The students rolled cans down ramps to see what properties affected their motion. (Size, weight, etc.)

    Here’s an excerpt from the article:
    The end result was that several of the students reached the correct conclusion — it’s the weight, not the size of an object, that determines its speed.
    “She fascinates me,” said Ronald Velez, 10, one of the first students to figure out that the lighter the contents in the can, the faster it will go (beef broth defeated the beans). “She can always give me a science fact, and she always helps me out when I have questions.”

    In fact, that’s *not* the correct answer – and it demonstrates quite vividly the problem with “Discovery Learning.” Had they learned this through a textbook first, they (and the teacher!!) might have thought to see if there was a different explanation for their results – for example, that the beans have to rotate with the can and the broth, being much less viscous, does not.

    Also, please don’t forget that it has taken us 450 years or so of very accomplished scientists (and, in some cases, difficult or expensive experiments) to get us to our present understanding of physics. Most students can’t expect to live that long.

  11. Mrs. du Toit says:

    Discovery learning looked good on paper, but didn’t work in practice. Modifying it to Student Directed Learning works great–allowing the child (or adult learner) some flexibility in what is learned when. They can decide if they want to tackle the subject superficially, or if they want to delve into it.

    Trying to teach a kid about something they have no interest in is nearly impossible (and is a waste of time), but floating choices and having the student pick one, or sticking with something until they’ve mastered it, is terrific.

    I think much of Discovery Learning was a method to obscure how badly most things were taught. If the kid got part way into something and didn’t want to do it anymore, the educator could use the excuse that the student chose something else–or there were peripheral exercises and hands-on tasks that allowed everyone to fool themselves into thinking the kid was studying geography, not fingerpainting map outlines. In actual fact, the student got into it and found it as boring and tedious as anything else.

  12. “The end result was that several of the students reached the correct conclusion — it’s the weight, not the size of an object, that determines its speed.”

    Aristotle would be proud. Unbelievable! This completely false belief was held throughout the middle ages, because no one bothered to look and see, and was disproved several hundred years ago.

  13. I just checked the WP article on the above, and they had a correction published…it may possibly be that the misunderstanding about weight was that of the WP reporter rather than the teacher…I hope so, anyway.

  14. We now know Archemedes had (to a great extent) discovered the calculus. Newton did not know that. Where would math and science be today if he had not had to discover it himself, but had gone on from there?

  15. I can help but reply to the rolling can. I doubt the teacher or report “got it” There is such a “thing” called angular momentum + translational momentum invovled here. The radius of the can has a bearing on the results (angular torque, moment of inertia) as well as the placement of the mass inside the can. Was the can shaken before rolling? Was it allowled to settle on the bottom (side on the ramp) before rolling or on the acutal side of the can and then placed on the ramp and rolled? This would affect the angular momentum of the can quite a bit. Get two, equal in radius disks. One is solid wood, metal what ever and the other is constructed like a hoop. The disks are equal in radius, and mass. Roll them both at the same time on a ramp and watch the results. Not what you expect.
    If the students where experimenting by predicting, analyzing data, revising their predictions, making conclusons, getting peer review then they were doing science. Otherwise they were rolling cans down a ramp, and their high school physics teacher will have to unteach what they have learned.

  16. The “heavier cans rolled faster” actually means that the ones with the largest ratio of angular moment to mass rolled slower. That is, most of the weight of the can is at the rim, where it has the most impact on angular momentum. So an empty can would roll slowest, a can with a light load faster, the can with the heaviest load the fastest.

    This could change if the load can slosh around inside.

  17. “The radius of the can has a bearing on the results”

    You might want to double check that….

  18. “…most of the weight of the can is at the rim, where it has the most impact on angular momentum. So an empty can would roll slowest, a can with a light load faster, the can with the heaviest load the fastest.”

    True; but for most cans of foodstuffs, the mass at the rim is a small fraction of the mass of the full can.

    In this particular experiment, the beans were viscous, so they rotated with the can: more energy went into rotational motion. The soup was thin, so it didn’t all rotate with the can: less energy went into rotational motion (some of the soup was only undergoing translational motion).

    For the scientifically inclined: Which would roll faster: a can full of water, or a can full of carbonated water?

  19. Tim, I don’t know, but shake it and poke a tiny hole in one end and it will sure slide faster than a can can roll. 😉

  20. My children have been suffering through Chicago Math and it is awful. Sometimes, you just need to know how to get the correct answer. The algorithms Chicago Math teaches for division are IMHO extremely confusing, especially for brighter students who don’t really want to take the longest road to the answer.

  21. Let’s see, instead of teaching kids the normal way, we’ll force them to spend hours engaged in frustrating mental exercises in order to learn the most basic information (while also missing important other principles that are not “discovered”), thus ensuring that all the kids develop the attitude that learning is difficult, tedious, and unrewarding.

    It would also make sure that the dumbest kids are the most discouraged, by reinforcing how dumb they are instead of educating them, thus leading to a lifetime habit of avoiding problem solving for fear of revealing their ignorance.

    Yeah, that’s a great idea.



  1. Constructed Guided Discovered Learning

    I had my greatest Ah-ha! about teaching around 13 years ago when I took a math course designed to help elementary school teachers provide more meaningful math instruction. The first task assigned was to take wooden tiles from a pile