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A few years after I learned German, I got the chance to learn French. That experience gave me lots of ideas for why our teaching of many subjects, especially science and mathematics, is so unsuccessful—and for how we can improve our learning.
I studied French in school for five years. However, when I went to France after college, I could barely buy a train ticket. The impetus to try again came a few years later, in the summer of 1993. Our whole family was going to spend two months in Lyon while my father took a sabbatical. The rest of us enrolled in a four-week language course at the Alliance Française.
While still in America, to get more benefit from the language course, I started relearning French. On the recommendation of a friend who is a linguist and mathematician, I got the self-study French course made by Assimil entitled Le Nouveau Français sans Peine (New French With Ease). (Many other self-study courses should also work well. I have not tried them, so I do not have the knowledge to draw out lessons for learning other subjects, which is my main interest here. But to learn about language programs, I recommend the excellent “How to learn any language” site.)
I did one French lesson daily starting from Lesson 1. I read a short, idiomatic dialogue out loud using the pronunciation key, then listened to it on the tape, repeating it sentence by sentence. The lesson finished with 2 minutes of fill-in-the-word exercises using the vocabulary from the dialogue. Each lesson took about 30 minutes. After three months of this preparation, when I landed in France I could converse with random French people on the train. There was plenty of time to try, for it was a summer of discontent with strikes across the country. That’s how I learned la grève (strike). When I took the Alliance Française’s placement exam, they gave me the choice of the intermediate or advanced level. I think it was a fair assessment: Although not fluent, I could survive well.
Thus, I learned far more from 3 months with the Assimil self-study course than from 5 years of school French. The absurdity of that comparison only grows upon comparing the hours spent. The Assimil method took 0.5 hours per day for about 90 days: That’s 45 hours. The 5 years of school French happened every school day for roughly 50 minutes. A school year has roughly 180 days, for a total of 750 hours over the 5 years. Including homework, the total is probably 900 hours.
That’s a time-invested ratio of 20 to 1. Thus, despite spending 5 percent of the hours that I spent in school, with the self-study method I became far more competent in the language. As I think back on what made this self study so efficient, I’ve come up with several reasons that can be used in redesigning many kinds of learning:
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Active. In the Assimil course, you talk for most of the 30 minutes by repeating the conversation on the tape or CD. In school French, you mostly listen to the teacher talk or do grammar exercises (e.g. you conjugate verbs).
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Daily practice. The Assimil course happened every day, including weekends, holidays, and summers. (Stephen King writes every single day, including Christmas, July 4th, and his birthday.)
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No fear of mistakes. Speaking to myself, at home, I didn’t worry whether I was saying it right or about my grade. I just tried to match the syllable sounds and sentence intonations on the tape. As I found when learning German, and as Benny, the Irish polyglot, explains so well—for examples, see here, for learning German—the willingness to make mistakes is the stuff of learning. (Thanks to blog reader Jack for pointing out this excellent site.)
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Inductive (rather than deductive). In the Assimil course, you learn grammar first by using it in the dialogues. However, every seventh lesson has no dialogue. Instead you review, and slightly extend, the grammar that you have been using for the past week. By which time it has become easy! In school French, at least in my day, you mostly learn and practice grammar in isolation. Heaven for-fend that you might use a construction incorrectly. Better not to speak at all.
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Idiomatic. The dialogues used phrases that living humans might say, rather than, “My hat is green but my dog is brown.”
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Fun! The dialogues were amusing. Almost twenty years later, I still remember the punch line of the first dialogue. (And I have heard that earlier editions of the Assimil program were even more enjoyable.)
If we learned our first language like we usually learn second languages, it might look like this. A young child says, “I am hungry.” The parent replies, “Wait! Before saying am, you first must learn to conjugate to be in all persons and number, in the indicative, imperative, and subjunctive moods, and in the past, perfect, and future tenses.” After a few months, or maybe weeks, of this teaching, the child would conclude that it has no aptitude for languages and become mute. And human culture would perish in a generation.
If we taught math or science like we normally teach languages…oh, wait, we do! (And I believe, although with less direct knowledge, that we teach most subjects this way.) Look at the factors on the preceding list:
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Active? Most of the learning is spent passively copying down what the teacher puts on the board or, in the high-tech version, using ghastly PowerPoint slides. This method of knowledge reproduction made sense 800 years ago, when a book cost $20,000 (in today’s dollars). The invention of the printing press has changed book prices but not how schools and universities organize learning.
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Daily practice? The practice, at least in many college courses, usually happens once a week on the homework problems.
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No fear of mistakes? The biggest fear students have is making mistakes, for they lead to punishment: bad grades.
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Inductive? Rather than teaching inductively, we teach students a system of axioms or rules (the grammar)—for example, Maxwell’s equations of electromagnetism or the rules of arithmetic. Then we ask students to construct grammatical sentences, which the “good” students learn to do. But they cannot speak: That is, they cannot use the language of mathematics or science to understand or express their ideas about the world.
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Idiomatic? Hardly any of the usual examples (such as Atwood’s machine) help students explain any feature of the real world. I know from my own experience. After four years of getting A’s in physics courses, if you had asked me, “Why is the sky blue?” I would have been flummoxed, for neither skies nor colors were among my course topics.
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Fun? When I used to go to parties (before becoming a parent), I used to tell people that I was a physicist or a mathematician. However, I stopped because the invariable response, “Oh, I was never good at physics [or math]!” illustrated how rarely anyone enjoyed learning physics or math. When I start going to parties again, I have my rejoinder: “It’s not your fault. It’s because of the teaching… and I’d like to do something about it.”
Instead of teaching physics or mathematics as we teach second languages, then blaming the victims for not doing well, and expecting them to internalize the blame (an example of the Stockholm syndrome), why not use physics and mathematics to ask and answer questions about the world? Rather than starting the course with “motion in a straight line at constant speed” (it’s hard to imagine a topic more dull or, alas, more typical), we can use physics concepts such as force and energy to estimate the gas mileage of a 747 by dropping coffee filters—thereby giving the concepts depth and meaning.
Following these thoughts, I stopped teaching physics the usual way. Now on the first day of class we make a related estimate, of the world-record cycling speed. Later we find out why toast always lands butter side down (and it’s not because the butter side is heavier!).
These changes are but a start. Let’s take inspiration from skillfully constructed language courses to design a whole new physics and mathematics curriculum—and extend the principles to all areas of learning.
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Nice post. Reminds me somewhat of the Khan approach to learning. In fact, some of your reasons why you believe your French course was successful are the same reasons Khan thinks his videos and practice approach is successful (active, daily practice, no fear of mistakes).
In my basic math class that was required in the GenEd curriculum at my college, our prof got us outside (in January!) with 3×5 cards and rulers. My partner and I calculated the circumference of the sun within 1,000 miles.
I’ve been teaching for seven years. I have tried different strategies, some of which have been “effective” and some of which did not work for me. I could never figure out why. My enthusiasm didn’t seem to affect it- I have enthusiastically failed and succeeded despite boredom- and neither did the strategy (student-led, teacher-led, lecture-intensive, activity-intensive, and so on). Finally, I realized something, and it’s true for the example above, as well:
You can lead a horse to water, but you can’t make it drink.
The common denominator in students who achieve above their ability level is motivation, whether intrinsic or given at home or because of a perceived reward. It doesn’t excuse me from doing my damnedest, but it also doesn’t excuse experts, pundits, and the vox populi from acknowledging it.
Those who want to succeed, will achieve beyond their ability level. Those who are neutral, but are willing to play along, may be inclined at various times, depending on a myriad of factors (what happened at home, general mood, strategy used, etc.) to achieve, but they will also be disinclined (depending on those factors). Those who are disinterested, who refuse to work, who refuse to practice, who are not forced to achieve at home, will not achieve above their ability level.
Bottom line: reach the kid, and you succeed. But sometimes, the kid doesn’t reach back. Again, this doesn’t excuse me from trying, but it needs to be stated.
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I agre wholeheartedly! I have had the same epiphany recently. I teach university French (and German in the past as well). Regardlessof approach, methodology, textbook, types of exercices, partnerwork, teacher-directed work, etc., if some students are not interested in learning, they will not learn. In addition, I’ve noticed (and this is true mostly for American students) a fundamental ignorance of BASIC grammar conepts. I’m not talking about the pluperfect here, I mean, what is an adjective or adverb sprt of thing. At some point, one MUST understand the concepts of basic human language if a second and third language is to be mastered as an adult (which is cognitively anyone above about the age of 10). On the other hand, I have noticed that using French in class everyday 95% of the time, and MAKING every student answer (in complete sentences) has worked much better than explaing things in English. I use English sparingly, to sum up at the end, or explain particularly difficult concepts (the pluperfect!). Some student shate it, most love it. I’d rathe rteach to the A and B students than cater to the lowest common denominator of the D students…we’d spend all year on 2 chapters (and they’d still be mediocre), because as you rightly point out: the ignored factor in all modern pedagogy is STUDENT MOTIVATION. Until they realize the practical value of speaking a handful of world languages, they won’t learn. Thos ethat do have come back and thanked me for insisting on things like complete sentences, expanding their vocabulary when they thought all they really needed was a handful of “everyday” words. Language profs have the most thankless and difficult job in the teahcing profession, especially in the U.S., but also the most rewarding for those handful of students who are intellectually engaged and motivated and welcome the opportunities that you give them to go out linguistically equipped to survive in the 21st century global community.
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one MUST understand the concepts of basic human language if a second and third language is to be mastered as an adult
Really? Why would that be? I recently had my son’s teacher tell me that while he reads and writes at college level, that he MUST master the distinction between a compound and a composite predicate or all is lost. I haven’t gotten back to her about that yet, but I don’t see it. Apparently he both reads and writes these things correctly but doesn’t yet know the terminology… neither do I.
I think that one needs a mastery of “basic” technical terms, jargon, and analysis in the fields of grammar and linguistics in order to communicate with experts in those fields who are unable or unwilling to communicate without them.
I wonder how many people reading this would be using their computers this way on those same terms; the necessity to have an understanding of electrical engineering or computer science terminology and concepts which are ordinarily used for design and analysis.
Try this sometime, I have: Interrupt someone speaking whether it be their native language or a second language, extra points if it a language teacher. Ask them, “what case and gender was that second noun you just used?” or something similar. Some will not be able to answer at all, most will pause for the better part of a minute, trying to rewind and analyze what they said. That is because while they claim they’re using all of that technical analysis and jargon they’ve actually learned the language in a much more natural way and are merely applying that stuff after the fact.
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Ask them, “what case and gender was that second noun you just used?” or something similar. Some will not be able to answer at all, most will pause for the better part of a minute, trying to rewind and analyze what they said.
That’s the point of the post above, the native speaker learned the language from birth so does not need to understand these concepts. The natural way of learning language can’t be repeated, because our minds are fundamentally different as adults.
Of course, there are different goals to learning a language. If the goal is survival, than basic grammar isn’t all that important. I’ve certainly gotten my point across with rudimentary language skills. If the goal is to converse and not sound like a 2-3 year old then a bit more is needed. I’ll also add that for an native speaker, learning the natural way is also not enough to sound educated in their language. It typically takes formal schooling to learn how to read, write and speak properly.
“That’s the point of the post above, the native speaker learned the language from birth so does not need to understand these concepts. The natural way of learning language can’t be repeated, because our minds are fundamentally different as adults.”
Hi, I think the gist of this essay is that you *can* repeat the natural method! The fundamental difference is that adults think they need to learn all the rules, get the vocab in order, and then, hesitantly, learn to “speak” (i.e. fit the vocab into a memorized grammatical rule).
The child doesn’t care for this nonsense and just starts speaking, making mistakes, and rapidly improving.
Apples and oranges. Nobody doubts that you and your son can use your own native language correctly without knowing the details of grammar. But you were replying to a comment that referred to mastering a second or third language, and doing so as an adult. And we’re talking about “mastering” it, not just learning to communicate effectively. And “mastering” a language doesn’t mean being able to navigate across town, order a meal, or chat up local girls in a bar, valuable as such skills are. It means using it at close to native fluency, but it also means being able to appreciate the nuances of advanced texts — novels, poems, scholarship — with sophistication.
And don’t belittle poor, neglected “grammar.” All grammar is is a model for how language works, and a common vocabulary for describing the functions of language. If you’re going to “master” something, you ought to be able to talk about it. And you talk “about” language in grammatical terms.
I disagree that we MUST all master technical terms for grammar. Other people’s names for it have little relevance, as long as we can explain how the rules function. Knowing what “pluperfect” means helps me as an analytical person, and it makes me feel smarter, part of the in-crowd, but it is not essential to my communication skills, which are largely unaffected by that knowledge.
This is coming from a Summa Cum Laude English major who’s dabbled in 3 other languages and now teaches high school Spanish.
I agree, TRULY basic terms like noun, verb, adjective are useful, but case does nothing for me or for my students, and to ask someone on the street to parse a sentence is just silly and elitist.
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There are plenty of kids in school who will not learn, but some are held back because they don’t learn all they can. I never got an A- in school, but I know I could have learned so much more using the principles Mahajan outlines. I have learned French in France and advanced calculus and probability from a tutor (after 4 years of no math classes). In both cases, I think that Mahajan’s 20:1 time ratio held roughly true.
I am sure you do a great job for your students, since you apparently care about their success, but if you are the best teacher you can be, you can make more of a difference to a few of the ones who are really motivated.
The U.S. DOD has a very extensive linguist program and has done careful testing of its programs to determine effectiveness. What’s the number one correlating factor? Students motivation. Motivated students succeed _despite_ the quality of the teacher.
The Pareto principle can explain a lot of interesting phenomena, including what kind of change in teaching methods will take place in our schools.
Private tuition will still be the prime mover in producing “excellent” (however you define it) students. You can use the Pareto principle to analyse if this is the current situation and predict that it will not change.
The rest of the debates are almost irrelevant ….
Is this explained in more detail anywhere? For a specific topic like Newton’s laws of motion or the quadratic formula, I would like to see how you would teach the topic and how it is usually taught, so that I could compare the two teaching methods.
(By the way, this question may support your point about inductive learning. You have given me a general principle and I don’t understand it, so I need examples.)
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Is this explained in more detail anywhere? For a specific topic like Newton’s laws of motion or the quadratic formula, I would like to see how you would teach the topic and how it is usually taught, so that I could compare the two teaching methods.
(By the way, this question may support your point about inductive learning. You have given me a general principle and I don’t understand it, so I need examples.)
It is probably worth noting that there are some in the education world who have known this for decades, and just knowing that a system is wrong, doesn’t necessarily lead to improvement.
Piaget and Papert have both had the same observation as you (that many people teach language, math and science all wrong), and they discovered this fact about how we teach 50 and 40 years ago respectively.
This is part of the point of the constructivist teaching movement, which is often decried in media as being “fuzzy.”
Horror: The ultimate tool for education — Google Scholar (scholar.google.com)
What would be the the youngest age of students who would be able to use Google Scholar?
Indeed, David!
Furthermore, the system can’t be changed if we continue to target teachers and politicians. Parents have to be on board. Let me rephrase that: Parents have to lead the way.
So the vital behavior in changing all of this is getting the parents to believe independently everything written above.
How do we do that? Good question. One I’m attempting to answer.
I agree that some have known this for a long time. But: “Everything that needs to be said has already been said. But since no one was listening, everything must be said again.” –Andre Gide
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Excellent article, provocative thinking…
And, by the way, I also took the Assimil courses… I actually learned both French & English using Assimil books and cassettes… Based on my own experience, I believe your analysis is very accurate. Now, for “active” learning you need to have an “active” learner which means someone who is deeply interested in learning. “How do you initiate that fire?” is a key question.
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I disagree that memorizing counts as “active.” Starting a fire starts with tapping into prior knowledge and interests, topics that matter to the learners, not dictated by cassette tapes.