# Helping Children See Math From Different Perspectives

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.

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.

About the Author

"Helping ALL to Succeed"

http://www.leading-online-business.com

Don Alexander, Published Author & Online Business Mentor

http://www.leading-online-business.com

Don Alexander, Published Author & Online Business Mentor

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