Score another point for my mother.
My mother is a really good cook. She is also an unrepentant violator of recipes. My earliest cookbook related memory involves noticing that, while Mom had a recipe in front of her, she was flagrantly measuring different amounts of ingredients than those called for, and combining them in a way that clearly contravened the method described on the page.
It turns out that this manifestation of her issues with authority may also explain why she has such a good understanding of what she's doing in the kitchen.
At least, that's a conclusion I'm inclined to draw from research done by Ohio State University professor Steve Rissing on two different approaches to an enzyme laboratory experiment in an introductory biology course:
During a talk at the annual meeting of the American Association for the Advancement of Science in San Francisco, Rissing cited one particularly difficult laboratory experiment in which students worked with enzymes. Students often struggled through this exercise, and usually scored poorly when later tested on the implications of the experiment's findings.Rissing asked the laboratory instructors - usually graduate students in biology - to use two different approaches over two academic quarters when teaching the experiment. Roughly 300 students, all taking an introductory biology course for science majors, were in each group. The first group used what Rissing calls the "cookbook method" - they followed step-by-step instructions on how to carry out the experiment and display their results. These students were provided with a standard, prepared enzyme solution.
The second group of students had to prepare their own enzyme solutions from a piece of raw turnip. They were also given more freedom to think through their approach to the same experiment, and were encouraged to use critical thinking and hands-on discovery to come up with their approach.
At the end of their respective experiments, both groups of students were asked one simple question: Where do enzymes occur in nature?
About one out of five students (23 percent) in the "cookbook" group answered the question correctly. But 83 percent of the students who developed their own approach gave the right answer, which was that enzymes come from living tissue.
"The students in the first group were just as intelligent as those in the second group," Rissing said. "They just lacked confidence. No teacher had ever asked them something as simple as how do they want to display what they saw in the experiment. They had always been told how to do that."
What we're looking at is the difference between being able to follow instructions and understanding why a particular sequence of steps produces the desired result. Following instructions in a lab protocol precisely is often harder than it seems like it should be, especially if you factor in inexperienced hands (belonging to undergraduates who might not even be science majors) and aging equipment. If you're a novice in the lab and someone gives you the step-by-step recipe, your attempts to complete the experiment successfully usually come down to trying to complete each step just as described in the recipe. If the experiment doesn't work, you go back and figure out which step(s) you screwed up. If the experiment does work, what you know is that you must not have screwed up any of the steps too badly.
Unfortunately, that may be all you know: Correctly following this recipe brings about that result. Why this recipe and not another? That might be something the lab instructor knows, but it's not knowledge that magically penetrates your skull just in virtue of your having performed each step of the experiment correctly.
If, on the other hand, you're presented with a task and less precise information about how you should accomplish it, it seems like you have to think harder about possible strategies for completing that task. Given the turnip, you need to mull over the range of things you might do to it in order to extract its enzymes, not to mention the possible ways you might determine whether what you've gotten from you turnip really contains enzymes (and from there to measure the activity of those enzymes, etc.). Your work is less about performing particular steps in a recipe correctly or incorrectly, and more a matter of sizing up the extent to which particular things you could do bring you closer to, or farther away from, your goal. Messing around in this way gives you a much better feel for what could be happening when you perform a particular operation. You aren't just following someone else's map -- you're making your own, and in the process, you're getting a much better feel for the terrain.
If memory serves me right, one of the constraints that might make the cookbook approach to intro labs appealing is time. You have a finite interval (often 4 or 5 hours tops) in which to get results. Sometimes that gives you room to work through the steps in the prescribed recipe twice, but often you have one shot to make it work.
Coming up with your own protocol means having time for trial and error and gradual refinements. For certain tasks, this approach could easily take multiple lab sessions. These sessions, of course, would be cutting into all the other essential stuff that needs to be crammed into the lab portion of an intro course.
Maybe we should ask if what makes the canonical lab experiments "essential" is that the students have mechanically performed all the steps associated with them, or that the students come out with a good understanding of what is happening when they follow those procedures and of why those procedures work.
In the meantime, on the assumption that it will take time to apply Rissing's approach to retooling intro lab curricula, I suspect it might be useful if some lab instructors deployed my mother's attitude toward recipes -- helping students to understand how violating different steps of the protocol in systematic ways makes a difference in what happens.
I'm a flagrant violator of recipes (rules are meant to be broken, aren't they?).
The creativity in improvisation makes the exercise all the more fun. If you give the kids more leeway, they may enjoy the labs more as well.
In my experience, the key factor that differentiates mere "knowledge" from "mastery" is just this: The ability to Play With [whatever it is].
I absolutely HATE the "cookbook" labs I've had to take, but have greatly enjoyed the less constrained (though no less demanding) ones. I find myself rushed in the former to such an extent that there's no time left to actually understand the implications of what's going on beyond the basic mandated facts that need to be memorized, while I think I've gained much more useful learning (and skills) from labs where there's more leeway to actually "hack[1]" the problem at hand.
Actually, the same holds true for the "book-learnin'" classes as well. The amount of actual learning I get from practical-application exams is much greater than from "standardized-testing"-style fact-regurgitation exercises.
[1] for "hacking", I use the definition "finding novel, unexpected, or inobvious applications of any system" which implies a certain amount of actual understanding of how and why said system works.
I hold the cookbook approach partly responsible for the fact that despite getting a chemistry degree, I still have trouble working out what needs to be done in some chemistry stuff.
On the other hand, my gran, after almost 80 years of baking, could throw together any random ingredients she had left over and make something edible, and often rather nice.
I am currently trying to replicate some medieval technology, from metal casting to alchemy. Even with some manuals and suchlike, this requires thought and learning. For example, it has taken a while to learn the best shape to set up my furnace (made of insulating bricks) and then what colour charcoal and flames are at over 1,000C. Or how wet the clay should be before you use it to make a casting mould.
These things are hard to do with old technology, you have to learn them by practise, but once you know them, you can do all sorts of things that look impossible.
In my family, we call what your mother does "ruining the integrity of the recipe."
I guess Mom was always more concerned with the integrity of the dish (or that of her culinary skills) than with the integrity of the recipe.
Well, in my defense nobody ever went away from my table starving (even vegetarians, although they might have left a bit hungrier). Taste and imagination of desired results were always better guides than a single recipe.
Alright, now apply this thinking about the lab learning experience to upper elementary math instruction. Testing comparing M/F differences in math "expertise" early in 7th grade* has often turned up results that seem baffling, since until that age M/F have shared the same classrooms and math instructors (some better/some worse). Differences seem to persist for the majority of the population, as seen upon college entrance.** So why the differences?
My theory is that while they share the same classroom and instruction, 9-12 old males generally pay less attention than their female counterparts to learning the rules (provided so no student is actually required to think about how one might produce a legitimate result for any math problem given -- primarily on "The Test", and so also in class and on homework). Teachers are most comfortable with teaching, and correcting work done applying the fewest, simplest rules, with the least amount of variance in execution, to achieve the "correct" known answer.
Females of the same age range try to curry adult approval by learning all the rules VERY WELL. In applying those rules to the given problems they get the right answers the first time. They never find an opportunity to think about quantity, relative sizes, applying math concepts to verbal (real life?) problems, or tackling problems beyond the set of rules taught thus far.
Males find that they need to think beyond memory just to pass "The Test", and therefore develop mathematical thinking skills that allow them to move outside the "box" our elementary math education generally builds. They get their right answers, often, in alternate ways.
Males and females may be in the same classrooms being given the same math instruction through elementary school, but I suspect they are getting very different math education due to differences in attention, behavior, risk and reward systems in school and sometimes even at home.
* e.g. Johns Hopkins and other gifted & talent searches via SATs in 7th grade [http://cty.jhu.edu/]
** e.g. New Jersey College Basic Skills tests administered to all entering students in NJ public and some private colleges given from about 1975-1991 at least
Super Sally, I think you may be onto something. I have had similar thoughts myself (ever since high school, in fact) and as a generalization I think there may be truth in what you say about the different experiences/approaches of male vs. female students in pre-college math. (Non-white female students seem if anything even more prone to it, if my impressions can be trusted.)
I wonder if anyone has done research on this.
On a vaguely related note:
One of my colleagues sent around a very funny "Quadratic formula as the IRS would present it" form. [First line: "Enter A here. If line 1 is zero, stop. You cannot use Form QF"]
In thinking about why it was funny (and whether or not my algebra students would get the joke), it occurred to me that there might be some of them who would prefer to be taught the formula this way: The "recipe-followers". And, my goodness, it has (let me see) 16 steps, not counting the 9 additional steps in the "Negative Discriminant Worksheet." [hee hee] None of which steps make any sense at all unless you can step back and see what the whole thing is doing, of course.
If anyone had ever asked me to follow such a procedure I would have run screaming (silently) from math, never to return. Sort of how I feel about tax forms, come to think of it.
That thought (that there were students who think this is what math instruction SHOULD be) kind of scared me.
My own experience offers a minor counterexample: My Mom is also a "creative-type" cook. Growing up, our experience was that whenever she tried something new, it'd be "okay" about half the time, "really good" maybe 40% of the time, but that last 10% could be pretty nasty.
Of course, the proportion of disasters declined as we all got older and she continued to gain experience -- but in a chem lab, a disaster could really be a disaster! (Heck, it kinda can in the kitchen. Once she melted a pot to the stove-burner, and another time... well, I don't think we ever got the egg stains off the ceiling!)
These things are hard to do with old technology, you have to learn them by practise, but once you know them, you can do all sorts of things that look impossible.
Which is why blacksmiths were once considered a sort of wizard....
In my experience, the key factor that differentiates mere "knowledge" from "mastery" is just this: The ability to Play With [whatever it is].
(r)Amen!
Oh, the number of times I've had to listen to my mother say "What does the recipe say?" when I'm either completely winging it or running on autopilot.
Recipes are great if you want to do something now, or copy something that's already been done. But I get more from just browsing through the cookbook rather than homing in on one recipe.
On the math/science instruction by rules versus problem solving: I took an AP physics class, and pretty much the whole class learned all the steps to solving various kinds of equations/problems, and could easily regurgitate them on all the tests in class. For whatever reason I never really was able to memorize them and wound up "making up" equations (usually built from simpler equations on a cheat sheet we were allowed to use). About 2/3 of the time they worked, and the rest of the time they failed spectacularly (although the teacher made the comment once that he looked forward to grading my tests to see what unusual ways I came up with for solving the problems!)
Then, we took the AP test, and everybody said it was really hard because of one problem on it that didn't fit into any of the predefined formulas we'd all memorized. But to me, it made sense, and seemed like a fairly obvious problem, and in retrospect I think it was because by not having memorized essentially a set of specialized cases I was able to work through how to create what the problem wanted, rather than just saying "I need these steps to solve this kind of problem".
So I guess what I'm trying to say is that while the cookbook approach gets short term results, it doesn't work in the "real world" where things might deviate from the set of predefined rules. But that's all that really gets taught in school, even to the "best of the best" students.
What a perfect example of why titration labs are maybe not the best way to teach about acids and bases.
One of my life ambitions is to design effective labs for a living. Because students can learn so much more if they have to think.
krya:
I'm a physics grad student. Our undergrads are divided into three intro physics classes, one of which is "physics for biology majors". These students are the most flagrant users of the "memorize the steps" method - and the most flagrant whiners when a test question doesn't conform exactly to a problem they've done already and memorized. How does that make you feel about our future medical professionals?
I'm definitely a creative type cook. I like recipies, but unless I know that I want exactly what the recipie says, I tend to tweak. Generally, I look at them to see which kinds of things produce which kinds of reactions... how do I mix this with that to keep it from curdling? What gives it that distinctive scent? Then I take that specific thing and apply it to what I'm doing at the moment.
Unless it's a pastry, in which case I stick to the recipie because those tend to be really finicky.
My undergrad college eliminated science courses for non-majors (there weren't any non-science courses for non-majors in the first place). They were very big on everyone getting an intensive science experience. Overall, it worked well. I have some specific learning differences that made it really annoying for me, but I got a lot out of it nonetheless.
We started with some fairly cookbookish experiments - here's how this piece of equipment works, this is what this technique is like, etc. Each one focused on a different aspect of the process (so for one it might be about learning the technique, another about doing all the calculations properly, another about writing a really good lab report, and another about applying the results to a different problem), and they built on each other. A technique used in one lab would be used in a different way in the next, and you were expected to be able to apply techniques in conjunction with one another.
The final lab was a long one, and deservedly (in)famous. Each student was given nine numbered test tubes with nine different odorless, colorless liquids. Since the instructors filled all the tubes, no one had the same combinations in the same order (so working with your lab partner wouldn't help you, because you had different solutions). Everyone knew what the nine solutions were in advance (so you weren't testing for anything super bizarre), and had a day to plan and prepare tests, and another day to perform tests and do out all the calculations. We had access to everything in the lab, but we had to determine all of the steps that needed to be done, and all of the calculations we'd need to figure out what was in each vial.
There was no lab writeup - each student just had to turn in a list with each substance and the number of the vial it came in. People did a lot of really creative things to turn them in, mostly for fun. I had a friend turn hers in by baking fortune cookies and putting the answers inside like fortunes. I found a hubcap and engraved my answers into it with a metal tool. Someone else turned in an entire car door.
Although I didn't do perfectly on that lab, it was really cool, and reminded me of why I had liked chemistry in high school. The ability to think through a problem using the tools at hand is useful, and it made me feel like I could do science, even though I have a lot of problems with math and cookbook science (much in the same way that I have trouble with the 'names and dates' method of teaching history. There's no thought in it).
Alas, the department wasn't entirely sucessful in keeping that atmosphere cultivated in its students. I knew some who went in with a love of science and a good mind for exploration and technique, who left bitter and vaguely broken, and completely soured on science. (Not to mention so uncertain about their own skills mixing stuff that given an actual cookbook, they had trouble following the recipie for cornbread)
Granted, it also produced some wonderful scientists. It was just a tossup, depending on who you got for your thesis advisor.
I think that the 'memorize the steps' method has its values, depending on the purpose of the course. Then again, I also don't think that it's completely at odds with teaching thinking. A set of memorizes steps is just a tool. Learning how and when to wield that tool gives you a discipline. It is extremely hard to balance, because it requires a particular mindset of the professor and a lot of investment from the students, but it can happen. When it does, it works really well.
Perhaps the distinction could be taught between the two styles (which I see as a continuum rather than an either or situation).
As my children learn to cook I encourage them to think about what they like to eat, what flavors they don't like and how certain ingredients combine. When they're beginning cooks, following a recipe makes sense. If you're trying to juggle all the steps involved in making butterscotch brownies when everything's unfamiliar nothing beats the Joy of Cooking.
A couple of the kids spend lots of time reading cookbooks, one is a very pragmatic cook (he's responsible for the cooking at his dad's house and he likes to minimize the effort/maximize quantity, and doesn't mind eating the same thing three days or so in a row if it means less time cooking) and my oldest tends to show up with great ingredients and get other people to cook them.
I don't know how analogous lab chemistry is to cooking (although my 8yo pointed out that the tomato sauce on the lasagna that stuck to the aluminum foil created a battery) but it seems to me that if you're beginning in the lab following the steps is sensible. I don't want my young lab rat indiscriminately mixing things, so he has to run his ideas past me first. If I have any questions about what's going to happen he has to run it by the world's nicest chemistry professor.
Then as you become more familiar with the elements and how they behave, stressing problem solving techniques rather than rote work is more appropriate.
Here's hoping the kids made cookies while I'm at work....
Well, I should be doing something like writing a report, but I'm here instead (sound familiar?).
My department uses "cookbook" labs for freshmen (and to a lesser extent for upperclassmen). Last semester (Gen Chem I), nearly all lab exercises used spectrophotometers to analyze a variety of problems.
This semester is titration-intensive for the chemistry majors (and to a lesser extent the nonmajors). They've performed potentiometric and colorometric titrations, looked at chelation, equilibrium, acid dissociation constants, and content analysis of vit. C pills. Officially, our labs run 3 hours but it is not uncommon for me to be waiting 4 or even up to 6 for everyone to finish their labs.
These labs aren't as "fun" as the nonmajors labs (which use different techniques every week), but I think there's considerable benefit to the repetition of a particular lab technique to explore a wide variety of concepts. The students, the first time they encounter a new technique, are quite nervous and concentrate more on technique execution than exploring the points of the lab. The weeks we learn ar new technique are likely to run the longest and have the most frustration among students: repetition of techniques frees them from this constraint. The second and third time using a technique (albeit to a different goal), they hardly think about the mechanics of the experiment and instead focus on the learning concept. It is pretty fun to see them come to the realization that with a very small toolset they can do an amazing number of things, and then from there to realize that there aren't too many discrete skills that scientists really use (instead there's a lot of variations on a handful of themes).
Of course, I generally think the labs are much more interesting than they do, at least at first, and spend much of my time "selling" just how exciting their lab is and all the amazing things they get to learn (general observation: excited T.A. leads much more often to excited students; tired T.A. usually leads to much clock-watching. My school should really consider this before giving 30 hr-week appointments to grad students).
I hear from students quite frequently, "I learn so much more in lab than in lecture." So many students sit back and try to passively learn chemistry in lecture (or just show up and play computer games, shocking but true), but in the lab, even with a "cookbook", there is no way to avoid active engagement in learning. It might be frustrating, not work right, have lousy accuracy... but everyone is involved. I've had students take pictures of the results of the "cookbook" experiments and share them with friends because they were "so cool" (more than once; once I thought was an oddity but it has become a theme.. SOMEBODY gets excited enough in every class to find a burning need to send a photo message of a reaction that turned out really neat or blew up or something).
One thing I've found that helps is to constantly engage my students in asking "why" and "how". Why are you adding acid? Why do you need to wash your glassware out with distilled water? Why does THIS procedure call for deionized water while THAT one doesn't? Is a particular step important for accuracy or is it just to prevent an undesireable side reaction? Why is calcium disodium EDTA an ingredient in 7-up? Why are you boiling your water before preparing the sodium hydroxide solution?
If these questions were ALL in the lab manual, the students would expire of boredom and frustration when their hands cramp up from writing, but the verbal interchange has the typical effect (after they get over being asked questions) of exciting the students. They start asking each other the same types of questions, and giving good answers. They begin to challenge my statements as simplifications because they get used to thinking of the reasons behind things. This is pretty exciting, and it occurs frequently in labs (far more frequently than in lectures, particularly large lecture hall experiences).
The experiment doesn't have to be a guided-exploration (or whatever they're calling them now) lab to engage students in the process of creative and critical thinking. Often spending two hours on "cookbook" formulas and then throwing in one "design-your-own-test" at the end will suffice, and with the cookbook experience, the students generally have a basis to start their design on (not unlike Periphrasis's experience above).
One thing I take umbrage with (and probably accounts at least to some extent for your miserable lab experience) is the reliance of many schools (and obviously others) on night labs. I've found that night lab sections go longer and the students make more mistakes than in day labs. The students are tired, distracted, and often hungry. When you finally get everyone through the experiment, its time to perform calculations.. and the LAST thing they're concentrating at 9 pm on Friday night is how to use logarithms.
I'm a theoretical chemist. I recall with horror 9-hour p-chem labs. There were entire weeks in organic where I had messy brown gunk where I was supposed to get a beautiful white powder. I've worked as a bench chemist and known the humiliation of having nothing work right for six weeks, only to find out I set up a reaction wrong (come to think of it, this happens in theory, too, but I didn't realize that when I started messing around with modeling chemistry instead of performing it). Yet, I do not believe you can adequately learn or appreciate chemistry without performing chemistry experiments. Ultimately, chemistry is a field of pragmatism and physical reality, and nothing reinforces that like the actual experience of carrying out reactions, observing them, and realizing that all of those algebra word-problems in your lecture text describe things that really happen.