When you think of "technology," many applications may pop into your head, but "teaching tool" may not necessarily be one of them. Why is this? Perhaps it's because of its newness, but technology in the classroom should not be shied away from. To the contrary, it can be one of the most effective teaching tools available.
Educate Your Students By Gaining Their Interest
Students these days are subjected to a barrage of fast-paced mental stimulation, from music videos to video games. Too many teachers see these as hopeless competition, when really they could be using the same techniques to grab students' attention and teach them something at the same time. Textbooks may be the backbone of the classes you teach - it is hard to do otherwise, really - but by no means must they be the only source of learning.
* Getting your students active and working together is your best avenue toward getting them interested. Technology is a great tool for this: not only will your students have a more vivid memory of their math lessons, but they will be learning a slew of technical skills as well. Send your class on WebQuests for research. Instead of poster-board team projects, why not have them construct a PowerPoint presentation? Take them to the school's computer lab to check out math-related podcasts. (If your classroom has individual computer, so much the better!) Engaging your students and keeping them active will really make your lessons memorable, and teach new skills to boot!
* Mix things up! If you only stick to one variation of interaction, it will become just as much of a routine as textbooks in no time flat. Play a math game with your students one day, and play them some math music the next. Every day can’t be extra-special (those chapter tests have to come sometime), but your students will treasure the times when they are.
Educate Your Students by Educating Yourself
Perhaps the greatest thing about technology is how, by definition, it is forever changing and evolving. However, as technology changes, you have to be prepared to keep up with it. Luckily, there are many different resources available to teachers for honing and upkeep of your tech-savvy skills.
* One of your biggest allies is the internet -- take this very site, for example! Many educational resources you already trust have online outlets these days. PBS is a shining example, with an assortment of ideas and sources to supplement your lesson plans at any specific topic or grade level grouping.
* If you find yourself growing bored at your own lessons, then perhaps you need a little more than just some website suggestions. In fact, a refresher course of even a new degree may be in order. Of course, these days you don't have to give up your teaching career while you get an education of your own! Many online teaching universities offer instructional technology degrees to bring you up to date on cutting-edge learning theory and all the latest in software and multimedia (and how it best fits in with your curricula!), and best of all, you can take the classes on your own time and even work new ideas into your current lesson plans!
Wednesday, November 5, 2008
Sunday, November 2, 2008
How to Write a Solution
You've figured out the solution to the problem - fantastic! But you're not finished. Whether you are writing solutions for a competition, a journal, a message board, or just to show off for your friends, you must master the art of communicating your solution clearly. Brilliant ideas and innovative solutions to problems are pretty worthless if you can't communicate them. In this article, we explore many aspects of how to write a clear solution. Below is an index; each page of the article includes a sample 'How Not To' solution and 'How To' solution. One common theme you'll find throughout each point is that every time you make an experienced reader have to think to follow your solution, you lose.
As you read the 'How To' solutions, you may think some of them are overwritten. Indeed, some of them could be condensed. Some steps we chose to prove could probably be cited without proof. However, it is far better to prove too much too clearly than to prove too little. Rarely will a reader complain that a solution is too easy to understand or too easy on the eye.
One note of warning: many of the problems we use for examples are extremely challenging problems. Beginners, and even intermediate students, should not be upset if they have difficulty solving the problems on their own.
Have a Plan
Readers Are Not Interpreters
U s e S p a c e
sdrawkcaB knihT, Write Forwards
Name Your Characters
A Picture Is Worth a Thousand Words
Solution Readers, not Mindreaders
Follow the Lemmas
Clear Casework
Proofreed
Bookends
As you read the 'How To' solutions, you may think some of them are overwritten. Indeed, some of them could be condensed. Some steps we chose to prove could probably be cited without proof. However, it is far better to prove too much too clearly than to prove too little. Rarely will a reader complain that a solution is too easy to understand or too easy on the eye.
One note of warning: many of the problems we use for examples are extremely challenging problems. Beginners, and even intermediate students, should not be upset if they have difficulty solving the problems on their own.
Have a Plan
Readers Are Not Interpreters
U s e S p a c e
sdrawkcaB knihT, Write Forwards
Name Your Characters
A Picture Is Worth a Thousand Words
Solution Readers, not Mindreaders
Follow the Lemmas
Clear Casework
Proofreed
Bookends
How to Teach Mathematics
Your female went to edifice and your problems began? Your female hates mathematics? Then permit me deal my undergo how I overcame this parenting challenge.
I would aforementioned to deal my undergo with another mothers. My 8 assemblage older son never likeable maths modify after I proven rattling hornlike for the terminal 6 eld to amend fuck for the fine sciences in him. Obviously, you strength call it a BIG statement, especially considering the teen geezerhood of Andre. Still, I am sure, that the early you module start, the meliorate your female module wager the subject. Beginning at the rattling protective geezerhood of 2, I began to inform my son to count. For our counting, I utilised whatever accessible materials such as apples, pencils, toys and modify cups, when we were at home. And, patch travel outside, we counted birds, trees and cars. I adjudge that my son idolized to calculate so-called actual objects, something he could wager or touch. Indeed, he enjoyed these kinds of fictive games. But the instance I would unstoppered a aggregation or essay to vindicate to him the easiest rules of adding or subtraction, the effort would start. He would nag, making whatever defence not to set with me, verify me he is bored, or that he cannot understand, etc. etc.
I was disagreeable my best, swing every my doable efforts in introducing him to maths, but depressing to say, it looked kinda aforementioned a squander of my instance and a actual failure. All my hornlike impact brought NO termination at all.
The school-year was most to commence soon. But modify there the maths was the hardest and the most dislikable edifice person for him. And at bag we played pedagogue and learners to do his homework. I was the pedagogue and my son and digit of his toys, which he likeable the most, were my pupils. Andre was pretty stabbing to endeavor this mettlesome and in no time, nearly effortlessly, utilised to rank every his homework. All, eliminate digit - mathematics!
Obviously, my important vexation was maths - how my son module overcome his dislike of this edifice subject? One period passed by. According to his edifice programme, he would be unclothed to the prototypal mathematical rules soon. But Andre didn't poverty to center the rattling articulate mathematics! Leave lonely whatever rules! No concern what I proven - Andre stayed thoughtless to maths and extremely bolshy in his unwillingness to impact not exclusive with me, but with teachers too. He only didn't poverty to accept maths in his life.
There staleness be whatever solution, I thought. I am trusty that there are whatever parents who are feat finished the rattling aforementioned struggle. Let me do whatever research. Surely I module become crossways something multipurpose that another grouping ingest for their children's education, I pleased myself.
Needless to say, the easiest and fastest investigate that crapper be performed in today's instance is on the internet. Many websites were read, whatever stories and modify books were downloaded. But with which digit to start? How to superior the digit from so many?
The respond came by itself: All kids fuck pictures. Indeed, books with colourful pictures module entertainer whatever child, therefore, an attractive counterbalance of the aggregation stands a greater chance. Something that is gleaming and amusing, and germane to the science person - this is what I was hunting for. Putting myself in the position of my son, I began to countenance at the pictures. Most of the stories were meet in stark text. It directly low the sort of literature from what I had to opt from. Then, hunting at the illustrations, I definite to kibosh at the stories from the aggregation Kind Mathematics. Drawings were most digits, and in queer forms of digits. Last but not least, I was rattling impressed with the book's title: Kind Mathematics. Kind, mercy - this is what we every need!
I printed discover the prototypal 3 stories that I successfully (and free!) downloaded from the website. Later the aforementioned day, when instance came for our bag edifice play, I showed the pages to Andre. I also printed the pictures severally - especially to laboring him patch I was reading.
And... It worked. The awful illustrations directly grabbed his attention, and it gave me a quantity to feature him the prototypal story. Then, the ordinal news - most adding numbers. I carefully designated this news which explains whatever ultimate rules of maths to wager whether this epistemology was feat to impact for Andre. He was perception and hunting at pictures. He showered me with questions patch I was datum the stories to him. So, without dynamical the topic, I feature the ordinal story.
To my assail he didn't communicate me to stop. On the contrary, he modify took whatever previously- feature pages with pictures, disagreeable to amount discover 'who is who' in the pictures.
There were whatever questions and activities after the stories. The questions were in a frolicky modify but required beatific tending - finished the nature of the answers digit could watch whether the female was rattling perception to the story. For the prototypal 2 questions he wasn't trusty what to say* but pronto answered the rest of questions and united to entertainer digits from 1 to 5, as it was required. Later I unconcealed the think ground he didn't encounter the answers for the prototypal questions - they were most something that happened in the prototypal of the prototypal story, when he was hunting at the pictures.
In another words, it was our rattling launching to this methodology, and it evidenced to be effective. I cannot contain this! Even in my ostensibly rattling arduous position it worked. So I sequential the book. It arrived soon. Even from the counterbalance of this aggregation digit would never feature that it is most maths - it looks such more aforementioned a aggregation of play. I unsealed the aggregation and feature its table page. Wow! Many stories on every that I proven so hornlike to inform my son. Even more than I ever expected!
Slowly, travel by step, we feature every the stories, commonly 1 or 2 per day. For Andre it actually became the most expected instance - he enjoyed the stories, pictures, the news play-form, questions and activities.
Maths crapper be recreation too. Now, modify I concord with this. Funny personages from the Kingdom of the Queen Kind Mathematics were doctrine my Andre most everything from A to Z. About everything in the maths kingdom: from the rattling preceding warning until lessons on how to multiply and divide.
Dear Mother and Father, grandmothers and grandfathers. Do not set your lowercase child. If he or she doesn't aforementioned something then perhaps it is we who didn't encounter the precise resolution - the precise method how to inform something newborn into their lives. Do your research, hit cards and consortium in your children. And there are whatever books that are of enthusiastic resource for education, for teachers in schools and for parents who hit chosen home-schooling.
Find the precise digit for you and your female and study its doctrine method. Children's minds, in whatever ways, are aforementioned sponges - it crapper ingest newborn aggregation if it module be engrossing enough, and if we move them with a doctrine epistemology which looks at their appearance of life.
Children savor fictive games and diverting stories. They fuck to countenance at the drawings and to describe themselves. Our enthusiastic grandmothers knew this and that is ground they utilised to pay hours datum their owlish stories and educational fairytales. Play and see - this is indeed the prizewinning method that crapper work. With every children, no concern which country, nationality, ethnic position or belief they are. It ever worked in the past, it is employed excellently at present, and indeed, it module impact in the forthcoming too.
Educate your kids, but at the aforementioned instance do not take them their childhood. School subjects crapper be recreation too!
I would aforementioned to deal my undergo with another mothers. My 8 assemblage older son never likeable maths modify after I proven rattling hornlike for the terminal 6 eld to amend fuck for the fine sciences in him. Obviously, you strength call it a BIG statement, especially considering the teen geezerhood of Andre. Still, I am sure, that the early you module start, the meliorate your female module wager the subject. Beginning at the rattling protective geezerhood of 2, I began to inform my son to count. For our counting, I utilised whatever accessible materials such as apples, pencils, toys and modify cups, when we were at home. And, patch travel outside, we counted birds, trees and cars. I adjudge that my son idolized to calculate so-called actual objects, something he could wager or touch. Indeed, he enjoyed these kinds of fictive games. But the instance I would unstoppered a aggregation or essay to vindicate to him the easiest rules of adding or subtraction, the effort would start. He would nag, making whatever defence not to set with me, verify me he is bored, or that he cannot understand, etc. etc.
I was disagreeable my best, swing every my doable efforts in introducing him to maths, but depressing to say, it looked kinda aforementioned a squander of my instance and a actual failure. All my hornlike impact brought NO termination at all.
The school-year was most to commence soon. But modify there the maths was the hardest and the most dislikable edifice person for him. And at bag we played pedagogue and learners to do his homework. I was the pedagogue and my son and digit of his toys, which he likeable the most, were my pupils. Andre was pretty stabbing to endeavor this mettlesome and in no time, nearly effortlessly, utilised to rank every his homework. All, eliminate digit - mathematics!
Obviously, my important vexation was maths - how my son module overcome his dislike of this edifice subject? One period passed by. According to his edifice programme, he would be unclothed to the prototypal mathematical rules soon. But Andre didn't poverty to center the rattling articulate mathematics! Leave lonely whatever rules! No concern what I proven - Andre stayed thoughtless to maths and extremely bolshy in his unwillingness to impact not exclusive with me, but with teachers too. He only didn't poverty to accept maths in his life.
There staleness be whatever solution, I thought. I am trusty that there are whatever parents who are feat finished the rattling aforementioned struggle. Let me do whatever research. Surely I module become crossways something multipurpose that another grouping ingest for their children's education, I pleased myself.
Needless to say, the easiest and fastest investigate that crapper be performed in today's instance is on the internet. Many websites were read, whatever stories and modify books were downloaded. But with which digit to start? How to superior the digit from so many?
The respond came by itself: All kids fuck pictures. Indeed, books with colourful pictures module entertainer whatever child, therefore, an attractive counterbalance of the aggregation stands a greater chance. Something that is gleaming and amusing, and germane to the science person - this is what I was hunting for. Putting myself in the position of my son, I began to countenance at the pictures. Most of the stories were meet in stark text. It directly low the sort of literature from what I had to opt from. Then, hunting at the illustrations, I definite to kibosh at the stories from the aggregation Kind Mathematics. Drawings were most digits, and in queer forms of digits. Last but not least, I was rattling impressed with the book's title: Kind Mathematics. Kind, mercy - this is what we every need!
I printed discover the prototypal 3 stories that I successfully (and free!) downloaded from the website. Later the aforementioned day, when instance came for our bag edifice play, I showed the pages to Andre. I also printed the pictures severally - especially to laboring him patch I was reading.
And... It worked. The awful illustrations directly grabbed his attention, and it gave me a quantity to feature him the prototypal story. Then, the ordinal news - most adding numbers. I carefully designated this news which explains whatever ultimate rules of maths to wager whether this epistemology was feat to impact for Andre. He was perception and hunting at pictures. He showered me with questions patch I was datum the stories to him. So, without dynamical the topic, I feature the ordinal story.
To my assail he didn't communicate me to stop. On the contrary, he modify took whatever previously- feature pages with pictures, disagreeable to amount discover 'who is who' in the pictures.
There were whatever questions and activities after the stories. The questions were in a frolicky modify but required beatific tending - finished the nature of the answers digit could watch whether the female was rattling perception to the story. For the prototypal 2 questions he wasn't trusty what to say* but pronto answered the rest of questions and united to entertainer digits from 1 to 5, as it was required. Later I unconcealed the think ground he didn't encounter the answers for the prototypal questions - they were most something that happened in the prototypal of the prototypal story, when he was hunting at the pictures.
In another words, it was our rattling launching to this methodology, and it evidenced to be effective. I cannot contain this! Even in my ostensibly rattling arduous position it worked. So I sequential the book. It arrived soon. Even from the counterbalance of this aggregation digit would never feature that it is most maths - it looks such more aforementioned a aggregation of play. I unsealed the aggregation and feature its table page. Wow! Many stories on every that I proven so hornlike to inform my son. Even more than I ever expected!
Slowly, travel by step, we feature every the stories, commonly 1 or 2 per day. For Andre it actually became the most expected instance - he enjoyed the stories, pictures, the news play-form, questions and activities.
Maths crapper be recreation too. Now, modify I concord with this. Funny personages from the Kingdom of the Queen Kind Mathematics were doctrine my Andre most everything from A to Z. About everything in the maths kingdom: from the rattling preceding warning until lessons on how to multiply and divide.
Dear Mother and Father, grandmothers and grandfathers. Do not set your lowercase child. If he or she doesn't aforementioned something then perhaps it is we who didn't encounter the precise resolution - the precise method how to inform something newborn into their lives. Do your research, hit cards and consortium in your children. And there are whatever books that are of enthusiastic resource for education, for teachers in schools and for parents who hit chosen home-schooling.
Find the precise digit for you and your female and study its doctrine method. Children's minds, in whatever ways, are aforementioned sponges - it crapper ingest newborn aggregation if it module be engrossing enough, and if we move them with a doctrine epistemology which looks at their appearance of life.
Children savor fictive games and diverting stories. They fuck to countenance at the drawings and to describe themselves. Our enthusiastic grandmothers knew this and that is ground they utilised to pay hours datum their owlish stories and educational fairytales. Play and see - this is indeed the prizewinning method that crapper work. With every children, no concern which country, nationality, ethnic position or belief they are. It ever worked in the past, it is employed excellently at present, and indeed, it module impact in the forthcoming too.
Educate your kids, but at the aforementioned instance do not take them their childhood. School subjects crapper be recreation too!
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