這篇短文只要三十七秒就能讀完-- 醫院的那扇窗
有兩個人都生了重病，住在同一間病房裡。其中一個人，每天下午可以在病床上坐起 一小時，以便排除肺部的積水，他的病床靠著病房唯一的窗戶，另外一個人必須整天平躺在病床上。
兩個人整天聊個不停，聊妻子家人，聊房子工作，聊部隊與度假。
每天下午，靠窗的人在坐起來的時候，會向室友寒喧幾句，把窗戶外的景象一一描述 出來，另外一個人也開始靠著這個小時，經由外面的活動與色彩，
讓自己的世界變得更開闊、更有生氣。
從窗戶看出去，可以看到一座公園，裡面有一個美麗的湖，鴨子與天鵝在水面上，孩童在駕駛玩具船，年輕的情侶在繽紛的花叢裡怜飽A遠處可以看到美麗的城市地平 線。
靠窗的人在描述的時候，巨細無遺，另外一個人會閉起雙眼，想像這幅美麗的景象。
在一個溫暖的下午，有一隊遊行經過，靠窗的人開始描述起來，另外一個人卻聽不到樂隊聲，但是他可以看，在他心裡的眼睛裡，看到靠窗的先生口中的話語。
日子一天一天過去。一天早上，日班護士進來準備洗澡水，發現靠窗的人已經失去了生命，在睡夢中平靜安詳死去。護士很難過，醫院人員隨後把屍體移走。
不久，一切似乎恢復正常，另外一個人問護士，是否可以移到靠窗的病床，
護士欣然同意，在確定病人舒適後，隨即離去。
另外一個人忍著痛，用手緩緩撐起自己，想看看外面的真實世界。
他緩慢而勉強的轉頭，看到的卻是一面白色的牆壁。
他問護士，他那位亡故的室友為什麼要把窗外描述的這麼五彩繽紛。
護士說道，這位室友是個盲人，是看不到牆壁的，「或許他只是想給你打氣」。
收場白：姑且不管自己的情況，給別人帶來快樂，也會帶給自己莫大的快樂。
同悲會讓悲傷減半，同樂卻會讓快樂加倍。
如果你想感覺富有，就倚靠你自己，倚靠那些金錢買不到的一切所有。
「今天就是一件禮物，知道為什麼今天與金添同音嗎？」。
這封信不知起自何人，但是讀過的人會帶來好運。
2007年4月9日星期一
52 PROVEN STRESS REDUCERS
| 1. Get up fifteen minutes earlier in the morning. The inevitable morning mishaps will be less stressful. 2. Prepare for the morning the evening before. Set the breakfast table. Make lunches. Put out the clothes you plan to wear, etc. 3. Don't rely on your memory. Write down appointment times, when to pick up the laundry, when library books are due, etc. ("The palest ink is better than the most retentive memory."- Old Chinese Proverb) 4. Do nothing you have to lie about later. 5. Make copies of all keys. Bury a house key in a secret spot in the garden. Carry a duplicate car key in your wallet, apart from your key ring. 6. Practice preventive maintenance. Your car, appliances, home and relationships will be less likely to break down "at the worst possible moment." 7. Be prepared to wait. A paperback book can make a wait in a post office line almost pleasant. 8. Procrastination is stressful. Whatever you want to do tomorrow, do today; whatever you want to do today, do it now. 9. Plan ahead. Don't let the gas tank get below onequarter full, keep a well- stocked "emergency shelf'' of home staples, don't wait until you're down to your last bus token or postage stamp to buy more, etc. 10. Don't put up with something that doesn't work right. If your alarm clock wallet, shoe laces, windshield wipers-whatever-are a constant aggravation, get them fixed or get new ones. 11. Allow 15 minutes of extra time to get to appointments. Plan to arrive at an airport one hour before domestic departures. 12. Eliminate (or restrict) the amount of caffeine in your diet. 13. Always set up contingency plans, "just in case." ("If for some reason either of us is delayed, here's what we'll do..." Or, "If we get split up in the shopping center, here's where we'll meet.") 14. Relax your standards. The world will not end if the grass doesn't get mowed this weekend. 15. Pollyanna-Power! For every one thing that goes wrong, there are probably 10 or 50 or 100 blessings. Count 'em! 16. Ask questions. Taking a few moments to repeat back the directions that someone expects of you, etc., can save hours. (The old "the hurrieder I go, the behinder I get" idea.) 17. Say "No!" Saying no to extra projects, social activities and invitations you know you don't have the time or energy for takes practice, self-respect and a belief that everyone, everyday, needs quiet time to relax and to be alone. 18. Unplug your phone. Want to take a long bath, meditate, sleep or read without interruption? Drum up the courage to temporarily disconnect. (The possibility of there being a terrible emergency in the next hour or so is almost nil.) 19. Turn "needs" into preferences. Our basic physical needs translate into food, water, and keeping warm. Everything else is a preference. Don't get attached to preferences. 20. Simplify, simplify, simplify. 21. Make friends with nonworriers. Chronic worrywarts are contagious. 22. Take many stretch breaks when you sit a lot. | 23. If you can't find quiet at home, wear earplugs. 24. Get enough sleep. Set your alarm for bedtime. 25. Organize! A place for everything and everything in its place. Losing things is stressful. 26. Monitor your body for stress signs. If your stomach muscles are knotted and your breathing is shallow, relax your muscles and take some deep, slow breaths. 27. Write your thoughts and feelings down on paper. It can help you clarify and give you a renewed perspective. 28. Do this yoga exercise when you need to relax: Inhale through your nose to the count of eight. Pucker your lips and exhale slowly to the count of 16. Concentrate on the long sighing sound and feel the tension dissolve. Repeat 10 times. 29. Visualize success before any experience you fear. Take time to go over every part of the event in your mind. Imagine how great you will look, and how well you will present yourself. 30. If the stress of deadlines gets in the way of doing a job, use diversion. Take your mind off the task and you will focus better when you're on task. 31. Talk out your problems with a friend. It helps to relieve confusion. 32. Avoid people and places that don't fit your personal needs and desires. If you hate politics, don't spend time with politically excited people. 33. Learn to live one day at a time. 34. Everyday, do something you really enjoy. 35. Add an ounce of love to everything you do. 36. Take a bath or shower to relieve tension. 37. Do a favor for someone every day. 38. Focus on understanding rather than on being under stood, on loving rather than on being loved. 39. Looking good makes you feel better. 40. Take more time between tasks to relax. Schedule a realistic day. 41. Be flexible. Some things are not worth perfection. 42. Stop negative self-talk: "I'm too fat, too old, etc..." 43. Change pace on weekends. If your week was slow, be active. If you felt nothing was accomplished during the week, do a weekend project. 44. "Worry about the pennies, and the dollars will take care of themselves." Pay attention to the details in front of you. 45. Do one thing at a time. When you are working on one thing, don't think about everything else you have to do. 46. Allow time every day for privacy, quiet and thinking. 47. Do unpleasant tasks early and enjoy the rest of the day. 48. Delegate responsibility to capable people. 49. Take lunch breaks. Get away from your work in body and in mind. 50. Count to 1,000, not 10, before you say something that could make matters worse. 51. Forgive people and events. Accept that we live in an imperfect world. 52. Have an optimistic view of the world. Most people do the best they can. |
The Top 5 Brain Health Foods
The Top 5 Brain Health Foods
The BrainReady Top 5 Brain Health Foods
Many of you have asked us for a simple list of the very best, proven natural foods & drinks for optimum brain (and body) health.
Ah, everyone loves lists these days, it seems. So while there are numerous natural foods, drinks, herbs and supplemental products that possess brain & body-enhancing properties, we've done the research for you and created a list of five all-natural, widely-available foods that we believe represent the BrainReady Top 5 Brain Health Foods in the world.
How did we pick? Our list is based a variety of factors, ranging from overall proven health benefits (through multiple peer-reviewed, valid scientific studies from around the world over many years), our own experience here at BrainReady using these foods regularly, general reports from consumers of these foods over the years, proven safety and lack of contraindications from these foods, and general availability/ease of incorporation of these foods by the most people in most countries.
It's important to keep in mind that just because we didn't include a food like Turmeric or Sage or Walnuts in our Top 5, this doesn't mean that those foods aren't incredibly brain and health-friendly too; it's just that the foods in our Top 5 have been demonstrated to possess more 'yes' counts across our range of criteria, particularly brain health benefits.
So without further adieu, here are the BrainReady Top 5 Brain Health Foods worth considering adding to your diet if you haven't already (of course, make sure you don't have any contraindications with any of these foods by consulting your health care provider first if you're not sure). These are not listed in order of priority, as all are beneficial in different ways and via different mechanisms:
1) Wild Salmon
Wild salmon is not only an incredible food for brain health, it qualifies as incredible across virtually every other health standard as well and is clearly one of the healthiest foods that one can eat. Period. As we've discussed in our BrainReady Blog feature on salmon, wild salmon (not farm-raised) in particular is a true brain food: one of the best sources of Essential Fatty Acids (such as the all-important Omega-3), a rich source of high-quality non-land animal protein, low saturated fat, generally among the lowest amounts of contaminants (such as mercury) among seafood, and other health properties -- wild salmon can help do everything from improve your brain matter, your mood, your synaptic connections, your arteries, reduce your risk of stroke and Dementia and Alzheimer's and much more.
It's also important to know that only WILD salmon has been shown to contain the highest levels of the good stuff that your brain & body crave...as wild-caught fish grow and evolve their muscles, tissues and fat levels the hard way, fighting for survival of the fittest in the oceans and rivers. By contrast, many or most farm-raised salmon exist in a locked-up, artificial and sometimes contaminated environment and thus have to be fed food (or worse, color added later just before going to market!) to make them LOOK orange and healthy instead of white and sickly. Ewww!
While there ARE some good sustainable, eco-friendly, health-focused farmed salmon operations out there, I'll take my salmon fresh and wild and naturally orange in color, thank you...as long as wild salmon remains a mostly non-endangered fish species (particularly in the Pacific Northwest and Alaska). Even if it costs more. Your brain and body are worth it.
2) Cacao Beans
Wait, you mean chocolate, right? Hurray! I've been looking for an excuse to hit that vending machine and grab a candy bar...it has chocolate in it, so now it's actually healthy, right?
WRONG. Well, mostly wrong: what's healthy is the cacao bean, minimally processed. This amazing, hedonistic bean is one of the world's longest-revered foods (think 'time of the Aztecs' old) and has in recent years been shown to be a veritable powerhouse of cognitive enhancement, mood and bliss-enhancement (thanks in part to the Theobromine in cacao), antioxidants, flavonoids, catechins and many other brain & body-enhancing elements. In fact, chocolate has been very recently cited by some top health professionals and researchers to be THE single most exciting health food, and as more research continues to pour in, the more true this appears to be. And we discussed the health benefits of chocolate (and walnuts) in our BrainReady Blog feature recently (click here to read it)
How is this possible, something that only recently was thought of as an unhealthy, dangerous, guilty indulgence...a sign of dietary decadence, now being hailed as beneficial to everything from brain health to skin elasticity to cardiovascular health to anti-cancer and pretty much everything in between? It's simple: chocolate does not equal cacao bean, nor vice-versa; most candy and chocolate bars contain not only low levels of cacao bean compared to other unhealthy ingredients such as sugars, milk fat, artificial flavorings and so on, but the quality and processing of the cacao used in these products is often of low health benefits due to everything from alkalization (e.g. "Dutch process cocoa") to refining and processing and over-roasting the healthy elements right out of the beans.
So if you want the real stuff, the best bet is to either use 100% organic non-alkalized cocoa powder from a high-quality maker who minimally processes the cocoa to ensure that the health properties are retained, or, second best, choose only high cacao percentage dark chocolate bars (typically at least 75% cacao content or higher, but we suggest 85% or higher), also from a high-quality provider.
Here at BrainReady, we've found it easiest to just mix a large spoonful of 100% organic cocoa powder with a bit of espresso, organic unsweetened soy milk and some cinnamon, even a sprinkle of cayenne red pepper...yes, cayenne pepper!) in the morning (and sometimes again in the afternoon) to make a drink not unlike what the ancient Aztecs used to make: it's one tasty, brain & body-fueling drink that gives you your pure cacao bean dose without the sugars and milk fat, you get your protein from the soy milk, brain-enhancing (and blood sugar-stabilizing) cinnamon, a little brain-enhancing caffeine from the espresso and theobromine (plus more) from the chocolate, and a digestion, brain-enhancing and respiratory-enhancing kick from the cayenne pepper. No sweetener needed (sweet is overrated these days...but we'll save that topic for another BrainReady feature).
All that in one tasty drink that really gets you going!
In summary, yes: chocolate is a brain health food. Or more specifically, the cacao bean is a true brain health and body health food. And worth considering adding to your diet (barring any allergies to chocolate or contraindications, of course).
For some recommendations on our favorite dark chocolate and cocoa sources/makers out there, feel free to send us an email at info@brainready.com and we'd be happy to share some of our favorites (also check our BrainReady Store for links to a couple widely available).
3) Matcha (Tencha-grade green tea powder)
So those green tea bags at the office water cooler aren't the ultimate form of green tea? Do I need something better? What brand of tea bags ARE better?
Oh dear. Where to begin. If you're used to getting your tea from tea bags, you'll need to put aside notions of brands, tea bags, and tea in general for a moment and take a big step back: as we discussed in our BrainReady health feature on the health benefits of Matcha, Matcha -- which is the finely-ground powder of the highest-quality, most revered part of the shade-grown green tea plant (Gyokuru leaves...the very top part of the shade-grown green tea plant then dried to become"Tencha") carefully grown, selected, dried, stone-ground, processed and prepared according to an ancient Japanese tradition, is not your average green tea. Nor does it come in tea bags. Nor do you brew it, boil it, or consume the watery extract from leaves.
When you drink real stone-ground Japanese Matcha, you're not only drinking the arguably highest-quality, most carefully cultivated green tea variety, you're actually consuming it all -- you're eating the whole thing, you're drinking the green tea leaf itself, whole, in powdered form mixed with hot (but not boiling!) water. The powder itself is so rich in chlorophyl (from the shade growing) that it's literally bright green, and when mixed with water it becomes a rich, bitter-sweet, Kermit-colored concoction whose effects you can actually FEEL almost immediately after drinking a cup (or small bowl, if doing it the traditional Japanese way) of it.
Perhaps best known as the traditional, ceremonial drink tightly interwoven with the Buddhist ceremonies and tradition, Matcha's unique effects on the brain were a perfect fit for those monks in Japan preparing to endure 12-hour straight meditation sessions: calming and focusing while stimulating at the same time, it's no wonder that Matcha became integrated into the monks' meditative practices (thanks in large part to the amino acid L-Theanine).
And when you drink real Matcha yourself, you too will...understand.
But as Matcha has become more known (and researched) in the West recently, even more exciting are the health properties being discovered and reported (and yes, now marketed as buzzwords by tea companies..have you seen that EGCG commercial for a bottled green tea maker?). You've probably already heard about many of the health benefits of green tea in general, so imagine those benefits amplified exponentially (up to 10x or more!) in the case of Matcha...as you're drinking an extremely concentrated, ultra-high quality form, straight. Antioxidants, catechins, vitamins such as C and A, even Fluoride. And the meditatively calming yet focusing effects of L-Theanine.
But perhaps best known is EGCG: Epigallocatechin Gallate, a compound found uniquely in green teas which has been shown to possess almost unbelievable anti-cancer, anti-aging and overall health benefits...so much so that 'EGCG' has become a health marketing buzzword for tea companies. Here's where Matcha is really unprecedented: Matcha contains exponentially higher amounts of EGCG than regular brewed green tea (including high-quality fresh Sencha green tea). Matcha also has over 33 times the antioxidant levels of antioxidant powerhouse blueberries(!)...hard to believe, but real.
So if you're looking for a great way to get a veritable blast of antioxidants (not to mention EGCG, vitamins, minerals, etc.), boost your brain with Zen-like concentration and physical benefits, it's hard to beat Matcha. And you can't get that with a tea bag.
A word of warning: not all Matcha is created equal! There are many non-Japanese (as well as Japanese) products out there called 'Matcha' that are often nothing more than powdered low-quality green tea, or worse, a mixture of ingredients with artificial green coloring(!). The stone grinding method is also very important, as low-quality Matcha is sometimes 'exploded' instead of stone-ground, reducing the health properties.
For more details on Matcha, check out our BrainReady Blog article entitled "Dump those green tea bags: go Matcha!", or email us here at info@brainready.com
4) Acai berries & Blueberries (tie)
We recently reported on the comprehensive health benefits from the highly unusual South American native berry called Acai...a berry that possesses not only all of the antioxidant, vitamin and brain benefits of other purple berries such as blueberries and blackberries but also (oddly, for a berry) contains Essential Fatty Acids like Omega-3's like salmon, and and is even high in protein.
Sounds like a a true superfood, right? It is. With proven ORAC antioxidant levels higher than any other berry ever tested, Acai's unique combination of health properties make it a true superfood for brain and body. Of course, we're talking about fresh Acai berries here...not some local generic health food shop pills claiming to contain Acai. And that's where the challenge can come in (hence our research and report on the best Acai products that we published recently), as Acai needs to be quickly processed (flash-freeze dried, flash-frozen, etc.) and maintained and processed if you're to get the full benefits of this berry outside of South America.
Fortunately, companies like Sambazon and Bolthouse have created amazing local growing and processing facilities to do exactly that, and we can now buy great Acai in various forms in the U.S., Australia, Europe and beyond these days including our personal favorite: the Sambazon organic Acai powder (their 'PowerScoop' product) as well as in Sambazon and Bolthouse refrigerated juice blends.
(You can read more about the amazing, unique health benefits of Acai in our BrainReady feature Acai here).
Then there's blueberries: it didn't seem fair to leave this time-honored, well-researched superfood off the list, particularly given its reputation as the 'brain berry' and its wide availability in fresh, original form (compared to Acai). And given how relatively easy it is to add blueberries to your daily diet, the combination of proven health benefits with ready availability make it a no-brainer to consider eating blueberries daily if possible. Think about it: what would your brain health, brain abilities, disease/risk profile, and overall health be like 5 or 10 or 20 years from now if you consumed blueberries every day? Exactly...
(For more specifics on blueberries, read our BrainReady feature entitled 'The Power of Blue, and You' by clicking here).
5) Coffee beans
Ah, coffee. So popular, so ubiquitous, yet still so surprisingly misunderstood when it comes to "healthy or not". How can this be?
You'd think that virtually everyone would be an expert on coffee these days, given the explosion of coffee chains like Starbucks over the last decade. Perhaps it's because the situation is much like chocolate: the coffee bean, much like the cacao bean, is incredibly rich with antioxidants, amino acids, vitamins and minerals. Fresh-ground gently roasted coffee bean powder (again, like with cacao) has numerous brain and body health benefits...yes, including the caffeine content which has recently been shown to be GOOD for the brain, not bad, and particularly in the area of antioxidants. Regular coffee consumption has been shown to actually reduce the risk of mental decline and diseases such as Dementia and Alzheimer's, and has also recently been found to be (shockingly) the "#1 source of antioxidants in the average American diet"...showing at once how health food-deprived the average diet continues to be while illustrating the surprising health benefits of something as common as coffee.
So where's the controversy and confusion? The problem comes in when coffee is combined with other unhealthy things, as is so commonly done: triple-carmel-double-whip-chocolate-creme-mocha-blast-freeze drinks, weak over-extracted brewed cheap poor quality coffee, coffee loaded up with artificial cream and sweeteners, you know the drill. Compare such carb, chemical and fat-laden concoctions with, say, a high-quality organic coffee freshly ground into an Espresso-grade powder and served as a couple shots of fresh espresso, straight? No comparison. This should be obvious, but surprisingly, many or even most people still don't get it.
Equally odd is that for many people, coffee is still viewed as a 'vice', something bad for you, something 'naughty' that should be avoided...as if it were akin to smoking cigarettes or pounding shots of tequila. The origin of this bizarre thinking comes partially from the effects of the caffeine (and other elements) which contribute to the stimulating effects of drinking coffee, and yes, for some people, coffee is contraindicated due to sensitivity to caffeine or gastrointestinal effects that coffee can sometimes produce.
But generally speaking, the coffee bean is a safe, true superfood. And when properly consumed in ideal forms (such as pure Espresso), it's one uniquely enjoyable beverage that also packs a host of brain and health-friendly properties to boot!
Read more about the specific health benefits of coffee (particularly Espresso) in our BrainReady Blog feature regarding Espresso versus regular coffee here).
So there you have it: a simple list of 5 brain health (and overall healthy) foods to consider adding to your diet (barring any allergies or contraindications) if you're interested in optimum brain health, overall health and longevity, and optimal aging.
It's important to note however that none of these foods nor any other food, drink, supplement or drug is a "wonder drug" that will produce miracles, especially overnight. There's no magic cure or wonder drug or superfood panacea that one should consume at the expense of an overall healthy diet and lifestyle, nor should you have unrealistic expectations around what any one of food can do for you. Rather, the foods cited here (like other healthy foods) are foods which have been shown to be particularly, often uniquely, beneficial when consumed consistently in moderation over time along with the rest of a healthy diet. And given that science is still in the comparative early days of understanding the complex mechanisms by which foods and nutrients affect the brain and body, it is likely that the subtle, complex interactions and combinations between several healthy food sources, combined with other healthy lifestyle practices such as exercise/healthy social interaction/genetic disposition and other factors, all work synergistically together to "balance the odds" in favor of (or against, if your diet is poor) optimum health.
Therefore, it's not enough to think "okay, I've added Matcha to my diet...I'm done!". That's why we here at BrainReady try to incorporate all of these five brain-friendly foods into the daily diet, along with other healthy foods and in combination with brain exercises, physical exercise, and overall well-being practices.
Nonetheless, these 5 foods are a great way to get started if you're interested in keeping your brain and body healthy as you age, and yes...one or more of them just might make that critical difference in your current and future health. So why not tip the scale in your favor, and feel great while doing it?
2007年4月5日星期四
The Socratic Method: Teaching by Asking Instead of by Telling
Teaching by Asking Instead of by Telling
by Rick Garlikov
The following is a transcript of a teaching experiment, using the Socratic method, with a regular third grade class in a suburban elementary school. I present my perspective and views on the session, and on the Socratic method as a teaching tool, following the transcript. The class was conducted on a Friday afternoon beginning at 1:30, late in May, with about two weeks left in the school year. This time was purposely chosen as one of the most difficult times to entice and hold these children's concentration about a somewhat complex intellectual matter. The point was to demonstrate the power of the Socratic method for both teaching and also for getting students involved and excited about the material being taught. There were 22 students in the class. I was told ahead of time by two different teachers (not the classroom teacher) that only a couple of students would be able to understand and follow what I would be presenting. When the class period ended, I and the classroom teacher believed that at least 19 of the 22 students had fully and excitedly participated and absorbed the entire material. The three other students' eyes were glazed over from the very beginning, and they did not seem to be involved in the class at all. The students' answers below are in capital letters.
The experiment was to see whether I could teach these students binary arithmetic (arithmetic using only two numbers, 0 and 1) only by asking them questions. None of them had been introduced to binary arithmetic before. Though the ostensible subject matter was binary arithmetic, my primary interest was to give a demonstration to the teacher of the power and benefit of the Socratic method where it is applicable. That is my interest here as well. I chose binary arithmetic as the vehicle for that because it is something very difficult for children, or anyone, to understand when it is taught normally; and I believe that a demonstration of a method that can teach such a difficult subject easily to children and also capture their enthusiasm about that subject is a very convincing demonstration of the value of the method. (As you will see below, understanding binary arithmetic is also about understanding "place-value" in general. For those who seek a much more detailed explanation about place-value, visit the long paper on The Concept and Teaching of Place-Value.) This was to be the Socratic method in what I consider its purest form, where questions (and only questions) are used to arouse curiosity and at the same time serve as a logical, incremental, step-wise guide that enables students to figure out about a complex topic or issue with their own thinking and insights. In a less pure form, which is normally the way it occurs, students tend to get stuck at some point and need a teacher's explanation of some aspect, or the teacher gets stuck and cannot figure out a question that will get the kind of answer or point desired, or it just becomes more efficient to "tell" what you want to get across. If "telling" does occur, hopefully by that time, the students have been aroused by the questions to a state of curious receptivity to absorb an explanation that might otherwise have been meaningless to them. Many of the questions are decided before the class; but depending on what answers are given, some questions have to be thought up extemporaneously. Sometimes this is very difficult to do, depending on how far from what is anticipated or expected some of the students' answers are. This particular attempt went better than my best possible expectation, and I had much higher expectations than any of the teachers I discussed it with prior to doing it.
I had one prior relationship with this class. About two weeks earlier I had shown three of the third grade classes together how to throw a boomerang and had let each student try it once. They had really enjoyed that. One girl and one boy from the 65 to 70 students had each actually caught their returning boomerang on their throws. That seemed to add to everyone's enjoyment. I had therefore already established a certain rapport with the students, rapport being something that I feel is important for getting them to comfortably and enthusiastically participate in an intellectually uninhibited manner in class and without being psychologically paralyzed by fear of "messing up".
When I got to the classroom for the binary math experiment, students were giving reports on famous people and were dressed up like the people they were describing. The student I came in on was reporting on John Glenn, but he had not mentioned the dramatic and scary problem of that first American trip in orbit. I asked whether anyone knew what really scary thing had happened on John Glenn's flight, and whether they knew what the flight was. Many said a trip to the moon, one thought Mars. I told them it was the first full earth orbit in space for an American. Then someone remembered hearing about something wrong with the heat shield, but didn't remember what. By now they were listening intently. I explained about how a light had come on that indicated the heat shield was loose or defective and that if so, Glenn would be incinerated coming back to earth. But he could not stay up there alive forever and they had nothing to send up to get him with. The engineers finally determined, or hoped, the problem was not with the heat shield, but with the warning light. They thought it was what was defective. Glenn came down. The shield was ok; it had been just the light. They thought that was neat.
"But what I am really here for today is to try an experiment with you. I am the subject of the experiment, not you. I want to see whether I can teach you a whole new kind of arithmetic only by asking you questions. I won't be allowed to tell you anything about it, just ask you things. When you think you know an answer, just call it out. You won't need to raise your hands and wait for me to call on you; that takes too long." [This took them a while to adapt to. They kept raising their hands; though after a while they simply called out the answers while raising their hands.] Here we go.
1) "How many is this?" [I held up ten fingers.]
TEN
2) "Who can write that on the board?" [virtually all hands up; I toss the chalk to one kid and indicate for her to come up and do it]. She writes
10
3) Who can write ten another way? [They hesitate than some hands go up. I toss the chalk to another kid.]
4) Another way?
5) Another way?
2 x 5 [inspired by the last idea]
6) That's very good, but there are lots of things that equal ten, right? [student nods agreement], so I'd rather not get into combinations that equal ten, but just things that represent or sort of mean ten. That will keep us from having a whole bunch of the same kind of thing. Anybody else?
TEN
7) One more?
X [Roman numeral]
8) [I point to the word "ten"]. What is this?
THE WORD TEN
9) What are written words made up of?
LETTERS
10) How many letters are there in the English alphabet?
26
11) How many words can you make out of them?
ZILLIONS
12) [Pointing to the number "10"] What is this way of writing numbers made up of?
NUMERALS
13) How many numerals are there?
NINE / TEN
14) Which, nine or ten?
TEN
15) Starting with zero, what are they? [They call out, I write them in the following way.]
0
1
2
3
4
5
6
7
8
9
16) How many numbers can you make out of these numerals?
MEGA-ZILLIONS, INFINITE, LOTS
17) How come we have ten numerals? Could it be because we have 10 fingers?
COULD BE
18) What if we were aliens with only two fingers? How many numerals might we have?
2
19) How many numbers could we write out of 2 numerals?
NOT MANY /
[one kid:] THERE WOULD BE A PROBLEM
20) What problem?
THEY COULDN'T DO THIS [he holds up seven fingers]
21) [This strikes me as a very quick, intelligent insight I did not expect so suddenly.] But how can you do fifty five?
[he flashes five fingers for an instant and then flashes them again]
22) How does someone know that is not ten? [I am not really happy with my question here but I don't want to get side-tracked by how to logically try to sign numbers without an established convention. I like that he sees the problem and has announced it, though he did it with fingers instead of words, which complicates the issue in a way. When he ponders my question for a second with a "hmmm", I think he sees the problem and I move on, saying...]
23) Well, let's see what they could do. Here's the numerals you wrote down [pointing to the column from 0 to 9] for our ten numerals. If we only have two numerals and do it like this, what numerals would we have.
0, 1
24) Okay, what can we write as we count? [I write as they call out answers.]
0 ZERO
1 ONE
[silence]
25) Is that it? What do we do on this planet when we run out of numerals at 9?
WRITE DOWN "ONE, ZERO"
26) Why?
[almost in unison] I DON'T KNOW; THAT'S JUST THE WAY YOU WRITE "TEN"
27) You have more than one numeral here and you have already used these numerals; how can you use them again?
WE PUT THE 1 IN A DIFFERENT COLUMN
28) What do you call that column you put it in?
TENS
29) Why do you call it that?
DON'T KNOW
30) Well, what does this 1 and this 0 mean when written in these columns?
1 TEN AND NO ONES
31) But why is this a ten? Why is this [pointing] the ten's column?
DON'T KNOW; IT JUST IS!
32) I'll bet there's a reason. What was the first number that needed a new column for you to be able to write it?
TEN
33) Could that be why it is called the ten's column?! What is the first number that needs the next column?
100
34) And what column is that?
HUNDREDS
35) After you write 19, what do you have to change to write down 20?
9 to a 0 and 1 to a 2
36) Meaning then 2 tens and no ones, right, because 2 tens are ___?
TWENTY
37) First number that needs a fourth column?
ONE THOUSAND
38) What column is that?
THOUSANDS
39) Okay, let's go back to our two-fingered aliens arithmetic. We have
0 zero
1 one.
What would we do to write "two" if we did the same thing we do over here [tens] to write the next number after you run out of numerals?
START ANOTHER COLUMN
40) What should we call it?
TWO'S COLUMN?
41) Right! Because the first number we need it for is ___?
TWO
42) So what do we put in the two's column? How many two's are there in two?
1
43) And how many one's extra?
ZERO
44) So then two looks like this: [pointing to "10"], right?
RIGHT, BUT THAT SURE LOOKS LIKE TEN.
45) No, only to you guys, because you were taught it wrong [grin] -- to the aliens it is two. They learn it that way in pre-school just as you learn to call one, zero [pointing to "10"] "ten". But it's not really ten, right? It's two -- if you only had two fingers. How long does it take a little kid in pre-school to learn to read numbers, especially numbers with more than one numeral or column?
TAKES A WHILE
46) Is there anything obvious about calling "one, zero" "ten" or do you have to be taught to call it "ten" instead of "one, zero"?
HAVE TO BE TAUGHT IT
47) Ok, I'm teaching you different. What is "1, 0" here?
TWO
48) Hard to see it that way, though, right?
RIGHT
49) Try to get used to it; the alien children do. What number comes next?
THREE
50) How do we write it with our numerals?
We need one "TWO" and a "ONE"
[I write down 11 for them] So we have
0 zero
1 one
10 two
11 three
51) Uh oh, now we're out of numerals again. How do we get to four?
START A NEW COLUMN!
52) Call it what?
THE FOUR'S COLUMN
53) Call it out to me; what do I write?
ONE, ZERO, ZERO
[I write "100 four" under the other numbers]
54) Next?
ONE, ZERO, ONE
I write "101 five"
55) Now let's add one more to it to get six. But be careful. [I point to the 1 in the one's column and ask] If we add 1 to 1, we can't write "2", we can only write zero in this column, so we need to carry ____?
ONE
56) And we get?
ONE, ONE, ZERO
57) Why is this six? What is it made of? [I point to columns, which I had been labeling at the top with the word "one", "two", and "four" as they had called out the names of them.]
a "FOUR" and a "TWO"
58) Which is ____?
SIX
59) Next? Seven?
ONE, ONE, ONE
I write "111 seven"
60) Out of numerals again. Eight?
NEW COLUMN; ONE, ZERO, ZERO, ZERO
I write "1000 eight"
[We do a couple more and I continue to write them one under the other with the word next to each number, so we have:]
0 zero
1 one
10 two
11 three
100 four
101 five
110 six
111 seven
1000 eight
1001 nine
1010 ten
61) So now, how many numbers do you think you can write with a one and a zero?
MEGA-ZILLIONS ALSO/ ALL OF THEM
62) Now, let's look at something. [Point to Roman numeral X that one kid had written on the board.] Could you easily multiply Roman numerals? Like MCXVII times LXXV?
NO
63) Let's see what happens if we try to multiply in alien here. Let's try two times three and you multiply just like you do in tens [in the "traditional" American style of writing out multiplication].
10 two
x 11 times three
They call out the "one, zero" for just below the line, and "one, zero, zero" for just below that and so I write:
10 two
x 11 times three
10
100
110
64) Ok, look on the list of numbers, up here [pointing to the "chart" where I have written down the numbers in numeral and word form] what is 110?
SIX
65) And how much is two times three in real life?
SIX
66) So alien arithmetic works just as well as your arithmetic, huh?
LOOKS LIKE IT
67) Even easier, right, because you just have to multiply or add zeroes and ones, which is easy, right?
YES!
68) There, now you know how to do it. Of course, until you get used to reading numbers this way, you need your chart, because it is hard to read something like "10011001011" in alien, right?
RIGHT
69) So who uses this stuff?
NOBODY/ ALIENS
70) No, I think you guys use this stuff every day. When do you use it?
NO WE DON'T
71) Yes you do. Any ideas where?
NO
72) [I walk over to the light switch and, pointing to it, ask:] What is this?
A SWITCH
73) [I flip it off and on a few times.] How many positions does it have?
TWO
74) What could you call these positions?
ON AND OFF/ UP AND DOWN
75) If you were going to give them numbers what would you call them?
ONE AND TWO/
[one student] OH!! ZERO AND ONE!
[other kids then:] OH, YEAH!
76) You got that right. I am going to end my experiment part here and just tell you this last part.
Computers and calculators have lots of circuits through essentially on/off switches, where one way represents 0 and the other way, 1. Electricity can go through these switches really fast and flip them on or off, depending on the calculation you are doing. Then, at the end, it translates the strings of zeroes and ones back into numbers or letters, so we humans, who can't read long strings of zeroes and ones very well can know what the answers are.
[at this point one of the kid's in the back yelled out, OH! NEEEAT!!]
I don't know exactly how these circuits work; so if your teacher ever gets some electronics engineer to come into talk to you, I want you to ask him what kind of circuit makes multiplication or alphabetical order, and so on. And I want you to invite me to sit in on the class with you.
Now, I have to tell you guys, I think you were leading me on about not knowing any of this stuff. You knew it all before we started, because I didn't tell you anything about this -- which by the way is called "binary arithmetic", "bi" meaning two like in "bicycle". I just asked you questions and you knew all the answers. You've studied this before, haven't you?
NO, WE HAVEN'T. REALLY.
Then how did you do this? You must be amazing. By the way, some of you may want to try it with other sets of numerals. You might try three numerals 0, 1, and 2. Or five numerals. Or you might even try twelve 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ~, and ^ -- see, you have to make up two new numerals to do twelve, because we are used to only ten. Then you can check your system by doing multiplication or addition, etc. Good luck.
After the part about John Glenn, the whole class took only 25 minutes.
Their teacher told me later that after I left the children talked about it until it was time to go home.
. . . . . . . . . . . . . .
My Views About This Whole Episode
The topic was "twos", but I think they learned just as much about the "tens" they had been using and not really understanding.
This method takes a lot of energy and concentration when you are doing it fast, the way I like to do it when beginning a new topic. A teacher cannot do this for every topic or all day long, at least not the first time one teaches particular topics this way. It takes a lot of preparation, and a lot of thought. When it goes well, as this did, it is so exciting for both the students and the teacher that it is difficult to stay at that peak and pace or to change gears or topics. When it does not go as well, it is very taxing trying to figure out what you need to modify or what you need to say. I practiced this particular sequence of questioning a little bit one time with a first grade teacher. I found a flaw in my sequence of questions. I had to figure out how to correct that. I had time to prepare this particular lesson; I am not a teacher but a volunteer; and I am not a mathematician. I came to the school just to do this topic that one period.
I did this fast. I personally like to do new topics fast originally and then re-visit them periodically at a more leisurely pace as you get to other ideas or circumstances that apply to, or make use of, them. As you re-visit, you fine tune.
The chief benefits of this method are that it excites students' curiosity and arouses their thinking, rather than stifling it. It also makes teaching more interesting, because most of the time, you learn more from the students -- or by what they make you think of -- than what you knew going into the class. Each group of students is just enough different, that it makes it stimulating. It is a very efficient teaching method, because the first time through tends to cover the topic very thoroughly, in terms of their understanding it. It is more efficient for their learning then lecturing to them is, though, of course, a teacher can lecture in less time.
It gives constant feed-back and thus allows monitoring of the students' understanding as you go. So you know what problems and misunderstandings or lack of understandings you need to address as you are presenting the material. You do not need to wait to give a quiz or exam; the whole thing is one big quiz as you go, though a quiz whose point is teaching, not grading. Though, to repeat, this is teaching by stimulating students' thinking in certain focused areas, in order to draw ideas out of them; it is not "teaching" by pushing ideas into students that they may or may not be able to absorb or assimilate. Further, by quizzing and monitoring their understanding as you go along, you have the time and opportunity to correct misunderstandings or someone's being lost at the immediate time, not at the end of six weeks when it is usually too late to try to "go back" over the material. And in some cases their ideas will jump ahead to new material so that you can meaningfully talk about some of it "out of (your!) order" (but in an order relevant to them). Or you can tell them you will get to exactly that in a little while, and will answer their question then. Or suggest they might want to think about it between now and then to see whether they can figure it out for themselves first. There are all kinds of options, but at least you know the material is "live" for them, which it is not always when you are lecturing or just telling them things or they are passively and dutifully reading or doing worksheets or listening without thinking.
If you can get the right questions in the right sequence, kids in the whole intellectual spectrum in a normal class can go at about the same pace without being bored; and they can "feed off" each others' answers. Gifted kids may have additional insights they may or may not share at the time, but will tend to reflect on later. This brings up the issue of teacher expectations. From what I have read about the supposed sin of tracking, one of the main complaints is that the students who are not in the "top" group have lower expectations of themselves and they get teachers who expect little of them, and who teach them in boring ways because of it. So tracking becomes a self-fulfilling prophecy about a kid's educability; it becomes dooming. That is a problem, not with tracking as such, but with teacher expectations of students (and their ability to teach). These kids were not tracked, and yet they would never have been exposed to anything like this by most of the teachers in that school, because most felt the way the two did whose expectations I reported. Most felt the kids would not be capable enough and certainly not in the afternoon, on a Friday near the end of the school year yet. One of the problems with not tracking is that many teachers have almost as low expectations of, and plans for, students grouped heterogeneously as they do with non-high-end tracked students. The point is to try to stimulate and challenge all students as much as possible. The Socratic method is an excellent way to do that. It works for any topics or any parts of topics that have any logical natures at all. It does not work for unrelated facts or for explaining conventions, such as the sounds of letters or the capitals of states whose capitals are more the result of historical accident than logical selection.
Of course, you will notice these questions are very specific, and as logically leading as possible. That is part of the point of the method. Not just any question will do, particularly not broad, very open ended questions, like "What is arithmetic?" or "How would you design an arithmetic with only two numbers?" (or if you are trying to teach them about why tall trees do not fall over when the wind blows "what is a tree?"). Students have nothing in particular to focus on when you ask such questions, and few come up with any sort of interesting answer.
And it forces the teacher to think about the logic of a topic, and how to make it most easily assimilated. In tandem with that, the teacher has to try to understand at what level the students are, and what prior knowledge they may have that will help them assimilate what the teacher wants them to learn. It emphasizes student understanding, rather than teacher presentation; student intake, interpretation, and "construction", rather than teacher output. And the point of education is that the students are helped most efficiently to learn by a teacher, not that a teacher make the finest apparent presentation, regardless of what students might be learning, or not learning. I was fortunate in this class that students already understood the difference between numbers and numerals, or I would have had to teach that by questions also. And it was an added help that they had already learned Roman numerals. It was also most fortunate that these students did not take very many, if any, wrong turns or have any firmly entrenched erroneous ideas that would have taken much effort to show to be mistaken.
I took a shortcut in question 15 although I did not have to; but I did it because I thought their answers to questions 13 and 14 showed an understanding that "0" was a numeral, and I didn't want to spend time in this particular lesson trying to get them to see where "0" best fit with regard to order. If they had said there were only nine numerals and said they were 1-9, then you could ask how they could write ten numerically using only those nine, and they would quickly come to see they needed to add "0" to their list of numerals.
These are the four critical points about the questions: 1) they must be interesting or intriguing to the students; they must lead by 2) incremental and 3) logical steps (from the students' prior knowledge or understanding) in order to be readily answered and, at some point, seen to be evidence toward a conclusion, not just individual, isolated points; and 4) they must be designed to get the student to see particular points. You are essentially trying to get students to use their own logic and therefore see, by their own reflections on your questions, either the good new ideas or the obviously erroneous ideas that are the consequences of their established ideas, knowledge, or beliefs. Therefore you have to know or to be able to find out what the students' ideas and beliefs are. You cannot ask just any question or start just anywhere.
It is crucial to understand the difference between "logically" leading questions and "psychologically" leading questions. Logically leading questions require understanding of the concepts and principles involved in order to be answered correctly; psychologically leading questions can be answered by students' keying in on clues other than the logic of the content. Question 39 above is psychologically leading, since I did not want to cover in this lesson the concept of value-representation but just wanted to use "columnar-place" value, so I psychologically led them into saying "Start another column" rather than getting them to see the reasoning behind columnar-place as merely one form of value representation. I wanted them to see how to use columnar-place value logically without trying here to get them to totally understand its logic. (A common form of value-representation that is not "place" value is color value in poker chips, where colors determine the value of the individual chips in ways similar to how columnar place does it in writing. For example if white chips are worth "one" unit and blue chips are worth "ten" units, 4 blue chips and 3 white chips is the same value as a "4" written in the "tens" column and a "3" written in the "ones" column for almost the same reasons.)
For the Socratic method to work as a teaching tool and not just as a magic trick to get kids to give right answers with no real understanding, it is crucial that the important questions in the sequence must be logically leading rather than psychologically leading. There is no magic formula for doing this, but one of the tests for determining whether you have likely done it is to try to see whether leaving out some key steps still allows people to give correct answers to things they are not likely to really understand. Further, in the case of binary numbers, I found that when you used this sequence of questions with impatient or math-phobic adults who didn't want to have to think but just wanted you to "get to the point", they could not correctly answer very far into even the above sequence. That leads me to believe that answering most of these questions correctly, requires understandingof the topic rather than picking up some "external" sorts of clues in order to just guess correctly. Plus, generally when one uses the Socratic method, it tends to become pretty clear when people get lost and are either mistaken or just guessing. Their demeanor tends to change when they are guessing, and they answer with a questioning tone in their voice. Further, when they are logically understanding as they go, they tend to say out loud insights they have or reasons they have for their answers. When they are just guessing, they tend to just give short answers with almost no comment or enthusiasm. They don't tend to want to sustain the activity.
Finally, two of the interesting, perhaps side, benefits of using the Socratic method are that it gives the students a chance to experience the attendant joy and excitement of discovering (often complex) ideas on their own. And it gives teachers a chance to learn how much more inventive and bright a great many more students are than usually appear to be when they are primarily passive.
[Some additional comments about the Socratic method of teaching are in a letter, "Using the Socratic Method".]
[For a more general approach to teaching, of which the Socratic Method is just one specific
form, see "Teaching Effectively: Helping Students Absorb and Assimilate Material"]
Hidden messages in words? Cool.
 clipped from mail.google.comThis
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2007年4月4日星期三
2007年3月26日星期一
Funny Quotes
clipped from: We spend the first twelve months of our children's lives teaching them to walk and talk and the next twelve telling them to sit down and shut up.
Phyllis Diller
People used to explore the dimensions of reality by taking LSD to make the world look weird.
Now the world is weird and they take Prozac to make it look normal.
Bangstrom
Health nuts are going to feel stupid someday, lying in hospitals dying of nothing.
Redd Foxx
Some people like my advice so much that they frame it upon the wall instead of using it.
Gordon R. Dickson
| If you wind up with a boring, miserable life because you listened to your mom, your dad, your teacher, your priest or some guy on TV telling you how to do , then YOU DESERVE IT. I never set out to be weird. It was always the other people who called me weird. Frank Zappa |
If a person wants to be atheistic, it's his God-given right to be an atheist.
Michael Patton
If you don't want to work, you have to work to earn enough money so that you won't have to work.
Ogden Nash
Half our life is spent trying to find something to do with the time we have rushed through life trying to save.
Will Rogers
God gave us a penis and a brain, but only enough blood to run one at a time.
Robin Williams
Have you ever noticed? Anybody going slower than you is an idiot, and anyone going faster than you is a maniac.
George Carlen
The less we know, the longer the explanation.
B.G.
Opinions are like feet. Everybody's got a couple, and they usually stink.
Jim Slattery
Who the hell wants to hear actors talk?
H. M. Warner, founder of Warner Brothers film studios, 1927
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