Rabu, Disember 05, 2012

Engaging Students in Mathematics


The last month has seen a plethora of discussions about the necessity for teaching math beyond what most jobs consider necessary. Much of it started from Andrew Hacker's now infamous article on whether math is necessary, to which a bunch of us replied with equal fervor (Dan Willingham's and Sherman Dorn's pieces are great rejoinders). What we all seem to agree on is that, indeed, the way we teach math matters. Lots. Having a positive environment for kids where they feel like they can actually do math without feeling like they're complete failures matters a lot.

Often, that starts with us as teachers.

Developing an environment where students can experiment and gain entry into the language of math starts with having a person who can facilitate what Stephen Krashen termed a low affective filter environment. While his study was applied to English Language Learners, his hypotheses should apply to all subject areas, math highest among them.

In my classroom, I have five principles for assuring that all students can enter into the math, and also for creating the conditions for math success.

1) Allow More Mistakes

I would suggest this to just about every teacher, but specifically math teachers, especially those of us who use the word "wrong" a lot. We should strike a balance between using direct instruction and exploration, leaning more on the exploration piece. Once we allow more mistakes, we let students into the process that our earliest mathematicians used in developing the axioms we believe today. Also, by admitting that we all make mistakes, it sends a clear signal to kids that they can be mathematicians, too. Surely, I'm not suggesting that we let the mistakes be. Yet, when I make a mistake on the board (intentionally or otherwise), I hope my students catch onto that, thus putting them in the position of expert. Speaking of which . . .

2) Support Their Struggle

At first, most of us get nervous when children struggle with mathematics, as if they need to get the math as soon as they receive the instruction. Even if it might look simple to us, the students may still be grappling with the skills, the concepts or both. That's OK. When students struggle with the material, they learn how to work problems out on their own as self-motivated workers. Of course, that also means the teacher needs to encourage them as often as possible to do so. If students think their efforts have no merit, then they often won't own it. In an environment where teachers support students' working through a problem, a teacher can tell when a student has quit. You have an option before you intervene . . .

3) Let the Kids Teach, Too

During the class period, I prefer the students speak more than I do. If I'm talking too much, that means I'm using too much of my speaking quota. In other words, they'll tune me out if I'm talking too much. Once I let the students speak (meaning, not just one student, but many), they take even more ownership of the math taught to them. This especially proves true during the class work time as well. Having them explain to each other (with the proper guidance) really empowers them to own the material and develop their own process for checking answers. Plus, I’m not exceeding my speaking quota. However . . .

4) Answer a Question with More Questions

If, in fact, a student asks us a question, we ought to validate their question by giving them another question. That way, we ensure that the onus for the "answer" falls on them. The type of questions we ask and the way we frame questions matters here, too. Questions that generate a "yes" or "no" answer simply won't do. Instead, we can leave them with a question that they can answer. I do emphasize the word "leave" because it's always good for you to walk away without explicitly telling them they were right. By the time you leave, they should already know this.

5) Personalize the Questions

Inserting children's names into the problems (appropriately) engages students in the material. As you start the problem, speaking about the student in the third person immediately gets him or her engaged, and gives the other students a window into the problem. Knowing the person in the problem (even if the situation itself is hypothetical) gives the entire class a sense of ownership and belonging within the math. Obviously, teachers should spread the wealth in naming people, because it may look like we're playing favorites or just focusing on the "struggling" children. All children need access to the math.

This advice obviously takes time and a teacher's willingness to fail. This also might push some of my colleagues out of a comfort zone. Yet we as teachers have to set a precedent for the success of lifelong learners, not just until a standardized test comes. One of the ways we set our students up for this type of success is by providing conditions for questioning, experimentation and ownership to happen. Those of us who only want to "skill and drill" students perpetuate attitudes that Hacker alluded to in his piece.

Math literacy matters. Let's do our part.

(Source: http://www.edutopia.org/blog/engaging-students-in-math-jose-vilson)

42 ulasan:

Tanpa Nama berkata...

[url=http://cialisdirectly.com/#vsuma]order cialis[/url] - cialis 20 mg , http://cialisdirectly.com/#serle cheap cialis online

Tanpa Nama berkata...

Barnardo felt he had to do something, so he placed an article in 'The Revival' saying he would hold a tea meeting service for children. http://www.ukdresshop.co.uk
[url=http://www.canadagoosehommes.com]canada goose chilliwack bomber[/url] So just do a little research and you are sure to find good yet cheap athletic shoes online.
5) Out on a summer picnic with your girlfriend you spy what looks like a rounded up pile of dog feces. [url=http://www.londongenuinepandora.com]pandora Sale[/url] WithinÂthe hour, I was pulled into the office of the head of the department at the company I am doing my contracting labor at. He put a picture of his family in the middle of the desk, and said basically "Screw them. That email was unbelievable. The title is a reference to the phrase "Luck Be a Lady Tonight", a song by Frank Sinatra. When it comes down to hair, makeup and accessories, the following tips will be helpful.
Not only learning in fashion school is important in order to get job in fashion industry of Phoenix but equally import is your networking skills and your performance in Internships.. [url=http://www.soldesgoosefr.com]Canada Goose Trillium Parka[/url] There are few G5 mobile models in India which have earned the sufficient popularity in the market are G five g3000, G five AP7, and G five u808.
Instead we will have people doing and dressing *however they want to* to the *Maximum* degree possible given their budgets.. Size charts are also available to make item selection easier. Of course, the career coach NY can help you a lot with that.. [url=http://www.promkleidde.com/]prom kleider lang[/url]

Tanpa Nama berkata...

I'll probably get the second lithograph when it's almost sold out, and probably some more merchandise down the line, but for now, I think I'm done with spending money on major releases from this particular franchise. [url=http://www.ukdresshop.co.uk]prom Dresses uk[/url]
http://www.canadagoosehommes.com Across town in 45 minutes is going to be cutting it close.
Prince St., sandwiches from $6.50), there's a three-block chain of studios and exhibit spaces called Gallery Row. [url=http://www.salemulberryshop.co.uk]Mulberry uk[/url] A black evening homecoming dress, which is shorter than it should be, shall also be highly tight to wear.. My laptop is a dv6t-qe with beats audio (I tried looking up the exact name of the integrated sound card but I can't find that or the specs).. Well, mistakes could be happen or it could be a wrong doing.
Sony digital camera price has been very reasonable. [url=http://www.soldesgoosefr.com]canada goose[/url] Body Shape : when looking at the plethora of tankinis it might be worth it looking at your particular shape, after which it pick out a costume for halloween that suits nearly all competently.
The f . We take a quick look on the changing patterns on children wear on junior clothing.. Some products can cause really bad reaction and when this happens, they can be cause to much pain to animals as well.. [url=http://www.promkleidde.com/]vergünstigte kleider[/url]

Tanpa Nama berkata...

But it, too, was just OK. [url=http://www.ukdresshop.co.uk]Evening Dresses uk[/url]
[url=http://www.canadagoosehommes.com]canada goose chilliwack[/url] It's far too beginning to think about fun shoes and high heel mules for summer season, so why not consider some wonderful shoes alternatives for the relax of the winter? Women shoes get an opportunity to glow during the cold month抯 period, so you are certain to find a look that is ideal for you.
The for kid safe chat rooms. [url=http://www.salemulberryshop.co.uk]Mulberry handbags[/url] If your hip hurts when you run, likely culprits include pirifiormis syndrome, an impingement of the sciatic nerve in the butt area; trochanteric bursitis, an inflammation of the fluid-filled sac that serves to reduce friction in the joint; and stress fractures of the top of the femur. Look through it for any add-ons or tweaks that you would like to fit in before you will be put to hand it in. Find shoes pageant girls from the selection vast of footwear girls .
The company launched its successful Jack Jones menswear line in 1990, targeting the young men's market. [url=http://www.soldesgoosefr.com]Canada Goose Chilliwack Bomber[/url] Since we carry footwear for women, men and children, there is something for everyone.".
This is the last component that holds the trim panel to the dash board once this is done then the trim panel can be easily removed. like their name suggests, these two styles are made from coated CANVAS, not leather. Trendy clothes and trendy clothing do add to the glamour of a person but to maintain that glamour one needs to remain alert about the ever-changing fashion trends. [url=http://www.promkleidde.com/]vergünstigte kleider[/url]

Tanpa Nama berkata...

their banks would fail unless the US government paid them $trillions inbailout money. [url=http://www.ukdresshop.co.uk]Bridesmaid Dresses uk[/url]
[url=http://www.canadagoosehommes.com]canada goose parka[/url] Its called modesty.
Switching to nose-only breathing initially slowed me down significantly, but in a couple of months I was right back where I started, but feeling much more relaxed when I run.. [url=http://www.salemulberryshop.co.uk]Mulberry Tote Bags[/url] James wants to focus in pediatrics even though John is bent on concentrating in orthopedic surgical treatment. Moreover, we do not select every advertiser or advertisement that appears on the web site-many of the advertisements are served by third party advertising companies.. Thank you for sharing this journey with us.
Computerization promotes fast growth, few. [url=http://www.soldesgoosefr.com]canada goose paris[/url] The first thing you need to do before you get yourself a replica bag is to check out the original and authentic bag that you want an imitation of.
Fashionable leather handbags tend to be widespread; they look excellent both at work and also at a party. These are actually unique ideas and great insights on creativity that may get the perfect reaction from your hoodie.. In addition to these physical qualities, we must add that the cotton is very durable. [url=http://www.promkleidde.com/]http://www.promkleidde.com/[/url]

Tanpa Nama berkata...

[ Okay you all dont know who Glen and Tim are so - here goes. [url=http://www.ukdresshop.co.uk]A Line Wedding Dresses[/url]
[url=http://www.canadagoosehommes.com]canada goose chilliwack[/url] She close enough with the Kardashians to be like an honorary sister.
There tend to be regarding three sorts of coupons; they are recipe coupons, world-wide-web coupons, grocery coupons. [url=http://www.salemulberryshop.co.uk]Mulberry uk[/url] It's a bit tough to pinpoint exact competition, especially since this category encompasses such a wide variety of vehicles. Why waste everyone's time? Changing the process without the data is cause for failure. It can be manufacturing fashionable and designer footwear in a very realistic pace to satisfy the budget ability of frequent people.
Think that you carry the upper deal in the situation. [url=http://www.soldesgoosefr.com]Canada Goose Langford Parka[/url] This frame from Ikea is easy to clean and the sharp lines of the wood will enhance the modern, urban style you should be aiming for on this budget.
Your cheek bones can appear to be much higher when you do this. Don expect a dog to be cheap, but I don think you looking for a lecture so much as a beginner dog. It is recommended that you purchase several martial arts gis, especially if you expect to go to class more than once a week. [url=http://www.promkleidde.com/]mac duggal ball gown [/url]

Tanpa Nama berkata...

They the mandy blake. http://www.ukdresshop.co.uk
[url=http://www.canadagoosehommes.com]canada goose parka[/url] I do not woman to become like my cousin and go missing.
Strangely, all shoes were still cut without any difference between the left and right foot.. [url=http://www.salemulberryshop.co.uk]Mulberry ooutlet sale[/url] If you make this correctly, you will not need a bra! I mean this for all body types, because I have done it (made them) and seen it done successfully (by others)! Calontir is chock full of ample women wearing kirtles and cotes! (This is probably my biggest pet peeve: the people who just dismiss this patterning and go to princess seams and a bra because they think they are "too big" to be supported.). Formal styles are made to facilitate engineers who have to take care of office work as well as on-site work. A favourite fantasy will tie you up in the boudoir.
Accelerated programs are commonly held in the online learning environment. [url=http://www.soldesgoosefr.com]Canada Goose Expedition Parka[/url] Generally, this type of clothing includes clothes that are quite baggy and have a distinct style about them.
Some watches come with many impressive features and a large memory, so you can store data with them.. Buy dresses either particularly for an event or in keeping with your general style, and always be sure to pick one that really makes you feel the way a dress ought to-confident and sexy!. But a designer hand bag worth thousands of pounds is beyond the means of many women as the high fashion that comes with these exclusive handbags also comes with a high price tag. [url=http://www.promkleidde.com/]mori lee prom dresses[/url]

Tanpa Nama berkata...

The reaction to the shooting was swift and rippled across the globe. [url=http://www.ukdresshop.co.uk]A Line Wedding Dresses[/url]
[url=http://www.canadagoosehommes.com]canada goose jackets[/url] Many sporting goods stores sell them, but some some department stores and pharmacies many carry them.
medical professional dre headphone in your head headsets having seem solitude solutions. [url=http://www.salemulberryshop.co.uk]Mulberry Tote Bags[/url] Losing your car keys or your glasses or your purse in your cluttered home is a sign of a lack of organization, but it is a pain in the neck too because it wastes so much time and usually precisely when you do not have time to waste.. However, you have to realize that the times have changed. Many ladies right now who are typically invited to any occasion during evening acquire wholesale evening dresses for they could opt for any dress that will completely fit the sort of bash and also special event they are going to attend and somehow the style and sizes definitely fits their body and also personality plus size clubwear.
As the French have known for ages, throwing on a scarf adds a certain je ne sais quoi to any ensemble. [url=http://www.soldesgoosefr.com]Canada Goose Banff Parka[/url] There are several ideas that are the most common ones for a fancy dress theme party.
Not because there better or more functional and definitely not because we need them. There are many top fashion designing institutes in India promising to proffer the best fashion designing courses in India.. I like to look cute when I work out but sheez, I don't want to spend a fortune on something I will sweat like a pig in for an hour at a time.. [url=http://www.promkleidde.com/]Prom Kleid 2013[/url]

Tanpa Nama berkata...

Way to go Lance for bringing the issue of cancer to the forefront. [url=http://www.ukdresshop.co.uk]prom Dresses uk[/url]
[url=http://www.canadagoosehommes.com]canada goose chilliwack[/url] Thanks!.
I do see the second season of this getting better. [url=http://www.salemulberryshop.co.uk]Mulberry Bags[/url] You can visit popular Internet forums which are similar to your website topic. Some of these family owned outlets will certainly be at the heart of most communities and, as long as they stay at the cutting edge of fashion, they can expect several generations of the same family to keep coming back for more.. Ben became wealthy at a young age, and seemed content with living the so called 'American Dream.' Ben says," …when I was seventeen I walked into the jungle…And by God I was rich" (Miller 48).
A few miles in the cable-throttle 2005 Rubicon show the difference. [url=http://www.soldesgoosefr.com]canada goose[/url] However, today parents can choose to not make their shopping experience stressful.
Great shoes for men, women and children in comfort, dress, casual, and athletic categories make Rack Room Shoes the family footwear retailer of choice. Fortunately for those of us newly interested in eating organic and raw foods, there are lots of products out there. She appeared in Trouble Bound, Inside Monkey Zetterland, and earned critical praise for her performance in Ethan Frome, opposite Liam Neeson. [url=http://www.promkleidde.com/]kleider abendkleider[/url]

Tanpa Nama berkata...

You will see a large selection of both new and used digital frames in all shapes and colors and MB sizes. [url=http://www.ukdresshop.co.uk]Homecoming Dresses[/url]
[url=http://www.canadagoosehommes.com]canada goose vest[/url] Each joint component relies on the others to function properly and without pain..
He just didn't remember that right now.. [url=http://www.salemulberryshop.co.uk]Mulberry Bags[/url] Don't forget the sunscreen. I had no lights on and it was approximately 2:00 pm on a sunny afternoon. Beats by dre wireless bluetooth headphones for sale $149.95 at hotsalemarts online shop..
For those with larger than average feet, this is a huge plus.. [url=http://www.soldesgoosefr.com]Canada Goose Kensington Parka[/url] Are you a trained truck driver searching for truck driving jobs in California? Perhaps you just graduated from one of the many truck driving schools all around the country.
In addition, the domestic corrugated Carton Industry vicious price Competition Also to the corrugated packaging business in China's development has brought a negative impact. Custom t-shirt design, jacket design, scarf design or hat design are available online and in stores. You can find real discounts that happen to be just as good (sometimes even better) than the more costly alternatives. [url=http://www.promkleidde.com/]mac duggal ball gown [/url]

Tanpa Nama berkata...

xanax buy pass drug test xanax my system - does 1mg xanax do

Tanpa Nama berkata...

xanax online xanax 8mg day - generic xanax dosage

Tanpa Nama berkata...

buy generic tramadol no prescription aspirin vs tramadol for dogs - tramadol 50 mg can you snort

Tanpa Nama berkata...

buy tramadol usa tramadol hydrochloride 50 mg high - tramadol purchase online no prescription

Tanpa Nama berkata...

buy tramadol online tramadol withdrawal and depression - tramadol 100mg buzz

Tanpa Nama berkata...

buy tramadol online tramadol high experience - tramadol online forum

Tanpa Nama berkata...

generic xanax xanax side effects urination - green xanax bars s 90

Tanpa Nama berkata...

xanax online xanax withdrawal neurontin - xanax withdrawal days

Tanpa Nama berkata...

generic xanax xanax side effects suicidal thoughts - 1mg xanax and weed

Tanpa Nama berkata...

purchase xanax alprazolam mylan 0 5 mg - xanax 2mg drugs.com

Tanpa Nama berkata...

buy carisoprodol c o d carisoprodol 350 mg strength - carisoprodol 350 mg strength

Tanpa Nama berkata...

buy tramadol online tramadol 100mg - tramadol hcl 50mg reviews

Tanpa Nama berkata...

buy tramadol online tramadol for dogs human use - ultram tramadol forum

Tanpa Nama berkata...

cialis drug cialis rebate coupon - price comparison of cialis

Tanpa Nama berkata...

cialis online best cialis price online - order cialis on the internet

Tanpa Nama berkata...

buy tadalafil cialis daily no prescription - cialis 30 oral suspension

Tanpa Nama berkata...

buy cialis online cialis 20 mg reviews - buy cialis online overnight shipping

Tanpa Nama berkata...

xanax online generic xanax mylan a4 - xanax and alcohol more drug_interactions

Tanpa Nama berkata...

20000 :) purchase effexor - effexor sale http://www.effexorfastorder.net/#effexor-sale , [url=http://www.effexorfastorder.net/#buy-effexor-no-prescription ]buy effexor no prescription [/url]

Tanpa Nama berkata...

http://landvoicelearning.com/#57594 tramadol for dogs addiction - tramadol 50mg for sale

Tanpa Nama berkata...

07 buy bupropion - zyban cost http://www.wellbutrinforsaleonline.net/#cheap-wellbutrin, [url=http://www.wellbutrinforsaleonline.net/#order-zyban]zyban sale[/url]

Tanpa Nama berkata...

03 generic prednisolone - order prednisone http://www.prednisoneonlinerx.net/index.html, [url=http://www.prednisoneonlinerx.net/index.html]order prednisone online [/url]

Tanpa Nama berkata...

4, cheap propecia 5mg - finasteride online no prescription http://www.propeciasaleonline.net/#cheap-propecia-5mg, [url=http://www.propeciasaleonline.net/#cheap-propecia-5mg]propecia sale[/url]

Tanpa Nama berkata...

buy tramadol online tramadol dosage usa - order tramadol overnight

Tanpa Nama berkata...

tramadol no rx tramadol hcl - tramadol hcl long term effects

Tanpa Nama berkata...

all, Biology Online - http://www.onlinewritinghelp101.com/biology.html#biology-project, [url=http://www.onlinewritinghelp101.com/biology.html#biology-project]Biology Online[/url]

Tanpa Nama berkata...

http://buytramadolonlinecool.com/#96430 tramadol online safe - tramadol 100 mg ampolla

Tanpa Nama berkata...

learn how to buy tramdadol how to buy tramadol - tramadol ultram 50

Tanpa Nama berkata...

ooo, escitalopram cost - escitalopram no prescription http://www.jangdailynews.com/#generic-lexapro, escitalopram online

Tanpa Nama berkata...

alprazolam 0.5mg xanax dosage 16 pound dog - xanax dosage 20 pound dog

Tanpa Nama berkata...

xanax online xanax no prescription mastercard - xanax memory loss

Tanpa Nama berkata...

Viagra has come a wish procedure since its inception. It is regarded as through some men as a miracle drug with a view the psychotherapy of erectile dysfunction and as a cure with a view other limited essence conditions. It assists men regain their self-confidence inside the bed room http://viagraonusa.net|viagra http://genericviagraok.net|buy viagra pills