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The Number Devil by Hans M. Enzensberger is an attractive and imaginative book for children that teaches math wonderfully and redefines the concept of "showing your work." In fact, throughout the bulk of the book, children are led by Robert and his devilish guide--into some of the most beautiful sites of mathematical discovery.
Robert has a lot of common sense and gradually over the course of the book he becomes more and more "ready" for his encounters with his crazy mentor: The Number Devil. The design of the book is appealing to the eye, contains excellent illustrations, and the clear and colorful lines and fonts attract students all the more to a greater attraction to the positive world of mathematics.
"How Children Can See Math in Different Perspectives," would be an excellent alternate title for the book. For example, looking at math today as a teacher, a big majority of students see math as impossible to accomplish.
After reading The Number Devil, I can conclude that the book gives the average math student options in how to look at a problem in many ways. rather than in one way. The author makes it quite clear that Robert hates math: "And besides, I hate everything that has to do with numbers" (Enzensberger 11).
Many people can relate to Robert and how he learns to enjoy math. Thus, by reading this book, a student can gain hope that math is not just learning one concept, but also by learning multiple ways to solve a mathematical problem.
The first mathematical concept recognized in the book was prima donnas. This idea reminds students of the concept of prime numbers. The recollection of prime numbers from students can be difficult. The way that The Number Devil explains this concept is by painting a picture that includes the numbers from two to fifty. The process of elimination includes deleting the odd numbers by way of seeing the prime numbers.
By giving a student a picture of what needs to be done, you have successfully led him through steps that need to take place, rather than rote memorization or doing it in their "head."
A second mathematical concept explained in The Number Devil is Bonacci Numbers. These are not just your everyday ordinary numbers. They are special numbers that are everlasting. These numbers are irrational numbers too, in that they divide certain numbers by their neighbor, and the result is a pile of numbers that do not stop. For example: one, two, three, five, eight, thirteen, twenty one, and thirty four are a prime example of how the added number added to the second number equals the third number.
A third mathematical concept in The Number Devil is the idea to simplify a number by multiplying it by itself. For example, ten times ten equals a hundred. In this situation The Number Devil shows that this can be so with the number twenty. Twenty to the fifth power is twenty thousand. This explanation can be illustrated by hopping the zero eight times to the left.
A fourth mathematical concept illustrated in The Number Devil explains irrational numbers. He says that these "unreasonable" numbers refuse to play by the "rules." By way of encouragement he recalls the "hopping" numbers-two, four, eight, sixteen, thirty two, etc.--and he explains the problem of hopping "backwards" which he calls "taking the rutabaga" square root.
This leads to the square root of two, which the number devil says is unreasonable. He then gives a rare and gorgeous geometric proof about why the diagonal of the unit square has length of square root of two. On the diagonal the number devil draws another square, which he illustrates four triangles, two of which can form the unit square. Then the larger square has twice the area of the unit square, which makes the problem make sense to the student!
The Number Devil shows many number concepts that will be more appealing to young minds. For example, math students learn math easier by using objects they can manipulate--like sticks, building blocks, cubes, or play money. Using these visual objects can enhance student learning by helping them learn basic number operations like the ordinary numbers two, three, and four, and hopping numbers 2-2, 3-2, 4-2, and 5-2.
I would teach a class of elementary students their hopping numbers much like the number devil did, by using visual and tactile objects. A lesson on hopping numbers would be as follows. I would use three numbers per day. I would line up the object discussed, such as building blocks. I would say one times one square equals one--modeling this for them visually. Then I would hold up two blocks and show them two times two equals four with four blocks.
Whatever number I was covering would correlate with the number of blocks or sticks utilized. For the students that didn't understand, I would pair up with someone who does understand, and instead of making them work with groups of three or four, I would allow them to start with groups of two or thereabouts. This will enable the student to learn and not feel left out or emotionally distressed by not understanding.
Another concept that is of utmost importance to our students from The Number Devil is multiplication. Introducing multiplication to students is of vital importance. Multiplication is something that can be totally misunderstood if it is not explained properly the first time. I would use bold as well as multi-colored numbers for the answers.
A variety of colors in multiplication are vital because the students can visually see that four times four (red) equals (green) sixteen (purple). A variety of colors can be utilized to explain the products and factors involved. In this case the factors of four times four equal the product of sixteen.
The use of colors will enhance the definitions for students by enabling them to remember them more accurately. I would also allow them to use colors on their papers if it helps in their memorization of facts, terms, and problem solving. I have a colleague at another school district that used to teach third grade and is now a vice principal. He taught for fifteen years and has had great success using a variety of colors in multiplication.
In conclusion, The Number Devil, by H. M. Enzensberger, is a book that I would have my students read. I found it appropriate for all levels of math students. Math should never be taught in just one way, but with a variety of methods. This book amplifies and explains how to problem solve in an exciting way and gives examples for students that they can identify with in their everyday world.
I would recommend the book for all teachers and especially teacher mentors because I believe that math is a subject that requires thinking beyond the problem and this book makes math fun, exciting, and a collaborative adventure for all students.
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Apple fans will be happy to know that iPod is currently working on a device that is a little bigger than their popular iPod Touch but smaller than their equally popular MacBook. The midsize device - which is rumored to have a screen that is about seven or eight inches - is scheduled to be released sometime during the early part of 2010 and is being described as a tablet sized device, similar to a media pad that has managed to get the nickname 'iTablet'. However, Apple and other companies have had past problems getting these 'middle ground' devices to fly in the consumer market, so they are going to have to do some serious work to make it appealing to fussy consumers.
There is a market for these smaller laptop, larger iPod type devices as the Netbook craze has already shown. According to Apple Interim CEO Tim Cook, the company is already pondering some interesting ideas for their 'iTablet'. If Apple does pump out these units they will need to be reasonably priced, somewhere between $389 and $500 in order to stay competitive with similar devices already on the market.
What would an 'iTablet' be like? It would definitely have to offer the average consumer something that the other tablets are not. That has been part of the problem with the Netbooks and similar electronics. They have not offered anything new that another device can accomplish just as easily in a small format. An 'iTablet' would have to be thinner, lighter than and not as clunky as some of the current devices. The operating system and software loaded onto the tablet would have to be such that the 'iTablet' could easily be considered a productivity tool, possibly pulling the best applications from the current Mac OS and the iPhone and combining them into one unit.
Additionally, built in 3G wireless would be a must. Consumers want to be able to jump on, do what they have to, and jump back off quickly and without a fuss and this could be a major selling point for an 'iTablet'. A multi touch screen, built-in App Store access and other features of the iPhone and iTouch that make consumers wild should be added to the device, and if Apple added a larger version of their virtual keyboard to where consumers could type with two hands the 'iTablet' could be a definite seller. Add to the device a built in camera and mike as well as an e-book reader, and Apple will have something to attract a consumer's attention away from the mediocre tablets right over to theirs.
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So you are drinking your coffee, reading your emails, typing up a document and designing a presentation. Then you realize that you have an appointment and can't be tied to your computer. With three projects do the next day, what are you going to do? Well switch to mobile computing, of course. You heard about that iPad Tablet. You also heard about other devices deemed the "iPad killers". Which one are you going to buy? This article will compare the iPad to its main competitors
The iPad. If you are reading this, chances are you already know what the specs of the iPad are. The iPad has a 9.7 inch multi-touch LCD screen; it has enough processing power to play HDTV video and is intuitive enough to allow you to make documents or presentations using iWork. There are two major criticisms however: multitasking and a closed OS. A closed OS means that you cannot install whatever you want on your iPad. The software must first be approved by Apple. While this is beneficial for security reasons, it might limit some users. The second criticisms - lack of multitasking can be both a cure and a poison. With no multitasking, you can only run one app at a time - this means that you would have no distractions. However if you are typing a report, and then need to verify some facts using Safari, you'll have to first close iWork, start safari, close safari and then re-open iWork. A tiresome process. Although this has not been officially announced, it is rumored that iPhoneOS 4.0 will have multitasking support.
HP Slate. The HP Slate will have a release price of slightly less than the iPad. It will have an atom CPU, include Flash support, USB connectivity, a memory card reader, and a back-mounted webcam. The major complaint against the HP Slate is that it is running Windows 7 on a touch screen device. All other tablets are running software that is optimized for the touch, yet HP is running Windows 7. Expect unresponsive controls, laggy interface and buggy programs. If you are looking for raw power, then the HP Slate is to go, however you'd get more bang for the buck from a netbook. And since HP Slate isn't optimized for touch, you'd be smarter to go for a netbook
The Notion Ink Adam. India's entry into the Tablet market. A significantly cheaper alternative to both the HP Slate and the iPad. The Adam features a bigger screen then the iPad, It uses a Pixel-Qi sceen (color e-ink), will be powered by a Tegra2 chip (1080p output), will have a swivel camera, will have a track pad and is powered by Android. If you can't afford the iPad, this device will give you the most bang for the buck. The touchscreen and trackpad is an intuitive combination. Apparently the explanation for the trackpad is to make surfing the web easier. One would think of the quality of the browser, if it requires a trackpad to achieve a positive experience. When I view the Notion Ink Adam, I can't help but get the feeling that it's software is of "cheap" quality. If you want good functionality at some GUI expense, go for the Adam. However, if you want quality software and hardware - I would recommend the iPad
The Microsoft Courier. I believe that the battle for the best Tablet device, will be fought, symbolically, between Microsoft and Apple. Right now, The Microsoft Courier is only a prototype, but a video has been leaked demonstrating its features. The courier is a dual screen concept. It measures only 5x7 when closed. Not much detail is known, only that the Courier is built on Tegra 2 and runs on Windows CE 6. Microsoft's emphasis is on mobility. I cannot recommend this device, at this point in time, as not much detail is known. But keep an eye on this one folks, it will be a major competitor to the iPad
Should you go with Apple's quality, yet slightly underpowered revolutionary device? HP's powerhouse, running the wrong OS? Notion Ink's cheaper alternative to mobile computing? Or Microsoft's mysterious Courier? Time will tell. Or more properly speaking, the consumers will.
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People love taking things on-the-go. And they love smaller versions of the real thing. One of the first real instances of this was the portable CD player. When they arrived, we no longer wanted to listen to music at home or in the car, because now we could listen to it in the grocery store. Yeah, that's right, the grocery store (Sounds strange, but I know a woman who's done that). Or how about popcorn chicken, or Pop Tarts, or iPods? All of these are examples of things we as humans have created to suffice our need to take things with us.
And up next, the mini notebook -- a smaller, lighter notebook (sometimes called a "netbook") which leans more toward the wireless internet side of laptop usage rather than it's program capability. This new craze is sweeping the nation. And rightfully so. These new notebooks are lighter, cheaper, and much faster than anyone had anticipated years ago. With the coolest sounding processor in recent memory, the Intel Atom has created a new way of thinking about computers with it's high speed on such a low-cost/small-sized device.
The Network Computer
The idea for the netbook can be traced back to the Network Computer of the 1990s. Oracle developed a desktop computer that relied solely on it's programming. That is, it had no external drives or disk inputs. This was an idea that was simply a decade ahead of it's time. Not only were desktop computers becoming more and more as essential to a home as a microwave, but the fastest Internet speed at the time only ran at 28.8 kb/s, much too slow for the Network Computer to be of any use. Of course, this idea was scrapped.
One Laptop Per Child
Then, in 2005, the One Laptop Per Child organization was founded. Their goal was to create an affordable device to educate children in developing countries. With funding from major corporations, they were able to create the XO-1 laptop by Christmas, 2007. The lightweight device was made to be durable and have a long battery life, and ended up with a price tag of 188 dollars, when purchased by thousand units. The creation of the XO-1 solidified the mini notebook as a real-deal device, and more netbooks followed in it's footsteps.
The Eee PC
Around that time, ASUS delivered what became the standard in mini notebooks, the Eee PC. It weighed about 2 pounds with a inch screen and a keyboard about 85% normal size. Shortly after, Everex, MSI, Dell, and HP all developed their own mini notebooks and by late 2008, mini notebooks were starting to take money away from normal laptop sales.
This craze is now just beginning to bloom. Who knows what the future holds for these devices? What we do know is that we are living on the cutting edge of technology, and we can count on much more to come.
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There are an increasing number of admissions consultants discussing the benefits of applying to college from either a public or private high school. Further, many parents and students want to know whether going to a private high school will give them a greater advantage in the admissions cycle. So we'll discuss the benefits of applying from either public or private schools.
Applying to College From Public High Schools:
o There's a greater chance that you might "stand out" more with higher SAT and ACT scores.
Most admissions offices have statistics of matriculated students from any given high school. These show the performance of students from any high school at their college. In fact, many high school admissions offices provide SAT and ACT medians from their respective school. So, if you score way higher or lower, it could be seen more or less favorably. If a recent study by the Center on Education Policy concluding that students score slightly higher on SAT Verbal / Math from public schools is correct, then you might stand out with a higher score.
o You are more likely to be the only one applying to a "Top" College
Because some public high schools are more worried about students attending high school at all, if you're one of the few students applying to an Ivy League School or to another "Top 50? college (based on U.S. News and World Report), admissions officers will make note of this fact. Often times students recall of X student of 300 total from Y public high school getting into Harvard. In some cases, this is true. But work on increasing your scores and improving your essays, and then apply to college. Don't worry about the fact that you have to apply from a public school.
Applying to College From Private High Schools:
o Many private schools have greater resources.
Simply put: because many private schools charge tuition and don't rely on state and local taxes to survive, private high schools can channel more resources into college counseling and other things like computer technology. So if you're going to a private school use the resources wisely. And our admissions consultants help both public and private school students, regardless.
o There's a better chance you can speak with current and former students at top schools.
Because there are more students from private schools at the top colleges, your private school is more likely to put you in touch with a current student who can help facilitate a campus tour or discussion with the admissions office. In addition, these contacts will help you find out what school is a good fit for you. So find out what graduates went to your choice schools and contact them, and even consider using admissions consultants to help you apply to college.
So now you know...
Overall, it is doubtful that an admissions office will think more or less favorably of your application whether at a public or private school; the most important thing is to create an application that shows you contributed to your high school (public or private) and will do the same in college.
Remember, the key to applying to colleges is making sure that you develop a strong theme in your admissions application that shows you stood out of the crowd, regardless of whether you went to a public or private high school. Don't worry about whether you're currently at a public or private school, the SAT and ACT create enough objective criteria to evaluate your applications that this fact becomes irrelevant.
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Are you seeking a career in the food industry and seeking food safety training? Perhaps your thinking about being a food or restaurant inspector. Whatever the reason that you are reading this, food safety has become a huge concern. The concern has risen not only in the United States, Canada but everywhere in the world. People need to know that the food they are consuming is safe for them and their families. Seeking a career in this field is a smart choice.
Who Needs Food Safety Training?
It would be an excellent idea for restaurant owners, managers and wait staff to be trained in this area. As an owner or manager of a food service entity, understanding the dynamics of food and safety concerns is necessary. After all, aren't you in charge of customer's health when they eat at your establishment? As a waiter having had some sort of food training puts you leaps ahead of your competition. Imagine applying for that upscale job with a certificate in food safety on your resume. To be knowledgeable and hold a certification in this area will make you more confident and marketable.
What is Involved With Food Safety?
There are many aspects associated with food safety. Employee hygiene is critical. Understanding when and how often hand-washing is necessary. What about employee illness and which foods can you not handle with bare hands? Workers need to learn safe cooking techniques. Temperatures are crucial when it comes to cooking and re-heating. Storage of, and the length of storage time for food must be understood. There are many important areas of working safely with food.
You Need Food Safety Training
The simple fact that you are reading this article indicates that the need or interest is there to receive education in this area. There is a saying that goes "you can never have too much education". I think this is a true statement. Everyone in the hotel, restaurant, cafeteria or any food industry should be required to have this type of knowledge under their hat. So no matter the reason that you've stumbled across this article, spruce up your career and get the training in food safety that will boost your career goals.
Managers, hotel owners, and supervisors of any food industry benefit from knowledge and certification in food safety. So when I ask "who needs this training?", I believe the answer is - You need it!
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1) Number Circles - Counting to 10
Draw 10 large circles on a colored card (you could also use paper plates). These can now be the focus of a number of activities.
Hold the circles up when counting to ten (they can be pointed to if fixed to a notice board).
Give a plate to each of 10 students and then ask them to move around until they are in the right order.
Mix the circles up and ask small groups of students to put them in the right order. They can lay them on the ground in a line.
Lay them on the ground, with 1 number missing. Ask the class to say what figure out what number is missing.
Lay them on the ground outside to make a stepping stone pathway to follow.
Lay them outside along an obstacle course to show the order of activities.
Students can draw with chalk a number pathway of their own on concrete.
This is a great time to introduce hopscotch. The numbers from 1 to 10 written on squares that you jump on are a perfect extension activity.
2) Patterns - Identifying and Continuing
Use Lego and/or wooden blocks to play with patterns. Individual or small groups of students can create small patterns by placing the blocks in a row. Other students can be challenged to finish them. If possible, photograph the patterns made and display them on the classroom noticeboard.
Draw the patterns made with the blocks on paper using crayons or pencils. Students can draw around the blocks and color in the shapes.
Create patterns with colored paper squares, rectangles and triangles and glue.
Create patterns with sponge shapes dipped in paint. Squares, circles, triangles, stars and moon shapes are easy to cut.
Create patterns out of found objects from nature (leaves, twigs, flowers and bark). Use patterns to decorate classroom storage boxes and noticeboard borders.
3) Grouping of Things - Sorting and Grouping
You can use wooden blocks, Lego, plastic animals, plastic cutlery, small cars or any other collection of items, for the following activity. Mix items up in a box and challenge students to sort them by color (red, blue, green), size (small, big), or type (cow, chicken, horse).
Use decks of cards for sorting. Sort by color, number, or royal position (jack, queen, king, ace).
Use students for sorting. Sort by hair color (red, black, brown, blonde), lunch choice (apple, mandarin, banana, grapes), or school transport method (bus, train, car, walking).
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Everyone Loves Exploring - Whether your ideal place to explore is a deep dark jungle, a long, sandy deserted beach or a marketplace in a distant, exotic land, we all have an idyllic place that we could spend hours and hours exploring and making wonderful discoveries.
Children are certainly keen explorers too, perhaps even keener than adults. Children still have a natural curiosity and an unending desire to explore and discover. So let's look at how that natural curiosity can be used to advance math skills.
We know that children love to explore and discover so how can we harness this to help them with math. The answer is simple - let them explore and discover in math. Give them numbers to play with, let them explore patterns, let them discover properties of numbers and shapes and measurements.
Best of all, when they learn this way they also develop a real understanding of these concepts because they haven't just been told that this is the way it is, they have discovered it for themselves.
Math games are a great way to explore in math. When children play with numbers they learn about numbers. They discover patterns. They discover properties of numbers. They discover relationships between numbers. They discover number concepts.
Best of all, when they learn this way they also develop a real understanding of these concepts because they haven't just been told that this is the way it is, they have discovered it for themselves.
Let's do some exploring of our own now and look at a few games we can use to explore math concepts.
Higher or Lower is a great game for exploring number order and place value.
To begin select the upper and lower number limits, e.g. between 10 and 100.
One player selects a number and records it on a piece of paper.
The other player/s guesses what they think the number might be. For each guess the first player tells if the chosen number is higher or lower. Play continues until the number is guessed. A more challenging game would be to explore larger numbers or decimal numbers. This game is always a favorite no matter what age group I am teaching. I just adjust the size of the numbers to the ability of the students.
Grab and Group is a great way to explore division. Players take turns to grab a group of items (marbles, toothpicks, counters or even pens). They then attempt to make groups of 2's with no remainders, then 3's, 4's, 5's and 6's. Players score points for each of the groups they can make, e.g. a player who grabs 9 can only make 3's so they score 3 points. A player who grabs 12 would score 2+3+4+6=15 points as they could make groups of 2's, 3's, 4's and 6's. This game is also easily adjusted to the abilities of the students. Younger students will manipulate the items to see if the number is divisible by the given number. Older children will simply count the items then mentally calculate what the number is divisible by.
You can also have children explore properties of numbers by posing a question for them to answer.
- How many prime numbers are there between two given numbers, e.g. 1 and 100 or 200 and 300?
- How many times do you write the digit 7 when you write all of the numbers between two given numbers, e.g. 1 and 100 or 500 and 700?
For more games to get your kids or your students exploring math you could try a number version of Hangman using a complete computation.
Tic Tac Toe can also be played in number versions, e.g. use the numbers 1-9 to fill the grid. The first player to create a line that totals 15 is the winner.
There are many other math games that are ideal for exploring in math. Playing games in math offers so much more than just a bit of fun. These games also help to develop a deep understanding of math concepts and a positive attitude towards a sometimes unpopular subject. Don't be surprised when you even hear, 'Gee that was fun! Can we do it again?'
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