>"To be (a corrector) or not to be (a corrector), that is the question!’ (with apologies to Shakespeare)

>Krashen tells an interesting story of the time he studied French. He talks about how his “excellent” teacher taught grammar and taught vocabulary and corrected errors — and how they learned through comprehensible input.


A Summer as an Intermediate French Student

By way of conclusion, I would like to report on some recent personal experiences as a student of French. The class I attended in the summer of 1978 in Los Angeles was a private class, with a small number of highly motivated, highly intelligent, and mature students. The official “method” used was the Pucciani-Hamil approach (Langue et Langage), used with much apparent success at UCLA and at many other schools. The method is “inductive”, that is, students are led to induce, or guess, the rules. In a typical lesson, the teacher asks what are hopefully meaningful, interesting questions of members of the class in hopes of preparing a context for the target structure. The following exchange is a good example (taken from the instructor’s manual, Pucciani and Hamel, 1974; p. 321). The purpose in this exercise is to teach the conjunction “bien que” and the fact that its presence requires that the following verb be in the subjunctive mood:

Teacher: Fait-il beau aujourd’hui?
Student: Non, il ne fait pas beau maintenant.
Teacher: Irez-vous cependant à la plage pendant le week-end?
Student: Oui, j’irai cependant à la plage pendant le week-end.
Teacher: Irez-vous à la plage bien qu’il ne fasse pas beau?
Student: Oui, j’irai à la plage bien qu’il ne …

My excellent teacher followed this sort of pattern, and often tailored questions to individual students’ interests. For example, one member of the class was a dedicated beachgoer, and the example given above was actually used with this student. My teacher also allowed some “free-play”. If the student did not give her the structure she was looking for, she tolerated some “conversation”, as long as it was in French (a cornerstone of the Pucciani-Hamil approach is the exclusive use of the target language in the classroom). Indeed, despite the fact that the class was a first-year (third quarter) level class, it often had the flavor of a conversation class.

The explicit goal of the class was learning, conscious control of structure. There was error correction, and after enough examples of the above sort had been elicited, there was explanation of the rule (in French), along with further examples if necessary.

What is particularly interesting is that many of the students felt that the obvious success of this class was due to grammar work. One excellent student (a man in his sixties) felt he needed to “firm up” his grammar before doing conversation in French, and he told me that he felt our teacher’s finest quality was her ability to explain complex rules of French grammar. My hypothesis is that much of the success of the class was due to the teacher’s use of teacher-talk, her ability to provide a simple code that provided nearly optimal input for acquisition. The class was conducted entirely in French, as mentioned above. Besides the actual pedagogical examples, such as exchanges of the sort given above, teacher-talk included explanation of grammar and vocabulary, the teacher’s participation in the “free play” surrounding the exercises, mentioned above, occasional anecdotes, classroom management, etc. My fellow students reported that they understood nearly everything the teacher said in class. The teacher-talk, not the grammar per se, was probably what motivated the same student who needed to firm up his grammar to comment: “She gives you a feeling for French … she makes you want to speak French.” This is language acquisition, not language learning.

>What can teaching students pronouns of gender teach teachers?


A teacher, implying the near impossibility of the effectiveness of Comprehensible Input, wrote:

“How many hours of standard, educated English will a native speaker have been exposed to by, say, age 15. Whatever number you pick, if you expect an EFL student to use the language at an equivalent level without error correction or grammar instruction, you’ll have to find a way to get that student an equal amount of exposure. Get out your calculators, folks at ten hours exposure to English per week (a generous amount for a Chinese EFL student), the number of YEARS required is going to be well into the triple digits. Your students great-great-grandchildren will all be retired before your students will have acquired the ability to write like a 15-year-old.”

Krashen’s theories on the “acquisition” of language facilitated through “comprehensible input” at a level of “i+1” is not just something that sounds like a good idea until someone pulls out a calculator and does the math. Although the subject is widely debated, there is a lot of evidence that it works and you can read research after research on Krashen’s website at: http://www.sdkrashen.com/.

Also, in what the teacher said, is the implied assumption that grammar teaching actually does work. There is no evidence that teaching grammar results in the student truly acquiring the grammar. A certain degree of retention is possible in the student’s conscious “monitor” (an internal editor), remembering some grammar rules, but this is limited.

Clearly grammar cannot be acquired in such a conscious way. One of my favorite examples of this, which I have brought out many times before is pronouns of gender (“he”, “she”, “his”, “hers”), a grammar rule that can be taught in ten minutes it is so simple but can take a student a year or two to master.

Grammar “teaching” doesn’t work.

>How students learn for tests

>When our students take the big exams are the only questions they get right the ones the teacher “taught” them? I don’t think so. I would like to know how effective is teacher “teaching” as compared to indirect learning.

I think they are answering some questions on the test correctly for items that they were not “taught”. If so, then how did they learn them? I believe Comprehensible Input is playing a bigger role than we realize.

Krashen tells the story of how his French teacher wanted to only speak French to them and was explaining a grammar point, in French. Finally frustrated, she told them in English. However, her effort to explain it in French, all that French speaking to explain something, actually constituted Comprehensible Input for the students and helped their French.

Every time the teacher talks to the students in the L2 is Comprehensible Input. Teachers are naturals for adjusting their English speaking so students can understand them.

So between the teacher’s speaking and the student’s own study they are getting a lot of CI.

Perhaps the student is reading a business text and it is talking about international finance and the teacher wants the student to learn some language about stocks, bonds, interest rates, prime lending rate, etc. Perhaps the student has some degree of success in learning some of those terms but there are many things in the text that the student was not studying but was learning such as “carry on” when it says “banks cannot carry on making risky loans” or something like that.

>Reverse engineering vocabulary learning

>We hear a lot of advice about how to teach vocabulary, how to bring the mass of vocabulary to the student so the student has the right word when she needs it. But instead of looking at it from the mass to the useful word, let us look at it from the useful word to the mass. In other words, how did that student actually acquire that word?…a sort of lexical forensics, if you will.

I have been pondering the CET4 English test used in China. This is the most important English test in China and it’s hard for Chinese to claim they know any useful amount of English if they haven’t passed this test. (Following this test is the CET6 and CET8). I’m looking at an official sample test right now and have chosen a question at random to study. This is one line in a long paragraph and we know it’s talking about home care for someone who is ill. This is a cloze test question and it goes like this:

The responsible one in the home ___ on with the rest of the care during the _interval_ between the nurse’s visits.

(a) works (b) carries (c) looks (d) depends

The answer is “carries”.

Now the question is, how did the student come to choose that word? What was the learning process that enabled that student to correctly choose that word over the others? Were those words in a vocabulary lesson? Were those words on the student’s vocabulary list of words to memorize? How did our student acquire those words to be able to answer the question correctly? How did the student know she cannot say “…WORKS on with…” That sounds almost possible. How exactly did the student know it is impossible? What lesson was given to the student on this?

If we take a look at the correct word we can see in the American Heritage Dictionary there are many definitions or usages for the word “carry” plus six phrasal verbs with multiple uses as well, these being:

carry off-2
carry out-3
carry over-7
carry a (or the) torch-1
carry the ball-1
carry the day-1


carry on-4
To conduct; maintain: carry on a thriving business.
To engage in: carry on a love affair.
To continue without halting; persevere: carry on in the face of disaster. To behave in an excited, improper, or silly manner.

This makes a total of 64. Certainly, our student did not need to know every usage of “carry” to be able to choose it as the correct answer. But the student had to learn many of them. And how did she learn them, did the teacher teach them to the student?

My suspicion is that our student has not had English lessons in the multiple uses of the word “carry” that enabled her to answer correctly. Perhaps the student never had any lesson on the word “carry”. I believe that once an elementary vocabulary has been reached, the vast bulk of learning takes place indirectly through vast amounts of input as suggested by Krashen in his theory of “Comprehensible Input”.

>Still more on error correction

>On the TESL-L mailing list, a teacher asked the question below about error correction. As it seems to be something we’re interested in, I’m including my reply. – dk

“I,m an English teacher in China. I’m teaching 2 classes with 56 students each. When I teach writing, I’ll use differnt methods to encourage my students to write about their own ideas. To my joy, they like writing very much though it is hard work. However, I find it very difficult for me to correct their errors. I know fluency is more important, but it dosn’t mean we can ignore accuracy. Error correcting will take lots of time and energy, and the students don’t want to see their composition after I correect errors. Is there anybody who can help me use a kind of more efficient method?”

This is a common problem faced by many writing teachers. We could say it is even a trap because teachers feel obligated to this idea of correcting everything.


John Truscott famously or infamously, depending on what side of the debate you are standing on, has brought up research[1] indicating that grammar correction doesn’t really help students at all. So, generally speaking, all time spent at correcting is time wasted.

Truscott is in the same vein of English learning as Krashen. Indeed, Krashen has referred to Truscott’s research[2]. In this direction of English learning it is understood that students learn from indirect ways of teaching, things like Extensive Reading, that the students will absorb the language through massive exposure to it at a difficulty level of i+1.

After studying Truscott’s paper, and even organizing a virtual seminar for him on the TEFL-China list[3] where we interviewed him for a week, I began to pay closer attention to how my students responded to corrections.

Personally, from observing my students carefully, I’ve seen that my students do respond to some corrections.

But to be effective in this area, we have to understand some things first.


Our students cannot have a lesson, or even a correction, and simply “know” it. They only begin to know it. All learning in an area as complex as language takes a lot of time and repetition.

Choose your targets. Don’t try to correct everything. Correct what you think will be easiest for them to learn, that they are ready to learn. Remember, it is more like teaching a baby how to walk than teaching the fine points of running to an Olympic athlete. Teach only what can be learned or you are wasting your time and frustrating your student.

When you read over the papers, understand that this is the whole class speaking to you. Through their errors they are telling you what they need to be taught. In this way you can respond and give your class exactly what they need.

Group the corrections. Choose the Top 5 errors the students were making in their papers and show them how to do it correctly. Of course, some students may have not made those errors on the paper they submitted to you. But if they didn’t make this error this time they may make it next time so teach it to all of them. Even if they know, more or less, how not to make that error, such instruction will strengthen their understanding. As mentioned before, students begin to know something and slowly understand it better and better.


Do your own research. If you want to see how responsive the students are to correction, after you have taught them the 5 main errors and how to avoid them, ask the students to return their papers to you and ask them to rewrite the assignment. Collect those papers and check them. You’ll find that most of them will not repeat those errors, that they have learned from the correction. About two weeks or a month later, ask them to write the very same assignment yet again. You will find that a lot of the students will not make the same errors although many may have forgotten your correction lesson and are slipping again.


Beware of the hurried writer. This guy really wastes so much teacher time. He’s the guy who forgot the homework and before the homework is to be handed in just dashes off a quick paper. He makes a lot of mistakes that, if he took his time, he would not have made. He knows they are errors but they were errors made in haste. But he doesn’t mind and he wants his paper to be corrected. The problem is, it takes your precious time to read his paper and deal with these errors. I refuse to check any papers unless the student has made it as perfect as he possibly can. Only then can I really help a student with what he doesn’t know. Check the paper for really basic errors, simple words misspelled, obvious grammar mistakes. If you find such things, hand the paper back to the student and tell him to correct it himself until he thinks it is perfect. If you find someone hastily finishing a writing assignment make sure you don’t accept it. If he doesn’t have time to try to write it well, you don’t have time to try to correct it.

[1] http://frenchgateway.coh.arizona.edu/F05/FREN579/truscott_grammar_writing.pdf
Also, see his webpage at his university:
Here you’ll find the grammar paper plus lots of other aspects of his research into correction.

[2] http://sdkrashen.com/pipermail/krashen_sdkrashen.com/2005-April/000102.html

[3] http://groups.yahoo.com/group/teflchina
This is a group of about 900 English teachers in China or involved with teaching Chinese students. If you are a teacher in China you certainly would benefit from joining this list.

>Making podcasts for low level English students

>Here are a few ideas for making podcasts for your students:

1. Make recordings of your experiences like the time you met someone famous or thought you were going to die in an accident. Don’t be boring but be simple.

2. Interview friends and other teachers. Don’t rely on the friends to be simple enough or talk slowly enough. If the friend is using some language that you feel is too advanced for your students then jump in and ask your friend to define it or define it or restate it yourself.

3. Take your students on a tour to a favorite local haunt. There is a shopping mall here that is immensely popular with all students in this area. Record a tour of the location that they could listen to and use to follow your footsteps. Describe what you see, tell some funny stories and go in to the shop and talk to some clerks about their products. I did this with my notebook computer in my bag running Audacity with a microphone clipped on my shirt. Many mobile phones have recording functions on them. You can include some insights into some of the businesses or some of the fashions even if you have to look them up on the Internet. Check this out.

4. Make your case for your method. Students always want to know what is the best/fastest/easiest way to learn English. Explain how you are teaching your students. Some of our teaching methods are counter intuitive. I think Grammar-Translation makes a lot of sense but is not as good as Communicative Approach. If our teaching method is not always easily accepted by students you should take every opportunity to “sell” your teaching methods over and over.

5. Don’t just make a recording on any subject but try to steer it in a way to augment units you are teaching in one of your courses. This way you can further the unit, even if you have to ‘assign’ the listening item, or you can use it as a collection of materials students can listen to on a voluntary basis. For example, if you have a unit discussing Human Resources you can interview a friend about their experience in hiring or with working with colleagues.

6. Record your lessons. This is normally quite boring but it can be very effective if you just extract some of the jewels, ancedotes you tell your students, special tips on learning English, fun facts, a story about your travels, etc.

I am also trying some projects along this line and am starting to post them at GCAST.

>Is English learning golf?

>At teacher compared learning various sports to practicing and drilling in English learning when he said, “This is like saying that the only way for a goalie to get better at soccer is by playing soccer games. Golf players should never go to driving ranges, because they can’t get a sense of the lie of the land there. Tennis players should never practice against a wall because the wall won’t spin the ball the way another player will. Baseball players should spurn hitting practice because it lacks the context of the position of the players.”

No, I don’t think it’s the same. Can we really compare becoming proficient in English to becoming proficient in sports? Wouldn’t we say that English communication is infinitly more complex than sports?

Take golf, for example, the number of variations for a putt are highly limited compared to the number of variations in expressing something in English. In fact, many skills in sports are dependant on the player being able to replicate the motions the same way every time.

That is why repetitious practice can help players. They practice their swing over and over and over until they are like a machine. Of course, in the game, the lay of the land may require some judgements in how to hit the ball but those judgments are calculated into the stroke that the player has mechanically practiced.

Perhaps there are only a few ways to sink a putt but there can be a hundred ways to explain you are going to the store to buy some sugar. I’m sure Tiger Woods would disagree but I believe language is more complex than golf and they cannot be learned in the same way.

Drilling and repeating is not effective. Students can learn English by using English following Krashen’s theories of Comprehensible Input.

>Grammar teaching – a fading star

>A teacher said, “That is what I wanted to hear – ‘Communicative Language Teaching doesn’t exclude grammar or even translation’ !!!”

Rest assured, Grammar will never be without a job.

Up until the 1970’s, Grammar used to be the mega movie star of English teaching, a true prima donna. Grammar was simply adored by all fans; teachers and students, alike. Grammar’s name featured prominently on every textbook or coursebook. People memorized every aspect of Grammar. It was near worship. Then Chomsky released his blockbuster which, while not widely accepted by the entire public, marked a new era and saw Grammar’s popularity begin to wane. Grammar suffered further humiliation when Krashen came along. Now many people respect Grammar just as many people regard Casablanca or Gone With The Wind, one of the greatest movies ever made. But when most people want real entertainment, they don’t go to these old movies any more.

That doesn’t mean Grammar is out of a job by any means. It still plays an important supporting role in many movies just like many former stars appear in smaller parts in movies and TV shows. (Alan Alda even won an Oscar for his supporting role in the new movie Little Miss Sunshine.)

As Krashen puts it:

“I recommend delaying the teaching of these rules until more advanced levels. I would first give acquisition a chance, and then use conscious knowledge to fill in some of the gaps. There is no sense teaching rules for Monitoring that will eventually be acquired. Grammar, thus, is not excluded. It is, however, no longer the star player but has only a supporting role.”

More from Krashen:

In my reviews of these studies, I have concluded that they confirm the correctness of the Comprehension and Monitor Hypotheses: they show only that even after substantial grammar study, even very motivated students show only modest gains in accuracy, and these gains occur only on measures that encourage a focus on form. Truscott (1998) has arrived at very similar conclusions.

Some have interpreted this position as a claim that all grammar teaching is forbidden. Not so. There are two good reasons for including grammar in the EFL curriculum.

The first is for “language appreciation,” otherwise known as “linguistics.” Linguistics includes language universals, language change, dialects, etc. The second is to fill gaps left by incomplete acquisition and places in which idiolects differ from the prestige dialect. Society’s standards for accuracy, especially in writing, are 100%: We are not allowed “mistakes” in punctuation, spelling or grammar. One public error, in fact, can result in humiliation. Even well-read native speakers have gaps, places where their grammatical competence differs from accepted use.

Consciously learned rules can fill some of these gaps, which are typically in aspects of language that do not affect communication of messages. The place to use this knowledge is in the editing stage of the composing process, when appealing to conscious rules will not interfere with communication.

I recommend delaying the teaching of these rules until more advanced levels. I would first give acquisition a chance, and then use conscious knowledge to fill in some of the gaps. There is no sense teaching rules for Monitoring that will eventually be acquired.

Grammar, thus, is not excluded. It is, however, no longer the star player but has only a supporting role.

More: http://www.sdkrashen.com/articles/eta_paper/02.html

>Teacher knows "Father Knows Best"!

>I have a sort of Krashenistic view on learning. I like to have tons of material to offer my students and let them select what particular items appeal to them. Although Krashen is focused on reading books, I think in our multimedia world we can extend that to films, TV shows, podcasts, etc. One problem is finding enough material to offer that is i + 1.

Here is a website with some “old time radio” shows. The English is about the same speed as VOA Special English but even slower, clearer and simpler and much more so compared to normal speech or movies. It would be suitable for mid to upper-intermediate students. Not all of the shows are at the same level.

Below is a sample of the dialog from “Father Knows Best” , an old radio show but very popular. Although some proper nouns are unique the rest of the dialog is fairly basic and actually very repetitive, all of which contributes greatly to comprehensibility.

Following the sample is a textual analysis, a frequency list of words used in the sample and the vocabulary levels of the words.

See how accessible this language is. Except for “poultry breeder”, “gazette”, “mining” and “Harvard”, I think intermediate students could understand nearly everything.

Jim: Margaret
Margaret: Yes, Dear?
Jim: What’s this?
Margaret: What’s what, Dear?
Jim: This.
Margaret: Oh, that. That’s a magazine.
Jim: I know it’s a magazine but what are we doing with a copy of the “Poultry Breeder’s Bulletin and Gazette”.
Margaret: Well, we had our choice between that and “Mining Engineers Monthly Manual”.
Jim: So you took the “Poultry Breeder’s Bulletin and Gazette”?
Margaret: Naturally, we wouldn’t have any use for a magazine about mining engineers, would we?
Jim: Margaret.
Margaret: Yes, Dear.
Jim: Have you developed a sudden interest in poultry?
Margaret: No.
Jim: Poultry breeders?
Margaret: Don’t be ridiculous.
Jim: Well, you don’t just go out and buy a thing like this without some reason.
Margaret: I didn’t go out. He brought it here.
Jim: Who did?
Margaret: Well, I don’t know his name but he was a very nice boy and he’s working his way through Harvard…
Jim: You mean…we bought a subscription for this thing?
Margaret: It was only four dollars, Jim. If I knew you were going to make all this fuss…
Jim: I’m not making a fuss. It’s just that I don’t see any reason to throw money away on things we don’t need.
Margaret: People ALWAYS need magazines.
Jim: Alright, but why did you have to choose the “Poultry Breeder’s Bulletin and Gazette”?
Margaret: I told you, Dear. It’s because we couldn’t use “Mining Engineers Monthly Manual”.

Find more Father Knows Best at RADIO LOVERS.


Here are the vocabulary level statistics, the percentage of words in each level. For contrast I included vocabulary levels for NY Times and Voice of America Special English. (These levels could vary as the samplings I used were not very large):

K1 Words – the list of the 1000 most common words:
84.07% (NYT 71.95, VOASE 77.02)

K2 Words – the list of the 1001-2000 most common words:
2.65% (NYT 3.96, VOASE 5.18)

AWL Words – the Academic Word List:
0.88% (NYT 8.52, VOASE 4.76)

Off-List Words:
12.39% (NYT 15.56, 11.94)


Family Word List
family_[number of tokens]

K1 Words:
about_[1] all_[1] always_[1] and_[6] any_[2] away_[1] be_[13] because_[1] between_[1] boy_[1] bring_[1] but_[3] buy_[2] choose_[2] could_[1] dear_[4] develop_[1] do_[9] dollar_[1] for_[2] four_[1] go_[3] have_[4] he_[5] here_[1] i_[7] if_[1] in_[1] interest_[1] it_[5] just_[2] know_[3] like_[1] make_[2] mean_[1] miner_[3] money_[1] month_[2] name_[1] nature_[1] need_[2] no_[1] not_[9] of_[1] oh_[1] on_[1] only_[1] out_[2] people_[1] reason_[2] see_[1] so_[1] some_[1] take_[1] tell_[1] the_[3] thing_[3] this_[9] through_[1] throw_[1] to_[3] use_[2] very_[1] way_[1] we_[8] well_[3] what_[4] who_[1] why_[1] with_[1] without_[1] work_[1] would_[2] yes_[2] you_[7]
all_[1] away_[1] boy_[1] bring_[1] buy_[2] could_[1] dear_[4] go_[3] here_[1] know_[3] like_[1] make_[2] money_[1] month_[2] need_[2] only_[1] see_[1] take_[1] tell_[1] thing_[3] through_[1] throw_[1] very_[1] way_[1] well_[3] work_[1] yes_[2]

K2 Words:
copy_[1] engine_[3] nice_[1] sudden_[1] nice_[1] sudden_[1]

AWL Words:
AWL families: [1:1:2] manual_[2]

Off-list words:
alright_[1] breeder_[3] breeders_[1] bulletin_[3] fuss_[2] gazette_[3] harvard_[1] jim_[1] magazine_[3] magazines_[1] margaret_[2] poultry_[5] ridiculous_[1] subscription_[1]

>The problem with teaching grammar

>A teacher asked me: “…how else will a non-native speaker approach the levels of accurately applied grammar needed to pass international standard oral English exams except by studying grammar?”

Well, I would suggest not that way.

Today I was speaking with Jack, an upper intermediate student at an American company, and he was telling me about Tom Hanks and that “she” has made many great movies.

Why did Jack, an upper intermediate student, call Tom Hanks a she? Because he was unfamiliar with the grammar rule? Could the problem be remedied if he had 26 people sitting around him telling him what grammar errors he made?

Immediately, I pointed out the mistake to Jack but in the course of the following conversation and with me continually pointing it out to him he only got it right about 50% of the time. All of you on this list have students like that, don’t you? What’s the problem with these students? Are they stupid? Are they lazy? I don’t think so.

Krashen is not against teaching grammar. He thinks it is useful to round out the training of a student who may be having a particular problem with a particular grammar point.
Some people are better than others at using their Monitor to correct their grammar. Heavy Monitor use hinders fluency. And even for the best of the Monitor users the efficiency of self-monitoring is very limited.

Many teachers will disagree with me but I think some rote learning and rule explanations can be helpful but not necessary to get a learner off the ground. But after the beginner stages the learner will need a lot of comprehensible input.

Then the teacher challenged me: “And is there any evidence, Dave, that CI has demonstrably improved Chinese students with their use of pronouns?”

Please note, I was only using the “he/she” to show in a simple way the difficulty of students employing even the simplest of grammar rules when speaking.

This is not only my observation and not limited to pronoun usage. As another teacher puts it,

“EFL students in Taiwan have studied English grammar extensively. However, it is interesting to note that most of these students make routine mistakes on structures which they know the rules for when speaking.

“Chinese students will, during classroom conversation, regularly omit the s that must be attached to the third – person singular form of verbs. The students indeed know the rules governing the third – person singular, as they have studied English grammar ad nauseam in high school.

“Unfortunately, most of these learners are not able to apply the rules during conversation. Mistakes include, “He live with his sister” or “She go to work at 8 o’clock.” Lightbown (Brown, 2000: 275) states that, ‘Knowing a language rule does not mean one will be able to use it in communicative interaction.’ Chinese students have learned and know many of the formal grammatical rules; however, they have not truly acquired the structures.”

Furthermore, Krashen points out that,

“Research consistently shows that conscious grammatical knowledge has a limited function, acting only as an editor of what is already produced.

“In support of this position are studies showing that even advanced students with a great deal of interest and experience with grammar are able to access only a small amount of their grammatical knowledge when actually using language. Even when students are deliberately focused on form and taught rules carefully, the impact of grammar study is weak.”