Construct validity vs. a tight ship

I have a fantasy where I’m one of those hardass disciplinarian teachers, the kind whose students march in synchronized rows to the auditorium where I’m given some kind of award that these kinds of teachers always seem to get. While I’m standing at the podium of my real-life classroom daydreaming like this, one of my students turns in a piece of paper with a coffee stain on it after walking into class 40 minutes late, and while imperfect, the assignment shows clear development in language control and engagement. Suddenly, my “runs a tight ship” fantasy collides with my inner applied linguist, which naturally wants to reward development, even as my inner disciplinarian threatens to complain about me to my inner department head.

Being a strict teacher sometimes works against the construct validity of  grades. That is, enforcing one’s lateness, makeup, and assignment format policies drags the crosshairs of one’s grades away from “English ability” (however one defines that) and toward “not annoying the teacher by making them put out small fires all semester” or more charitably “being a responsible person in general”.

This problem comes to vex me when I’m looking at a well-written paper turned in 30 minutes late without a cover sheet or a proper MLA header. Is the difference between A and C supposed to be the ability to follow abstract rules in principle? Where is that in the course outline, or to take a wider perspective, in any definition of linguistic competence?

I honestly can’t imagine a class where this (taking points away for non-language-related violations) doesn’t happen at all – and I can imagine my colleagues’ frowns of consternation that I would even consider loosening late work policies in favor of some persnickety notion of validity we all last heard about in our MA programs – but I’ve noticed a trend in my work recently of lots of points hinging on things like “finding parking before class” or “understanding the difference between submitting in Google Classroom and submitting on Canvas” which I don’t remember being a prominent part of any theory of SLA. After all, I do have more eggs in the basket of “effective pedagogue” than “well-oiled adjunct faculty cog”.

Below is a partial list of things that have been at times worth more points in my classes than any variety of English competence, hidden point-stealers from beyond the realm of language ability:

•  “Please read and follow the directions for this assignment” Actually, “being able to read an assignment” is clearly part of the competence that should be tested in an academic English class – but assignmentese tends to have its own idiom and in my view needs to be taught explicitly as its own topic. Ditto for lines like “work must be accomplished without external assistance beyond what is available to all students in the language lab” in the syllabus.
  
• “Please turn this assignment in on time” There is a clear relationship between accomplishing a specific language-related task within a time limit and linguistic competence. That said, I don’t think that extends to assignments that took all weekend and are being turned in 15 minutes late on Monday morning.
  
• “If you don’t understand the directions, email me instead of waiting for the due date to ask a question in person” There is an unhealthy tendency to run all competences in ESL through the bottleneck of writing on computers, but I don’t really see a way around this particular issue. After a sour experience with a student who abused the ability to contact me, I don’t give students any other ways to reach out.
  
• “Write your name” I do give points for people who forgot to write their names after I ask the class who this mysterious person named “Essay 2” is, but I definitely also give them a hard time about it. Some teachers don’t give points for work that is not gradable on time for any reason, and I certainly empathize. Not writing your name is essentially hijacking a few minutes of class time and precious mental resources of the teacher’s that could be going toward his seldom-read blog.
  
• “Have friends that you can ask for help for days that you were absent” Given that Canvas, while equally available to everyone and therefore “fair”, is nonetheless intimidating to the point of inaccessibility for some low-intermediate ESL students, a lot of assignments’ scores depend instead on having a friend who will collect homework sheets for you, explain them for you, and sometimes turn them in for you. If you don’t use Canvas and don’t have friends like this in class, your competence as reflected in grades will drop.

Parts of this list make me react the same way my colleagues probably would: “You can’t seriously be talking about accepting…” or “Well, SOME teachers may not want their students to be responsible, but in MY classes…” and I understand this. I just want to point out that being responsible isn’t one of the areas of linguistic competence we all learned in grad school.

New Kanji, pt. 2

今学期が終わるまでブログを書くつもりはなかったけど、ちょっとしたことがあったので、書かざるを得なかった。

火曜の朝、授業が終わったら「ページビューが激増中」とのWordpressからのプッシュ通知に気づいた。結構久しぶりなことだった（バイエマックニールさんがリツイートしてくれた時以来なかった）ので、興味津々でページビュー数表示を見てみた。2年前に書いたポストが、急に600ビューに達していたのは意外だった。次の日は1000ビュー近くまで上がった。かつて一番ビュー数が多かった偏差値についてのポストを、はるかに追い抜かしている。その急に人気が出たポストとは、New Kanjiというポスト。日本を出る直前に書いた、半分風刺・半分本気で「新しい漢字を作ろう」という趣旨だ。読者が、どのサイトからこのブログに辿り着いたかを見てみると、なんとRedditからだった。

Redditでリンク元のスレッドを読んで、ちょっとがっかりした。基本的に、「私たちの大切な日本語がこの馬鹿なアメリカ人に汚染されちまっている」とか、「日本人に説教しやがるアメリカ人よ、日本から出て行け」という、型にはまったネトウヨみたいなコメントばかりだった。しかもコメントを残している人は全員、日本滞在の英語圏の人（日本人から見れば「外国人」）のようだ。来日外国人のネットコミュニティーで、そういう輩が私のポストで、互いにvirtue signallingやin-group signallingのコメントをしあって、ネガティブなコメントが結構積み重なっていた。

その後、もう一つのスレッドに取り上げられていることに気づいた。それはbadlinguisticsというフォーラムで、先のRedditよりは、少しは知性レベルが高いことが書いてあった。でもコメントは、やっぱりほとんど「馬鹿アメリカ人は漢字を理解しない」というアングルから書いたもので、理論ではなくそのタブーに基づいていた。やっぱり匿名でコメントするサイトとはこういうものなんだ、と思った。意地の悪いコメントを読んでいると、もちろん不愉快な気分になるわけだけど、インターネット上では、誰でもバカになるという事実を改めて実感すると冷静にもなれる。

結局、日本で長く生活した経験があって、日本に家族がいて、家庭で今でも毎日日本語を使っていて、１２年前に日本語能力試験１級を取得して、応用言語学の修士号をとった私は、Redditのナルトファンボイに何を言われても構わないと思える。

さて…

By popular demand, here is another new kanji gallery! (Some by me, some by my wife)

 

チンパンジー

ダックスフンド

スーパーノバ（超新星）

酸素

排気ガス

ゾンビ

2-kanji compound: トランプ

One-kanji version: トランプ

アメリカンドッグ

A chunky good man

My first instinct when confronted with a hot political controversy is to go over the language used to express it with a fine-toothed comb*. It is in this spirit that I noticed the great frequency with which the chunk “a good man” being thrown about in reference to the recent Kavanaugh hearings, either for Kavanaugh himself or good men in the abstract.

Example courtesy of Lindsay Graham:

This good man should not be destroyed. If you legitimize this process by one vote short, woe be unto the next person.

My first thought was that if they had nominated a woman like Amy Coney Barrett instead, and she had had similar alleged incidents in her past, this rhetorical nugget would be unavailable for her defense. No phrase of similar cultural heft exists for women, although the phrase “a good woman” is just as grammatically possible as “a good man”. My guess as to why is that while the image that the phrase “good man” conjures up in people’s minds is an archetype of competence, dependability, and bonhomie (emphasis on the homme), “good woman” only vaguely summons the idea of something like a loyal wife. Woe be unto any woman nominated for a high position who needs her character defended with reference to implicit cultural norms.

PIctured: The tool of a good man, not a good woman. Photo by Pixabay on Pexels.com

I did a quick search of BYU’s corpora to see if the linguistic record backs up my instincts.

The string “a good man” gets 12372 hits on iWeb and 1643 on COCA.

I’ll leave it to you to dig into the contexts.

Meanwhile, “a good woman” gets 1807 on iWeb and 262 on COCA.

That’s almost 7x the frequency on iWeb (the larger of the two corpora) and more than 6x in the other.

COCA, unlike iWeb, allows you to separate hits by their source (magazines, academic journals, spoken, etc.), yielding a bit more information of what kinds of contexts “a good man” and “a good woman” are typically uttered in.

Within that about 6x overall on COCA, “a good man” is used about 10x as often in spoken contexts, 5x in fiction, 5x in magazines, 8x in newspapers, and almost 4x in academic writing. For some reason, Bush’s first term in particular also sees a spike in use of “a good man” – perhaps this relates to the politics of that time, including the 2004 election, where adherence to certain conceptions of manhood were a subtext for the Kerry and Bush campaigns.

For comparison, “man” and “men” occur a total of 582,307 times in COCA vs. 483,248 times for “woman” and “women”. This means that “a good man” does indeed occur much more often relative to “a good woman” than one would predict if the phrase were simply a matter of combining parts of speech according to the rules of grammar. “A good man” is a chunk bordering on an idiomatic expression for a certain, known, type of person, like a “people person” or a “person of faith”. This particular type of person’s goodness seems to depend on their not being a woman.

(* The iWeb Corpus lists “fine tooth comb” as about 3x as frequent as “fine toothed comb”, neither with a hyphen. This makes my usage rather pedantic to the point of being functionally incorrect.)

Nudgework

With my teacherly black robes in mind, I’ve been giving my students a particular type of assignment recently that maximizes use of the teacher’s ability to give orders. This type of homework, which I think is worth exploring as a new teacher- and student-friendly homework paradigm, has a few qualities in common:

• It places students in situations where input is likely.
• It does so with directions that on the surface have little to do with language learning.
• It involves minimal paperwork.
• It requires little or no reporting or reflecting.

This kind of homework is ideal for low-intermediate students, particularly in a place like Southern California where it is very easy to spend one’s entire life surrounded by L1 speakers (of Chinese, Korean, Spanish, Arabic, Farsi, or what have you), and a little nudge is all that might be needed to gain practically unlimited meaningful input or interaction. The goals are increasing input, building confidence, and setting up habits which will facilitate language learning throughout the students’ lives.

Photo by Pixabay on Pexels.com

As an example, one of my recent homework assignments requires students to get a tutor’s signature and then draw (not take) the tutor’s picture (our college offers a variety of tutoring services). There is nothing in the homework assignment that requires them to seek a specific lesson from the tutor or even to ask a question. The point of the homework is just to put the student in a situation (talking to a tutor face-to-face) where their instincts will lead them to inevitably have some kind of interaction, as well as give them the experience of having talked to a tutor and thus taking away some of their reticence to do so in the future.

This kind of homework tends to rely on human instincts to interact or to latch on to things that are interesting to them in any given situation to be effective for language learning. If a nudgework assignment is to “sit at a café for 30 minutes without your smartphone”, it’s very likely that their trip will include a conversation with a barista and incidental input from Auto Trader or Healthy Living magazines. It’s the kind of thing students could feasibly do anytime, but a directive from someone standing in front of the white board makes much more likely.

The downside is that input is simply likely with this type of assignment, not guaranteed. A much more straightforward language assignment, along the lines of “read this and then prove you read it with a detailed report”, makes input practically inescapable (and makes it much easier to talk about it as a class if everyone read the same thing). The downside of a traditional assignment is that the input will probably be of less interest to the students, and a large part of the time taken for the assignment will be devoted to proving to the teacher that the input happened rather than getting more input. Krashen isn’t the last word on these things anymore, but I still tend to think input is superior to reporting when it comes to moving the interlanguage ball forward.

In my teaching career, this nudgework idea evolved out of my Language Logs, which are a regular type of assignment I give that follow the format: “Find examples of grammar point X on the Internet or in real life. Copy and paste/post a photo on the discussion board and describe the grammatical form.” The Language Logs are still a regular part of all of my classes, but particularly in my lower intermediate classes, I wanted a kind of assignment that would facilitate more natural interaction/input and have less emphasis on metalinguistic analysis.

As a last perk, there isn’t much to grade.

The affective issues cliff

Some issues that exist in students’ lives affect their academic performance in ways that are unfair and impossible to ignore – kids and jobs are two massive time-sucks that interfere with schoolwork, but everything from mental illness to changing bus routes in the city mediate how well students do academically. Particularly at community colleges, which exist specifically to serve non-traditional students, teachers have a duty to incorporate some treatment of what we call “affective issues” such as anxiety, work or family obligations, or negative self-image into our courses. The duties can be written into law, as with mandated reporting of suspected abuse (a legal obligation) or simply commonly accepted but not required “best practices” such as accepting late work or generally making yourself available to meet with students outside of class. Then there are the students who don’t have anything that has been recognized as an “affective issue” but are clearly affected away from classwork and towards League of Legends, and not much in our training says we owe these students’ issues any particular redress at all.

In American healthcare, there exists a phenomenon known as the “Medicaid cliff”, which is an income threshold below which you are provided with cheap and reliable healthcare, and above which you are required to buy expensive, complicated private insurance. A lot of people decry the existence of this drop-off in public coverage even if they support Medicaid in principle (that principle being that people who cannot afford health insurance still deserve to live). The cliff comes about because our definition of “poverty” has to end somewhere, and once you’re out of poverty, the government no longer takes an active interest in how you afford to stay alive. Thus, you could have an income of 130% of the federal poverty line and qualify for single-payer health care in the form of Medicaid, or get a raise to 140% of the federal poverty line and suddenly have to buy a private health insurance plan with a $7500 deductible. Pass the magic line and you transform magically from a victim of forces beyond your control to an upstanding and responsible citizen.

Read on if my point isn’t obvious enough yet.

Photo by Danne on Pexels.com

Best class ever, except for gathering statistics

I just turned in grades for the summer intermediate skills class I had over the summer, and set out to compile some useful statistics just as in previous semesters. Unfortunately, the data doesn’t* say much… because the scores were too high. Every assignment category, from attendance to final exams, was higher than the same class in spring semester, sometimes by ridiculous amounts. For example:

Attendance

Spring 2018: 90.09%, standard deviation 12.9

Summer 2018: 95.85%, stdev 7.5
(including one student who was out of the country for 2 weeks in a row – otherwise it’d be 97.17% and stdev 3.97)

Homework

Spring 2018: 84.36%, stdev 14.0

Summer 2018: 96.19%, stdev 7.9

Grammar quizzes

Spring 2018: 83.9% stdev 15.5

Summer 2018: 87.95%, stdev 9.7

As the standard deviations imply, there wasn’t much spread between the highest- and lowest-performing students, and even less between the many varieties of average-performing students. This was basically a good thing – there is no upside to a large spread of homework scores for pedagogy or validity. It’s not as if my homework scores failed to validly** track some educational construct because everyone was doing uniformily well.

Summer classes have a lot of perks. They meet twice as often, 4 days instead of 2, letting you take 2 days out of the week for something like student presentations without creating a yawning 2-week gap between instructional days. The students are more dedicated – only 20% of my students in summer were taking any other classes. The class meetings are shorter too, which probably helped my students, about half of which worked. Of those who worked, 19% had morning shifts, 73% had afternoon shifts, 64% evening, and 30% night (between 10 PM and 5 AM). Despite these fairly high numbers, almost everyone did almost all the homework and did about equally well on projects, quizzes, and tests.

It’s a bit of a shame for data collection, because although I haven’t cracked the statistics textbook I was convinced to buy, I did start the term with a much more complete questionnaire on my students’ jobs, as you can see. In the end, presumably because of the narrow spread in grades overall, this yielded some correlations (evening shifts were most negatively correlated with final grades) but no significant differences between working and non-working students, even at p<0.05. Scores were too similar to yield differences among different types of students.

This didn’t confirm my big hypothesis, that working students are at an unfair disadvantage given that community colleges exist specifically to serve non-traditional college students. I have, however, narrowed my hypotheses for future work surveys a bit because “hours spent using English at work” was about as negatively correlated with final grades as “total weekly working hours” (-0.46 vs. -0.39). Next semester, I will have to compare hours of English use at work to overall hours of English use to see if working students have more opportunity for input and output, and if this is so, ask why this doesn’t yield significantly higher performance on at least some types of assignments. I can anecdotally see that students who use English at work benefit from doing so. I need to plan my classes so that this is reflected in their grades, or at least not reflected negatively.

If future classes continue to find a difference between working and non-working students irrespective of whether they use English at work, it may be that the type of competence fostered by having a service industry job where you use your L2 doesn’t outweigh the necessity of somewhat narrow means of assessment in an academic ESL class. For example, it’s inevitably my working students who have the most natural grasp of which modals can be used for formal and casual requests, offers, or requests for permission, but unless they can carve out time between the end of their shift and taking care of an elderly parent to show that grasp in an assignment, their homework scores won’t be commensurate with their abilities. The lens of assessment is only focused on students when they do assignments, not when they practice modals for hours at a time every day at work.

It may help make my classes more equitable in this regard if I minimize the amount of “assignment” they have to do to prove they’ve been getting input, while still being hard enough to fake to prevent cheating. I have a type of assignment that is aimed at dragging along as much real-world practice as possible for a minimum of “assignment”, which is sometimes very close to “go get some input, then check a box when you’re done”. An example is a book report where the students choose any graded reader from our library and then turn in a pretty perfunctory worksheet that they could probably do in 5 minutes. To me, this type of assignment is justified by 1) the high ratio of interlanguage-developing work to product, 2) the promotion of available outside resources, and 3) the high motivation levels of my intermediate students, which reduce the odds of cheating (also, the low grading time). If a similar assignment said “start 3 conversations and fill out a perfunctory report afterwards”, this could reward the time my working students spend talking without pandering specifically to them.

Maybe the future of all ESL homework is “get input, and prove you got it”. At least at the intermediate (i.e., not academic writing) level, this probably maximizes opportunities for interlanguage development while minimizing what are in my view the less valid aspects of the grading process.

*”Data” is an uncountable noun, unless you are writing for an academic journal or have a mobile datum plan like Titus Andromedon’s that just comes with the one.

**Now that we’ve split the infinitive, the only question is whether we’ll be able to fuse it in a stable way and provide unlimited, grammatical energy for the entire world.

Stereotype threat and ELT

When they speak their L2, our language students are undertaking something mentally taxing while monitoring themselves for mistakes and in the presence of people who expect them to struggle. This is almost a perfect recipe for stereotype threat.

What is stereotype threat?

In case you’re behind on your liberal intelligentsia required reading, stereotype threat (ST) is “subtle reminders of stereotypes that presume the incompetence of certain groups. This ‘threat in the air’ can cue a concern with confirming these stereotypes that can impair the ability to perform up to one’s potential” (Schmader, 2010, p. 14). In short, fear of confirming negative stereotypes about one’s group takes up mental overhead and reliably and demonstrably hurts performance, and triggering this effect is as simple as reminding people of the stereotype before giving the test. This effect is real and has been replicated many times with many different groups – men and women most often (Johns et al, 2005) , but also White men and Asian men (Aronson et al, 1999) – even tracking implicit bias scores on a national scale in a study with hundreds of thousands of subjects (citation too long – click here).

The precise psychological mechanism behind this is apparently under dispute, but general anxiety along the lines of an affective filter (I don’t think I need a citation for this) seems not to be it. Rather, mental resources seem to be taken up imagining ways to fail. Working memory available for the task is reduced in favor of monitoring oneself for mistakes and spontaneous, intrusive negative thoughts (Cadinu et al., 2005; Schmader, 2010).

What’s it got to do with ELT?

I think it should be clear that our students, to varying degrees, are under ST almost all the time. Less obvious is the fact that many teachers are, too. Learners and teachers alike may be facing a penalty to their language use that has a cause besides incomplete knowledge or acquisition.

If placed in a context where stereotypes are known and especially when ELLs are implicitly being compared to NSs, we can expect ELLs to perform worse than otherwise at language-mediated tasks (I’m reminded of this article in which the author recounts having found solace in the relatively language-free world of math in her teenage ESL years – the Asian math stereotype probably didn’t hurt either). We can expect NNS teachers also to make more errors when they know they are being evaluated by NS teachers. Performance is likely to be worse both for input and for output in both cases. As Rydell et al (2010) write, “At least in the present task setting, we see that overt emphasis on the existence of the stereotype both prevents learning … and, to a significant degree, prevents expression of learning that has already occurred” (p. 14046) (Yes, that is the real page number). ST is likely to affect students in the ELT classroom as well – an ESL class in the USA where everyone thinks “Asian students don’t talk” is probably worse for Asian students, all other things held equal, than an EFL class in Asia taught by a NNS.

These conditions follow NNSs outside the classroom, too. Even well-known ELLs like Arnold Schwarzenegger and Melania Trump have jokes made at the expense of their intelligence – mostly based on accent, the hardest part of NS speech to adopt. It doesn’t seem to have discouraged Arnold, but whenever he speaks in public he is one error away from confirming everyone’s perception of him. I have certainly experienced this feeling myself, and I didn’t have Arnold’s fortitude. Our students’ lives are replete with conditions in which they will be judged on their language use and stereotypes about their national group or ESL students in general are known.

The mechanisms of ST appear especially designed to vitiate SLA. Working memory is probably as relevant as a danger to language acquisition as it is to math, but hyperconsciousness of mistakes is clearly more relevant to language use than many other subjects. Teachers may be instructing students to do exactly that as an effort to encourage noticing (Schmidt, 1993), usually thought of as a good thing, while ST holds self-monitoring to be an inhibitor of performance (Schmader, 2010). It is possible that while noticing facilitates acquisition in the long run, it distracts from other essential processes (e.g. understanding the intentions of one’s conversation partner) in the short run.

In fact, one effect of ST has been described as reduced ability to sort relevant information from noise, which would clearly hurt students’ ability to notice and turn input to intake. One such experiment used Chinese characters to test women’s “visual processing”, and found a ST effect of clear relevance for language teachers (Rydell et al, 2010).

Questions for study

If you haven’t noticed yet, I haven’t done any research to back up my suspicions that ST is an extremely important future topic for SLA. I do have a few ideas for research questions:

• Assuming ST for SLA is real, how will we know? Grammaticality judgment tests seem the most analogous to the mathematics-based research on ST that has been the most common so far, but wouldn’t real-time processing skills (like participating in a conversation) show a larger effect?
• What constitutes a “trigger” for ST? Is the presence of NSs enough, or the possibility that NSs will read/see the students’ output, or just a box for “nationality” at the top of the test?
• For that matter, how would you avoid triggering ST or creating a control group? ST-inducing instructions often look something like Candinu et al’s: “recent research has shown that there are clear differences in the scores obtained by men and women in logical-mathematical tasks” (2005 p. 574) (Interestingly, they left it to the test-takers to infer that women did worse, not just different, on these tests.) Non-ST instructions either simply leave that part out or explicitly negate it, along the lines of “… that there are no differences in the scores…”. How would this condition be accomplished plausibly on a language test of NNSs? Would it be believable to preface a test with, “This grammar topc shows no measurable differences between American and Chinese test-takers”?
• What groups have relevant stereotypes that could trigger ST? Is “ESL student” enough of a stigma? (Many students act as if it were.)
• Are different ELT classes more threatening than others? Can interventions by the teacher mitigate ST, for example by making explicit the fact that students will not be judged by NS norms?

References

Aronson, J., Lustina, M. J., Good, C., Keough, K., Steele, C. M., & Brown, J. (1999). When white men can’t do math: Necessary and sufficient factors in stereotype threat. Journal of experimental social psychology 35/1, pp. 29-46.

Cadinu, M., Maass, A., Rosabianca, A., and Kiesner, J. (2005). Why Do Women Underperform under Stereotype Threat? Evidence for the Role of Negative Thinking. Psychological Science 16/7 pp. 572-578. Available at: http://www.jstor.org/stable/40064271

Johns, M., Schmader, T., & Martens, A. (2005). Knowing is half the battle: Teaching stereotype threat as a means of improving women’s math performance. Psychological Science 16/3, pp. 175-179.

Rydell, R. J., Shiffrin, R. M., Boucher, K. L., Van Loo, K., Rydell, M. T., & Steele, C. M. (2010). Stereotype threat prevents perceptual learning. Proceedings of the National Academy of Sciences of the United States of America, 107/32 pp. 14042-14047. Available at: http://www.jstor.org/stable/25708852

Schmader, T. (2010). Stereotype Threat Deconstructed. Current Directions in Psychological Science 19/1 pp. 14-18. Available at: http://www.jstor.org/stable/41038531

Schmidt, R. (1993). Awareness and Second Language Acquisition. Annual Review of Applied Linguistics 13, pp. 206-26.

Tokyo Medical University and anticipatory childcare penalties

As you may have heard, in a scandal that incorporates almost everything toxic about Japan’s educational, workplace, and oyaji cultures, Tokyo Medical University, a top medical school in Japan, was discovered to have had a secret policy of discriminating against female applicants to their medical program for almost the last decade. Specifically, they reduced female applicants’ entrance exam scores to 0.9 or 0.8 of their actual levels so as to keep the female population of incoming classes down to 30%. College entrance exams being pretty much the single most important determiner of a young person’s career prospects, lots of people are livid in Japan, and the international press has picked up the story. It’s quite a blood-boiler.

Here are a few random thoughts that squeak out between the anger:

The shortest physically productive pre-activity

It’s common knowledge among ESL teachers that any activity should be prefaced with a pre-activity. Not only textbooks, but handouts, powerpoint presentations, and even off-the-cuff improvisations by the teacher are prefaced by some schemata-activating questions, discussion points or pictures, the theory being that students are better able to engage with the main activity after their brains have all the context-appropriate neurons firing.

I have never seen any evidence that the principle of preparing students for any activity should only apply to main activities, however, so it stands to reason if we are right about the importance of schema activation that these pre-activities could use pre-activities of their own. If you follow my logic, responsible pedagogy should involve a preⁿ⁺¹-activity before any preⁿ-activity.

This presents a philosophical and practical pedagogical problem, as responsible language teaching now seems to entail an infinite series of increasingly small preⁿ-activities, which in an echo of Zeno’s arrow, mean that we can never actually physically reach the start of our main activity.

With an eye toward helping my fellow language teachers out of this conundrum, I would like to propose a pragmatic (no pun intended) solution to the preⁿ-activity dilemma, which is this:

Teachers should not have pre-activities whose length would be shorter than the time it takes for light to travel from the teacher to the nearest student. The last pre-activity whose length is longer than this time will be called the shortest physically productive pre-activity.

I will illustrate this principle by assuming a few values:

• The speed of light is 3.08 * 10⁸ m/s
• Our main activity is planned for 20 minutes (1200 seconds).
• Our pre¹-activity is 5 minutes, or 1/4 the main activity, and schemata-activating pre-activities for other pre-activities will also last 1/4 as long as the activity that they prepare for.
• For the sake of simplicity, the nearest student is seated 3.08 m from the teacher.

 

Given our values for the distance between the teacher and the nearest student, it takes 1/10⁸ seconds for light to travel from the teacher to the nearest student. Any preⁿ-activity that takes less time than that will be over before the last one can be physically sensed by the students.

It’s worth pointing out that light is the fastest known physical phenomenon in the universe; no cognitive activity (or any activity with a physical substrate) can outpace it, no matter how “quick” the student. The speed of light is, therefore, a crucial property to consider when planning preⁿ-activities whose length is measured in millionths of seconds.

The question then is what value of n in a preⁿ-activity yields an activity whose length is less than 1/10⁸ seconds. I solved for n by plugging in the values above:

1200/4ⁿ = 1/10⁸

1200=4ⁿ/10⁸

120000000000=4ⁿ

120000000000^1/n=4

Doing these calculations the old-fashioned way, I come up with a value of 18 for n as the last preⁿ-activity whose length is longer than the time it takes for light to travel from the teacher to the student. Therefore, with the assumptions above, a main activity should be preceded by exactly 18 pre-activities, the 18th pre-activity being the shortest physically productive pre-activity.

It is to be hoped that teachers integrate this knowledge into their lesson planning thoughtfully and responsibly.

Clichés of polyrhythm/meter in metal

Here is my fourth-ever metal post. The others continue to get a few views every day from people who are probably disappointed by the rest of the content of this blog (and vice versa for English teachers who collide with metal posts). Obviously, my music theory metalanguage is quite shabby, but I’m going to try here to describe a few things I’ve heard over and over again in metal bands.