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Empowering the Future

Posted on July 13, 2010 by in Gifted, Thinking Skills

This is the first in a sum­mer series of guest posts by mem­bers of my personal/​professional learn­ing net­work. Mary Beth Hertz is the tech­nol­ogy teacher and tech­nol­ogy inte­gra­tor at Alliance for Progress Char­ter School in North Philadel­phia. She can be found on Twit­ter at @mbteach and blogs at Philly Teacher.

What I want to express in this blog post is not any­thing new or inno­v­a­tive. It is noth­ing that hasn’t been said before.  How­ever, it is some­thing that’s been mulling about in my brain while I was drink­ing my morn­ing cof­fee and watch­ing the Twit­ter stream from the Dis­cov­ery Edu­ca­tors Net­work Lead­er­ship Coun­cil Symposium.

A video kept get­ting re-​​tweeted in the stream so I fig­ured I’d bet­ter check it out.

You can watch the 2 minute video, Microsoft Labs 2019 Vision:

httpv://www.youtube.com/watch?v=DQdGvfV4WnU

As soon as it started I felt like I was watch­ing a car com­mer­cial. It was flashy, well-​​produced and fast-​​paced. I hon­estly was not that impressed. I guess what peo­ple felt was that it was a win­dow into what the future holds for tech­nol­ogy and dig­i­tal devices.

That I won’t deny.

The name on the video is “Microsoft Office Labs 2019 Vision Mon­tage.” This is the vision that Microsoft has for our future.

What’s wrong with this picture?

Many things.

For one, why are we let­ting Microsoft dic­tate what the future of dig­i­tal life will look like? We could make the same state­ment about Apple or Sony or any other com­pa­nies who man­u­fac­ture dig­i­tal prod­ucts.  Many of these com­pa­nies do use cus­tomer input and feed­back to improve their prod­ucts, but in real­ity we are all con­sumers of what these com­pa­nies feed us.

What does this mean for edu­ca­tion? It means that we need to be putting our stu­dents to the task of decid­ing what THEY want their future to look like. We live in a time unlike any other in his­tory. Our nat­ural resources are dis­ap­pear­ing, we have devices that are more pow­er­ful than ever before and we have tools that allow us to con­nect with peo­ple thou­sands of miles away in a mat­ter of seconds.

Com­pa­nies like Microsoft are not in the busi­ness of plan­ning for the future of our chil­dren as mem­bers of soci­ety or for the future of our global com­mu­nity. We must empower our stu­dents with that charge. It is they who will inhabit the future. We must also ensure that we empower ALL stu­dents to take part in the build­ing of future soci­ety, not just the ones who are priv­i­leged and can afford it.

There are many obsta­cles to over­come when we begin to ask our stu­dents to solve real world prob­lems. Solu­tions to real world prob­lems don’t fit on a stan­dard­ized test. Solu­tions to real world prob­lems take time to under­stand and even more time to solve. Solu­tions to real world prob­lems require a restruc­tur­ing of school as we know it.

I have been hav­ing var­i­ous con­ver­sa­tions (and some­times debates) about what it means to be a teacher and a learner in the 21st Cen­tury. Some of the con­ver­sa­tion has been focused around guid­ing stu­dents to under­stand­ing rather than deliv­er­ing con­tent, cre­at­ing learn­ing envi­ron­ments where learn­ing is a con­nected and social expe­ri­ence, and infus­ing tech­nol­ogy into learn­ing when it can trans­form the learn­ing expe­ri­ence.  The world our stu­dents will inhabit will require them to col­lab­o­rate with peers, under­stand social media tools and be prob­lem solvers within their own com­mu­ni­ties and the larger world.  We need to pre­pare them for that world.

Schools need to allow for tin­ker­ing. Tin­ker­ing with ideas, tin­ker­ing with mate­ri­als, tin­ker­ing with stu­dents’ per­ceived lim­i­ta­tions. Tin­ker­ing teaches chil­dren how to learn from fail­ure. Tin­ker­ing teaches chil­dren how to think about a prob­lem or a project from many per­spec­tives. Tin­ker­ing allows chil­dren to build self esteem and feel pride in what they do. Stu­dents who tin­ker are the stu­dents who build our future.

Some exam­ples of what I’m talk­ing about:

There are those who will look at these words as a ‘pipe dream,’ ‘utopia’ or ‘fairy­tale.’  To them I would argue that we must have a Vision. If Microsoft can con­struct a vision of what it thinks the world will look like in 2019 then we as edu­ca­tors, par­ents, com­mu­nity mem­bers, law­mak­ers and gen­eral stake­hold­ers in the world need to have a vision, too. Even more impor­tantly, we need to let our chil­dren begin to build their own vision for their own future and give them skills to make it real.

Don't Be Creative

Posted on July 13, 2010 by in Thinking Skills

Spilling the Beans

How would you sort these?

Take a look at this pic­ture. If I asked you to sort them into piles, how would you do it? OK, now do it again a dif­fer­ent way. No prob­lem, right? Again. Took a lit­tle longer for you to think of a way to sort them this time, didn’t it?

I’ve done this with kids and adults of var­i­ous ages. The first few times we sort, it’s sim­ple and straight­for­ward. The next few times it starts to get more chal­leng­ing. Even­tu­ally there are peo­ple sit­ting there think­ing, “There is no other way to sort these!”

When peo­ple have got­ten to this point, I’ve said some­thing along the lines of, “You have to stretch your think­ing. Be cre­ative!” This would often just result in frus­tra­tion for both of us.

Now I know why. Accord­ing to this arti­cle in Newsweek, telling some­one to “be cre­ative” can actu­ally have the oppo­site effect, clos­ing off their think­ing and mak­ing it more rigid.

So how can we help our stu­dents become more cre­ative? Try some of these strategies:

  • Plant the seed. Instead of a vague “be cre­ative,” tell some­one, “give me an idea that only you could come up with.” Accord­ing to Marc Runco of the Uni­ver­sity of Geor­gia, this sim­ple switch in direc­tions can dou­ble the student’s cre­ative output.
  • Make it messy. Cre­ativ­ity is squashed when stu­dents feel like they are look­ing for one right answer. Give stu­dents prob­lems that have mul­ti­ple solu­tions. Even bet­ter, give them prob­lems with no clear solu­tion. Muck­ing around in the prob­lem solv­ing process can free up cre­ative thinking.
  • Never accept the first answer. Even if a stu­dent gives you the response you were expect­ing, say “Can any­one think of another answer?” or “Is there another way to do that?” It sets an expec­ta­tion that one answer, even if it works, isn’t the end of the process but just the beginning.
  • Teach cre­ativ­ity tech­niques. We often think of cre­ativ­ity as some sort of ethe­real aura that some peo­ple have and some peo­ple don’t. In fact cre­ativ­ity is a skill and a process. It takes work and it can be taught. Tech­niques like SCAMPER can give kids a con­crete han­dle on some­thing that can seem abstract and complicated.
  • Reverse the roles. Instead of giv­ing an assign­ment to stu­dents, ask them to tell you what they would do if they were the teacher. “What would you ask the class to do to show they under­stood this unit?” Share the best ideas with the class and let them pick their assignment.
  • Get out. Chang­ing the per­spec­tive can change stu­dents’ think­ing. Hold a class in the cafe­te­ria, or the audi­to­rium, or the foot­ball sta­dium. Or in a liv­ing room, on the side­walk, or in an amuse­ment park. Rearrange your class­room or your schedule.

And before you think, “That’s not pos­si­ble in my school,” take a minute and come up with a way to make it hap­pen that only you could think of. Or ask your stu­dents to fig­ure it out. You might be sur­prised at what they think of.

So what did I miss? What are your sure­fire meth­ods for get­ting your stu­dents to think and work creatively?

The Myth of Shortcuts

Posted on November 10, 2009 by in Content and Methods, Thinking Skills

Shortcut road
Image by Bacon­Stand via Flickr

When I first moved to Bucks County, I knew the major routes to get around the area. I could, by rote, drive from my house to my in-​​laws’ house. I could also drive from my house to the school where I worked. I could flaw­lessly and effi­ciently travel those well-​​worn paths and arrive promptly at my destination.

One day, I received a sim­ple phone call from my wife: “My par­ents are mak­ing din­ner for us tonight. Just come straight from school and meet us there.”

Not a prob­lem. I left work at my usual four o’clock and with traf­fic arrived a lit­tle after 5:30 PM.

“What took you so long? Did you have a meet­ing after school?”

“No, I left as soon as I could.”

“But it should only take a half hour.”

“That’s impos­si­ble. It’s more than that just to our house, then another 40 min­utes to your parents.”

“Um, no, dear. There’s a more direct route.”

Read More…

Z-minus 10,000 Meters, Mr. Spock

Posted on August 31, 2009 by in Thinking Skills

NCC-1701-A
Image via Wikipedia

Stu­dents come to our class­rooms with many assump­tions and mis­con­cep­tions, and it is the teacher’s job to antic­i­pate them, rec­og­nize them, and cor­rect them. Here are a few that I have seen or heard about:

  • When you add or sub­tract, always line up the num­bers on the right
  • When you mul­ti­ply, the answer is always bigger
  • Rock­ets work because the exhaust pushes against the Earth
  • Mag­nets stick to any­thing made of metal
  • Christo­pher Colum­bus was try­ing to prove the world was round
  • The Amer­i­can Rev­o­lu­tion was fought over high taxes

Many stu­dent mis­un­der­stand­ings are sim­ply a lack of expe­ri­ence. There is a scene in the 1982 movie, Star Trek II: The Wrath of Khan, where Khan, the vil­lain, is try­ing to hunt down our heroes. Kirk flies the Enter­prise into a neb­ula in order to obscure the ship from Khan’s scan­ners. After a few min­utes, Spock makes an obser­va­tion about Khan:

SPOCK: Spo­radic energy read­ings port side, aft. Could be an impulse turn.

KIRK: He won’t break off now. He fol­lowed me this far. He’ll be back. But from where…?

SPOCK: He’s intel­li­gent, but not expe­ri­enced. His pat­tern indicates…two-dimensional thinking…

Kirk looks at him, smiles.

KIRK: All stop.

SULU: All stop, sir.

KIRK: Z-​​minus ten thou­sand meters. Stand by pho­ton torpedoes.


Like Khan, our stu­dents are intel­li­gent but have lim­ited expe­ri­ence. I won­der, though, how often we rein­force mis­un­der­stand­ings instead of cor­rect­ing them?

Often in the name of mak­ing our lessons acces­si­ble or under­stand­able we sim­plify con­cepts and use stereo­typ­i­cal exam­ples. Con­sider geom­e­try, for instance. When we draw shapes, they always look essen­tially the same:

Standard pattern block shapes

Stan­dard pat­tern block shapes

Tri­an­gles are always equi­lat­eral and point up. Rec­tan­gles are always wider than they are long and are par­al­lel to the ground. At the extreme, we even refer to shapes by dif­fer­ent names depend­ing on their ori­en­ta­tion. I actu­ally heard this state­ment dur­ing a math les­son once:

And if you turn this dia­mond, it will become a square.


The shape was always a square; the direc­tion it faces doesn’t make any difference.

Try these sug­ges­tions to avoid rein­forc­ing the mis­con­cep­tions of your students:

  • Know your own mis­con­cep­tions. Begin with the assump­tion that you may have picked up your own wrong ideas in school or from pop­u­lar media. Review the mate­r­ial ahead of time and look for places where you your­self didn’t quite get it right. (Inci­den­tally, if you read any of the items in my orig­i­nal list and thought, “What’s wrong with that?” you may want to do a lit­tle research and find the sub­tle prob­lems with them.)
  • Plan ahead for stu­dent mis­un­der­stand­ing. Learn the places where your stu­dents are likely to get con­fused or have pre­con­ceived ideas about a topic. Many mis­con­cep­tions are com­mon and repeated, so it’s easy to pre­pare for them.
  • Use a wide vari­ety of exam­ples. Delib­er­ately choose exam­ples that stretch stu­dents’ think­ing. Use coun­terex­am­ples to help them bet­ter define con­cepts in their minds.
  • Let stu­dents con­struct their own def­i­n­i­tions. By let­ting stu­dents build def­i­n­i­tions and expla­na­tions around exam­ples you use, you are encour­ag­ing them to ana­lyze the exam­ples and under­stand the con­cept deeply instead of just mem­o­riz­ing a sen­tence some­one else has pro­vided them. After they attempt to build a student-​​friendly expla­na­tion, you can come in and pro­vide more pre­cise vocab­u­lary where nec­es­sary to give them a more con­cise way to express it.
  • Expect stu­dents to explain and jus­tify their rea­son­ing. Some­times stu­dents are able to apply a rote algo­rithm accu­rately and get a cor­rect answer to a prob­lem with­out really under­stand­ing what they are doing. Ask­ing them to explain, even when their process seems obvi­ous to you, will give you insight into whether their think­ing is accu­rate or has flaws that need to be corrected.

Soon after Kirk changed his tac­tics to account for Khan’s mis­con­cep­tion, he was able to sneak up behind Khan’s ship, ulti­mately win­ning the bat­tle. While it is unlikely that the mis­con­cep­tions our stu­dents carry through school will result in such life or death cir­cum­stances, we can make our own jobs eas­ier by pre­vent­ing them in the first place.

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SPOCK
                             Sporadic energy readings port side,
                             aft. Could be an impulse turn.

                                           KIRK
                             He won't break off now. If he
                             followed me this far he'll be back.
                             But from where...?

                                           SPOCK
                             He's intelligent, but not experienced.
                             His pattern indicates two dimensional
                             thinking...

                   Kirk looks at him, smiles.

                                           KIRK
                             Mr. Saavik, all stop.

                                           SAAVIK
                             All stop, sir.

                                           KIRK
                             Descend ten thousand meters. Stand
                             by photon torpedoes.




                


                
      
                	                
   

            

            
                                                                            
            
            


                 
				
                
Teachers Can't Read Minds!

                
                

    Posted on August 21, 2009
    by 
    in Thinking Skills
    

                
                

                    






Future predicters


Image by Freekz0r via Flickr








Every year I stand in front of a group of new fourth or fifth grade stu­dents and face the most chal­leng­ing teach­ing task I’ve ever had: train­ing them to be telepathic.


I always begin with a magic trick. Each stu­dent chooses a two-​​digit num­ber. Then I walk them through a series of sim­ple cal­cu­la­tions result­ing in a new num­ber. On that page in their math book, they choose a pic­ture and mem­o­rize it.


Ear­lier in the day, a mys­te­ri­ous enve­lope had arrived in the class­room, marked “DO NOT OPEN…TOP SECRET.” I now open that enve­lope, reveal­ing a dupli­cate of the photo they all have mem­o­rized. I can read minds!


Of course, it doesn’t take long for the class to real­ize it was a trick, and I don’t deny it. In fact, I remind them that I began the exer­cise by telling them I was going to do a magic trick. The point is why I had to do a trick: teacher’s can’t read minds.


“So what does this have to do with math?” they ask me.


“Ah, excel­lent ques­tion,” I reply. “When you put an answer down on a math test or a home­work prob­lem, how does your teacher know what you were think­ing when you solved it?”


“Uh…she doesn’t?”


“Pre­cisely. But for us to teach you, we need to know how you’re think­ing so we can help you learn how to solve prob­lems bet­ter. Since we can’t read minds, what’s the only way for us to know what’s going on in your head as you’re solv­ing a math problem?”


If the les­son were out­side at night, this ques­tion would nor­mally be answered by the sound of crick­ets chirp­ing. One brave soul usu­ally raises a cau­tious hand: “Uh…we tell you?”


A sim­ple con­cept. A dif­fi­cult task. Actu­ally get­ting the thoughts from their heads into words—and even­tu­ally onto paper—is some­thing that takes much prac­tice and many exam­ples. Yes­ter­day I talked about one of the ways to begin this process by teach­ing and using the cor­rect vocabulary.


We need to teach stu­dents that math is not about rote manip­u­la­tion of abstract sym­bols. Those sym­bols, and the ter­mi­nol­ogy that goes along with them, are tools with two pur­poses: solv­ing prob­lems, and com­mu­ni­cat­ing ideas.


I’ve devel­oped a struc­ture that helps stu­dents orga­nize their think­ing and chunk the way they com­mu­ni­cate it. I tell them, “Wear Your C.A.P.E.”:






C
Cal­cu­la­tions
Show all of your math work and computations




A
Answer
Be sure to answer the ques­tion or ques­tions that the prob­lem asks!




P
Pro­ce­dure or Plan
Show each step of how you solve the prob­lem, includ­ing draw­ings, tables, etc.




E
Expla­na­tion
Explain your math reasoning—tell why you did what you did






The most dif­fi­cult aspect of this, of course, is the explanation—describing the why, not just the what. In order to help with this, I teach them the Magic Words. Just like using clue words to iden­tify the oper­a­tion in a word prob­lem (like “all together” sig­ni­fies addi­tion), these words can help to sig­nify their math­e­mat­i­cal rea­son­ing when they talk or write. (This list is based on an arti­cle by Diane Hurst pub­lished sev­eral years ago in the PA Math Assess­ment Hand­book, but no longer appears to be available):






to get
because




to find
since




to fig­ure out
there­fore




to show
so that






Stu­dents who learn to use these words cor­rectly will begin to unpack the rea­son­ing that is going on in their heads.


How could you adapt this to your sit­u­a­tion? What other sub­ject areas might it work for? Do you have other ideas about teach­ing stu­dents to be “tele­pathic” and com­mu­ni­cate their think­ing to other people?


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Vocabulary for Developing Math Reasoning

                
                

    Posted on August 20, 2009
    by 
    in Thinking Skills
    

                
                

                    






Tyrannosaurus Rex


Image via Wikipedia








Teach­ers of math­e­mat­ics need to rec­og­nize that there is a strong link between lan­guage, writ­ing, and prob­lem solv­ing. In most of the assess­ments that states use to deter­mine stu­dent and school suc­cess, a stu­dent must demon­strate math rea­son­ing abil­i­ties through writ­ing. This skill is not auto­matic, though. It devel­ops through a recur­sive process:


Vocab­u­lary & Lan­guage <—> Rea­son­ing <—> Talk <—> Writing


Begin­ning with vocab­u­lary and lan­guage, a stu­dent learns to rea­son, then to com­mu­ni­cate those thoughts ver­bally, and finally to write. Each of the lev­els feeds back to the pre­vi­ous one, rein­forc­ing and fur­ther devel­op­ing it.


Thus if we’re going to teach rea­son­ing skills effec­tively, it fol­lows we need to care­fully con­sider the vocab­u­lary we use.


It isn’t uncom­mon, espe­cially in the pri­mary grades, for teach­ers to sim­plify the lan­guage we use with chil­dren to explain com­plex con­cepts. Although this is use­ful, it can also lead to sloppy lan­guage if we aren’t care­ful. It is par­tic­u­larly impor­tant that we don’t per­mit stu­dents to use pre­cise math terms improp­erly and that we teach the “real” terms as quickly as pos­si­ble. Even if stu­dents don’t use them right away, they should be hear­ing the cor­rect ter­mi­nol­ogy in con­text from the beginning.


Here are a few exam­ples of sloppy math lan­guage that I often hear from older stu­dents. If these go uncor­rected, stu­dents will have a very dif­fi­cult time com­mu­ni­cat­ing well when they need to explain their thought process–a skill that is essen­tial to upper level math.






Instead of these…
Use these…




take-​​away
minus




“plussed”
added




“minused”
sub­tracted




“timesed”
mul­ti­plied




answer
sum, dif­fer­ence, prod­uct, quotient




amount
length, height, vol­ume, num­ber, etc.




num­ber
digit, addend, fac­tor, div­i­dend, etc.




big­ger, smaller
greater than, less than






I believe it’s essen­tial to require stu­dents to be pre­cise when they com­mu­ni­cate. Often when stu­dents don’t use the cor­rect term, or use a valid term improp­erly, it is a sign they just don’t have the right words.


I’ve heard teach­ers argue that young chil­dren just aren’t capa­ble of such sophis­ti­cated lan­guage yet. My father, a retired pro­fes­sor of speech/​language pathol­ogy, has often said, how­ever, that if sec­ond graders can learn and cor­rectly use terms like “Tyran­nosaurus Rex” and “Diplodocus”, why on earth can’t we teach them to say “sub­tracted” instead of “minused”? Vocab­u­lary instruc­tion should be as much an inte­gral part of math­e­mat­ics as it is of read­ing, writ­ing, and other con­tent areas.


Tomor­row I will tackle a more chal­leng­ing vocabulary-​​related issue in math­e­mat­ics: ver­bal and writ­ten expla­na­tions of a student’s cog­ni­tive process.


(This arti­cle is based on mate­r­ial I orig­i­nally posted in Grandé With Room.)


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Supporting Student Thinking Skills

                
                

    Posted on June 15, 2009
    by 
    in Differentiation, Thinking Skills
    

                
                

                    


Scaffolding: Not just for construction workers...
Image by kevin­doo­ley via Flickr




Yes­ter­day, I shared some ques­tions that I often use to help cre­ate an atmos­phere of think­ing in my class­room. Unfor­tu­nately, when I ask a stu­dent to explain their rea­son­ing, they often aren’t able to reflect back on their thought process and ver­bal­ize what took place. In some cases, the best they can come up with is “it just popped into my head.”


In order to train stu­dents how to do this, I scaf­fold the process for them at first to give them a struc­ture within which they can build their own responses. They need to learn three skills to allow this to happen:


    

  1. Focus on the process before they start
    2. 

  2. Mon­i­tor their rea­son­ing as they are working
    3. 

  3. Reflect back and explain to some­one else what they were thinking
    4. 



Each of these skills needs to be mod­eled and prac­ticed, and stu­dents need many oppor­tu­ni­ties to use them. These think­ing skills are learned best when they are inte­grated into the reg­u­lar flow of instruc­tion rather than explic­itly taught as dis­crete top­ics. One way to do that is to build one or more of these scaf­fold­ing activ­i­ties into every lesson:


    

  • Think-​​Alouds
    • 

  • Lev­eled problems
    • 

  • Graphic orga­niz­ers (e.g. T-​​chart)
    • 

  • Using “magic words” that stu­dents can use which require expla­na­tion of reasoning
    • 

  • Ask­ing prompt ques­tions (such as those in yesterday’s post)
    • 

  • Give part of the solu­tion, then have stu­dents com­plete it
    • 

  • Give the answer, stu­dents write the solution
    • 

  • Give the expla­na­tion, stu­dents write the solution
    • 

  • Give the solu­tion, stu­dents write the explanation
    • 

  • Check­lists or mnemon­ics to aid recall of processes
    • 

  • Jour­nals to prac­tice infor­mal writ­ing about prob­lem solving
    • 

  • Vocab­u­lary games to build lan­guage skills and improve com­mu­ni­ca­tion about reasoning
    • 

  • Allow stu­dents to rewrite weak expla­na­tions to improve them
    • 

  • Show sam­ple stu­dent papers that demon­strate good skills
    • 

  • Teach stu­dents to score responses using a rubric
    • 

  • Have stu­dents score their own work or a partner’s work
    • 

  • Trade papers with another class and have stu­dents score
    • 



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Questioning for Thinking

                
                

    Posted on June 14, 2009
    by 
    in Thinking Skills
    

                
                

                    


I'm thinking of...
Image by gut­ter via Flickr




One of the things that I fre­quently see in class­rooms that I visit is stu­dents who can mechan­i­cally pro­duce an answer to a ques­tion or prob­lem but who don’t really under­stand how or why the process they used works. As teach­ers, we need to focus more on the think­ing process that a stu­dent used to get to an answer rather than on the answer itself.


Cer­tainly there are times when sim­ple recall is impor­tant, and when it’s best to give stu­dents a brief indi­ca­tion of whether their response is cor­rect or incor­rect. But for any ques­tion that involves rea­son­ing, judg­ment, assim­i­la­tion, syn­the­sis, or sim­i­lar higher level think­ing, I like to ask follow-​​up ques­tions like these:


    

  • “Why did you do that?”
    • 

  • “How did you get that?”
    • 

  • “How do you know?”
    • 

  • “What does that number/​fact/​word represent?”
    • 

  • “What does that mean?”
    • 

  • “Can you jus­tify your answer?”
    • 

  • “Can you prove it?”
    • 



I ask these regard­less of whether the ini­tial answer is right or wrong. This has sev­eral benefits:


    

  1. I can get a bet­ter under­stand­ing of both the right and wrong answers a stu­dent gives. Was it sim­ply an auto­matic appli­ca­tion of a rote process? Is there valid rea­son­ing going on with sim­ple mis­takes? Was the right answer a guess or a fluke? Does the stu­dents have a mis­con­cep­tion that hap­pens to work right in this instance?
    2. 

  2. Occa­sion­ally a stu­dent will have a good jus­ti­fi­ca­tion for an alter­na­tive answer I hadn’t con­sid­ered, and ask­ing for the ratio­nale saves me from a hasty dismissal.
    3. 

  3. It makes it clear to the stu­dent that they are respon­si­ble for their answers, not me.
    4. 

  4. It cre­ates an atmost­phere that is simul­ta­ne­ously more rig­or­ous and more open. It becomes safer to be “wrong”, because when they can explain their think­ing, we focus on the process instead of the result. It is rare that a stu­dent does noth­ing right in that think­ing process, and so we can begin with “I under­stand where you are com­ing from. This part was really good think­ing, but here is where you got off track and how you can fix it next time.”
    5. 



So many times I have been in a class­room where a stu­dent gives an incor­rect answer to a ques­tion, the teacher gets a cor­rect answer from another stu­dent (or sim­ply pro­vides it him– or her­self), and moves on. I’ll some­times go to that student’s desk and pri­vately ask for the expla­na­tion. “Show me how you got that,” I’ll say, and they’ll walk me through the process. It rarely takes me more than a few moments to explain the flaw in the think­ing and help the stu­dent understand.


Take the time to ques­tion every­thing your stu­dents do. Cre­ate an envi­ron­ment for think­ing in your classroom.


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