Mathematics in Daily Life

Waxing eloquently on the basic importance of Mathematics in human life, Roger Bacon (1214-1294), an English Franciscan friar, philosopher, scientist and scholar of the 13th century, once stated: "Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of the world." And the ingenuity of his statement is there before us to see, in this Internet era.

However, mathematics, in itself, has all the ingredients that make it a universal language shared by all human beings irrespective of culture, religion, or gender. Pi is always 3.14159 regardless of where we are. Similarly, the elemental mathematical processes (like addition, subtraction, etc.) never get changed due to a change in the location or for any other reason whatsoever. These all say about the close intertwining of mathematics in our daily life.

At a time when even a common man is being increasingly dependent upon the application of science and technology in the day-to-day activities of life, the role of mathematics has undoubtedly been redefined. Right from getting up in early hours of the day to the ringing of an alarm, to wait for the counts of whistles of the cooker, to exchange currency at a ticket outlet while availing a public conveyance, almost every next moment we do the simple calculations at the back of our mind. Of course, these are all done pretty unconsciously without a thought being spared for the use of mathematics on all such occasions.

Reading time on a watch, rounding a date on a calendar, checking up the mileage of your car, halting at the filling station, attending to a roll call at school, getting scores in the class exams, scoring in a game, betting on a horse race, preparing a recipe in the kitchen, - the list is just endless if one goes on to note down the situations when our computational skill, or more specifically, simple mathematics comes to play a role. It scares us to certain extent to think of a life without any knowledge of calculation or computation, or in other words mathematics. In many a case, lack of a formal education hardly affects gaining a relative mastery in these computational skills which are so essential in our daily life.

At a psychological level, exposure to mathematics helps in developing an analytic mind and assists in better organization of ideas and accurate expression of thoughts. At a more general level, far away from dealing with the higher mathematical concepts, the importance of mathematics for a common man is underpinned whenever he visits banks, shopping malls, railways, post offices, insurance companies, or deals with transport, business transactions, imports and exports, trade and commerce, and the ilk. Even when we think of role of mathematics in our recreational activities, we surprisingly have a list that runs quite long: video games, computer games, puzzles, riddles, and so on.

It ensues from the above discussion that a modern life style seems completely handicapped and at times, highly improbable, in the absence of mathematics. For, unless we are well versed in the language of numbers, we would find it difficult to reach at important decisions and perform everyday tasks. Be it to shop wisely, or buy the right insurance, or refashion a home within a budget, knowledge of mathematics holds the key, and hence, barely necessary.
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Learning Mathematics Through Mastery of Concepts

There are many ways to learn a subject. Different people has different learning style. However, regardless of learning style, there are two particular ways to learn knowledge within any style. The first way is memory method. This way of learning focuses on remembering facts and details, and recalling them when required. The second method is to understand the underlying concepts of the facts. It is the "what" versus the "how" and "why". Either way has their merits and demerits. It depends on the education level and complexity of the subject matters. Sometimes, a hybrid of both are necessary to reap the best possible results, especially in learning mathematics.

For elementary mathematics level, the amount of mathematical facts and concepts to be learned are marginal, and only serves to lay foundation for further advancement into higher mathematics learning. At the basic level, memory method of learning may be acceptable and manageable. But how about maintaining this way when one progresses into higher mathematics studies?

At a higher level of mathematics learning, the learning taxonomy moves into the application level and beyond. Mastery of concepts becomes an important factor in analyzing and solving more complex mathematics questions. Mathematical equations and expressions get more integrated with detailed concepts. Pure memory will not be able to extract out the true meaning of these equations and expressions. A few mathematical tools may be required to solve a mathematics problem. This combination of solving methods and concepts rendered pure memory way of learning mathematics unacceptable. The scope to cover all possible combinations of solving tools and questions is far too wide to manage. Staying firm with this facts-remembering method will only cause the performance and outcome to dwindle low. This will reduce the motivation to study and may decline towards the fearful mathematics anxiety situation.

Studying mathematics is different from other subjects in that a unique language is used to present mathematical meaning. Symbols and variables are used to form relationships and conditions. Many in-depth concepts are embedded into these few symbols and variables, including mathematical operators. True mastery of the mathematics concepts is therefore needed. However, it should not be said that memorising facts are completely useless at the higher level of mathematics education. It still serves its purpose in that they are the basic ingredients for the brain to link up with the solving methods and conceptual approach. It is these linkages or bondings that retain and strengthen the acquired knowledge longer. This is real mastery of the subject and its topics. A hybid of both learning methods is therefore necessary to achieve a level of acceptable comprehension with more emphasis going towards mastery of concepts.

In conclusion, time causes facts to fade off. Memorising facts will therefore not last long. A better learning platform is to focus on relationship and concept mastery. Linking facts to solving strategy becomes a useful problem-solving skill and has the benefit that it will last longer. Understanding the "why" and "how" is better when they complement the "what". Resistance to studying advance mathematics will then be lowered when the correct method of learning mathematics through mastery of concepts is applied.
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Manipulatives: The Missing Link in High School Math

by Marilyn Curtain- Phillips, M. Ed.

The thrill of achievement comes from overcoming adversity in the accomplishment of an important goal ~ UnknownAlgebra, Geometry and Trigonometry can be challenging and complex subjects for many high school students in the United States. These subjects are usually taught using textbooks, workbooks and examinations. While these resources are essential in developing learning skills in math, it doesn’t encourage problem-solving skills and retention. It is not surprising to learn many students view math as boring, difficult and irrelevant, rather than fun and interesting. The scope of what it means to be successful in mathematics expands beyond procedural knowledge and skill-acquisition to include sense-making and conceptual understanding (Buckley 2004). An integrated approach is needed to motivate students to learn math in a more relaxed environment, thus eliminating persistent math anxiety, the lack of math application skills and poor standardized test performance. The Third International Mathematics and Science Study (TIMSS) tested the students of 41 nations. Children in the United States were among the leaders in the fourth grade assessments, but by high school graduation, they were almost last. High school math should be taught in a way in which students can grasp and understand skills. Manipulatives are visual objects that help illustrate mathematical relationships and applications. These resources are used primarily in elementary schools and somewhat in middle schools. Manipulatives are valuable resources for accelerating and deepening students understanding of math, yet its use is almost non-existent in high school. Marilyn Burns, Creator of Math Solutions has "used manipulative materials at all levels for 30 years." In every decade since 1940, the National Council of Teachers of Mathematics (NCTM) has encouraged the use of manipulatives at all grade levels (Bellonio), yet many high school teachers are reluctant to use this type of resource.
Almost all mathematics-teaching activities take place at the abstract level (Sharma, 1997). According to Sharma, students have a tendency to forget when taught only at the abstract stage. Thus students become frustrated because mastery was never fully attained. Students will begin to have difficulty in learning mathematics. The results in failure will cause many students to develop a fear of mathematics (Sharma, 1997). Students’ attitudes towards any curriculum area can be related to their achievement in ways that reinforce higher or lower performance (timss.org). Full 88% of Bill and Melinda Gates Foundations’ survey respondents said they had passing grades in high school. Asked to name the reasons they had left school, more respondents named boredom than struggles with coursework. Over 1 million students drop out of school each year. That includes nearly half of all African Americans, Hispanics, and Native Americans who fail to graduate from public high school with their class. Leaving many of them with a host of poor outcomes to follow, from low lifetime earnings to high incarceration rates to a high likelihood that their children will drop out of high school thus eliminating the cycle (Thornburg, 2006).
Sharma (1997) feels there are six levels of mastery of mathematical concepts: intuitive, concrete, representation (pictorial), abstract, applications and communication. According to Sharma, ideally, each mathematics concept should be introduced beginning at the communication level. Manipulatives will teach concrete understanding to the abstract math process, especially when the student may not understand the concept behind the skill. When students develop a concrete understanding of math skills, then they are more likely to perform that math skill and understand math concepts at the abstract level. Manipulatives can make math concepts come alive. According to Spikell (1993), most learners whether adults or children, will master mathematical concepts and skills more readily, if they are presented first in concrete, pictorial and symbols. By using manipulatives, pictures and symbols to model or represent abstract ideas, the stage is set for learners to understand the abstractions they represent (Spikell, 1993). Students will be able to practice and demonstrate mastery using concrete objects. Manipulatives appeal to the learning style of kinesthetic learners because they actually touch the objects. Pictures appeal visually for visual/spatial learners. "Visualization is the natural way one begins to think. Before words, images emerge" (Sharma, 1987). "Almost every mathematics idea, except simple arithmetic facts, consists of three components: linguistic, conceptual and skill/procedural" (Sharma, 1987). Therefore manipulatives offer benefits to a variety of learning styles. They also provide a change from the textbook for mathematical/logical learners.
Games with manipulatives are also valuable with helping students to apply what they learned to the real world, as well as provide a means to improve their math skills interactively. Using board games and card games along with cooperative learning are ways that students can become involved in a positive mathematical environment. Games are highly motivational to students and can be used effectively to practice specific skills. "Using games in the classroom and at home will maximize students' problem-solving competence, ability to communicate and reason mathematically, perception of the value of mathematics, and self-confidence in their ability to apply mathematical knowledge to new situations." Cooperative groups provide students a chance to exchange ideas, to ask questions freely, to explain to one another, to clarify ideas in meaningful ways and to express feelings about their learning. These skills acquired at an early age will be greatly beneficial throughout their adult working life.
Many teachers feel as though they do not know how to teach using manipulatives and therefore, hesitate to use them in the classroom. Many math teachers, who attended college more than ten years ago, were usually taught on the abstract level, textbook, pencil and paper, all through their school days. There are classes and workshops for teachers to learn how to teach using manipulatives. The companies that make the manipulatives also provide books and pamphlets on ways the material can be used. There are articles on using manipulatives in mathematics teaching journal such as the National Council of Teachers of Mathematics’ Arithmetic Teacher magazine. Manipulatives help relieve boredom in children allowing them to explore and use their imagination.
Many manipulatives are inexpensive and can be everyday objects. Money, 2 –color counters, calculators, rulers, dominoes, playing cards, button and number cubes are a few of the commonly available manipulatives that can successfully be used in the classroom. These manipulatives can be used to teach such concepts such as angles, area, decimals, factoring, estimation, fractions, measurement, counting, percent, prime numbers, probability, geometry and whole numbers.
There are companies, which specialize in manipulatives that can be ordered from a catalog or online. No matter where a school is located, materials can be made available through the mail. These companies also make available to teachers such manipulatives as tangrams, pattern blocks, fraction towers, geoboards, algebra tiles, Cuisenaire rods, miras and polyhedral models.
When I initially introduced pattern blocks to my Geometry students, I was met with opposition and disbelief. It was a consensus that these students had not used pattern blocks since elementary school. However, many students actually began to explore and build figures with these blocks. I gave them this little bit of play time before taking on the task for that particular lesson, which was angle measurement of polygons. We must remember, everyone likes to play games even adults, look at our various hobbies, such as bowling, tennis, golf, art, race cars, chess, playing cards, etc. This holds true for high school students, they still enjoy playing games. Manipulatives require a great deal of prior planning and organization. But considering the many benefits that manipulatives offer, it is well worth the effort. Students will find math more attainable, fun and exciting, hopefully returning them to the prior successes of their early math experiences.

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REFERENCES:

Buckley, L. A. (2004, Oct) Course Taking and Equity: The Efforts of One High School Mathematics Department Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada Online <.PDF> Retrieved 2008-01-12 from <http://www.allacademic.com/meta/p117666_index.html>
Burns, M. How to make the most of math manipulatives – A fresh look at getting students’ heads — and hands! — around math concepts. Retrieved 2008-01-1-10 from <http://teacher.scholastic.com/lessonrepro/lessonplans/instructor/burns.htm>
Sharma, M. (1987). How to take a child from concrete to abstract. Math Note book, 5, 8-10
Sharma, M. (1997, July). Improving mathematics instruction for all. Fourth Lecture in Colloquium "Improving Schools from Within: Your Role. Pp. 2-12
Spikell, M. (1993). Teaching mathematics with manipulatives: A resource of activities for the K-12 teacher. New York: Allyn and Bacon.
Third International Mathematics and Science Study (TIMSS), Institute of Educational Sciences, United States Department of Education
Thornburg, N. (2006), April 7), Dropout Nation, Time Magazine
TIMSS 1999 International Mathematics Report. Findings from IEA's Repeat of the Third International Mathematics and Science Study at the Eighth Grade. Ina V.S. Mullis, Michael O. Martin, Eugenio J. Gonzalez, Kelvin D. Gregory, Robert A. Garden, Kathleen M. O'Connor, Steven J. Chrostowski, Teresa A. Smith. Retrieved 2008-01-12 from <http://timss.bc.edu/timss1999i/pdf/T99i_Math_TOC.pdf>
Yale-New Haven Teachers Institute Home Multi-Sensory Manipulatives in Mathematics: Linking the Abstract to the Concrete by Judith L. Bellonio Contents of Curriculum Unit 01.06.12: Narrative Math Anxiety Types of ... Retrieved 2008-01-12 from <http://www.yale.edu/ynhti/curriculum/units/2001/6/01.06.12.x.html>

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Marilyn Curtain-Phillips teaches high school mathematics and is the author of Math Attack: How to Reduce Math Anxiety in the Classroom, at Work and in Everyday Personal Use,(1999), $15.00. You can purchase her book through our Online Bookstore.

Algebra

Introduction to Algebra

What is algebra?

Algebra is a branch of mathematics that deals with generalized arithmetical operations. It is a collection of rules for translating words into the symbolic notation of mathematics, in a manner that leaves their truth unchanged. It can otherwise be defined as a branch of mathematics concerning the study of Structure, Relation and Quantity.

Roots of Algebra

The name "Algebra" is derived from the book written by a Persian Mathematician, Muhammad bin M?s? al-Khw?rizm?. In 9th century he wrote Al-Kitab al-Jabr wa-l-Muqabala, a book on symbolic operations and systematic solutions for Linear and Quadratic equations. The word “Algebra” is derived from al-Jabr.

Symbols

Symbols are the specialty of Algebra. They make our work more convenient. For example, instead of listing the natural numbers as 1, 2, 3… we just say ‘N’. This symbolic representation helps us to generalize the characteristics of natural numbers. Algebra involves a lot of symbols. The following are the other few notations: C – Complex Numbers R – Real Numbers Q – Rational Numbers. Z – Integers. W – Whole Numbers.

Variables in Algebra

Variables are symbols that stand for unknown quantities. It must not necessarily be an alphabet. It can be any symbol. But, generally, we use x, y, z, etc. as variables. In the first algebra book, Khw?rizm? did not use any variable, even though it was all about solving equations. It is only in the 16th century that François Viète, a French mathematician, started using variables. To have a clear idea about the importance of variables, we can have a look at the following example: Mom gave Isaac a bag of apples. He did not count the apples in the bag but started eating them. After eating 3 apples, he found 4 apples were remaining in the bag. How would he find how many apples were there in the bag initially? Here, we go for variables. Let the number of apples be "x" initially. Isaac ate 3 apples. So, x – 3 will be remaining. But there are 4 apples remaining. So, x – 3 = 4. We need to get the value of x. We should get rid of that – 3. We add 3 on both the sides, which will not affect the equality.

Thus we have x = 7. So, there were 7 apples initially

Classification of Algebra

Algebra can roughly have four specialized branches:
• Elementary Algebra
• Abstract Algebra
• Linear Algebra
• Universal Algebra
  
  In Elementary Algebra, the number system and generalization of rules are studied. Constants,
  variables, expressions, and equations are the key concepts of elementary algebra.
  Abstract Algebra represents a further generalization of elementary algebra, by defining such
  constructs as groups, based on a set of initial assumptions, called axioms.
  Linear Algebra involves the extension of techniques from elementary algebra
  to the solution of systems of linear equations.
  In Universal Algebra the properties common to all algebras are studied.
  

Applications of Algebra

TAlgebra has very wide applications. Even in our everyday life we need some algebra knowledge. The principles of algebra are applied in all branches of mathematics, like calculus, geometry, topology, etc. It has its application in all sciences though.

Additional Links for Algebra

• Click here for samples
• Click here for Mathematics Dictionary

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Algebra, Present and Past

What is Algebra? Algebra is one of the many branches of mathematics. This branch of math utilizes mathematical equations to describe the relationships between any two things that may change over a period of time. Whenever a math equation has to represent something that fluctuates and does not stay the same, letters or symbols are often used to represent the varying quantity. This letter or symbol is called a variable because it varies.

The very start of modern algebra began with the ancient Babylonians. They were the very first people who used an advanced math system for their time. This math used an algebraic system to do calculations, and it enabled the Babylonians to utilize formulas and calculate the answer using unknown values for a problem class that would be solved in the modern day by quadratic equations, linear equations, and indeterminate linear equations. During this same time period in the first millennium BC, most of the mathematicians in India, China, Greece, and Egypt were using geometric methods to solve such equations. The word algebra comes from the Arabic word al-jabar, which means reunion of the broken parts. A Persian Muslim
mathematician named Muhammad ibn Masa al-khwarizmi wrote a book in 820 whose title is translated to mean The book of Summary Concerning Calculating by Transposition and Reduction. There is debate in math circles on whether the mathematician Diophantes, who has always been known as the father of Algebra, or Al-Khwarizmi should actually be named the father of Algebra. There is support for Al-Khwarizmi instead of Diophantes because a lot of his work on reduction is still currently in use today. He also explained how to solve a quadratic very extensively.

In the fourteenth century the word algeber referred to bone setting, which is quite similar to the original meaning of the word. The mathematical form of the word that is spelled algebra had made its debut by the sixteenth century. A man by the name of Robert Recorde was the very first person to use the term algebra in its mathematical meaning. He was also the inventor of the equality symbol(=). The original meaning of the word Algebra would refer today to the sub class of elementary algebra. There are numerous different fields of algebra in the modern definition of the word.

Some of these other mathematic fields include elementary algebra, s-algebra, abstract algebra, geometric algebra, boolean algebra, linear algebra, and many more. The mastery of elementary algebra must be accomplished before calculus or any of the other advanced mathematics can be learned. Many careers today require that at least elementary algebra has been mastered. The symbolism that is first introduced in elementary algebra extends throughout all the fields of mathematics. This is because the symbolism is the letters in the language of math. Modern fields of algebra are vastly more advanced than the first equations and formulas that were developed by the Babylonians. Numerous jobs and careers in the modern work environment require that algebra is mastered as a legitimate requirement for employment.

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Boolean Algebra

One of the primary requirements when dealing with digital circuits is to find ways to make them as simple as possible. This constantly requires that complex logical expressions be reduced to simpler expressions that nevertheless produce the same results under all possible conditions. The simpler expression can then be implemented with a smaller, simpler circuit, which in turn saves the price of the unnecessary gates, reduces the number of gates needed, and reduces the power and the amount of space required by those gates.

One tool to reduce logical expressions is the mathematics of logical expressions, introduced by George Boole in 1854 and known today as Boolean Algebra. The rules of Boolean Algebra are simple and straight-forward, and can be applied to any logical expression. The resulting reduced expression can then be readily tested with a Truth Table, to verify that the reduction was valid.

This has a very great role to play in abstract algebra. In fact, in abstract algebra, Boolean algebra is an algebraic that captures essential properties of both set operation and logic operations. Specifically, it deals with the set operations of intersection, union, complement and the logic operations of AND, or, NOT.

Like any lattice, a Boolean algebra (A, land, lor) gives rise to a partially ordered set (A, ≤) by defining

a ≤ b precisely when a = a land b

(which is also equivalent to b = a lor b).

In fact one can also define a Boolean algebra to be a distributive lattice with least element 0 and greatest element 1, within which every element x has a complement x such that

x land x = 0 and x lor x = 1

Here land and lor are used to denote the infimum (meet) and supremum (join) of two elements. Again, if complements in the above sense exist, then they are uniquely determined.

The algebraic and the order theoretic perspective can usually be used interchangeably and both are of great use to import results and concepts from both universal algebra and order theory. In many practical examples an ordering relation, conjunction, disjunction, and negation are all naturally available, so that it is straightforward to exploit this relationship. One can also apply general insights from duality in order theory to Boolean algebras. Especially, the order dual of every Boolean algebra, or, equivalently, the algebra obtained by exchanging land and lor, is also a Boolean algebra. In general, any law valid for Boolean algebras can be transformed into another valid, dual law by exchanging 0 with 1, land with lor, and ≤ with ≥.

The operators of Boolean algebra may be represented in various ways. Often they are simply written as AND, OR and NOT. In describing circuits, NAND (Not AND), NOR (Not OR) and XOR may also be used. Mathematicians, engineers, and programmers often use + for OR and · for AND (since in some ways those operations are analogous to addition and multiplication in other algebraic structures and this notation makes it very easy to get sum of products form for people who are familiar with normal algebra) and represent NOT by a line drawn above the expression being negated. Sometimes, the symbol ~ or ! is used for NOT.

Every Boolean algebra (A, land, lor) gives rise to a ring (A, +, *) by defining a + b = (a land b) lor (b land a) (this operation is called symmetric difference in the case of sets and XOR in the case of logic) and a * b = a land b. The zero element of this ring coincides with the 0 of the Boolean algebra; the multiplicative identity element of the ring is the 1 of the Boolean algebra. This ring has the property that a * a = a, for all a in A; rings with this property are called Boolean rings.

Conversely, if a Boolean ring A is given, we can turn it into a Boolean algebra by defining x lor y = x + y + xy and x land y = xy. Since these two operations are inverses of each other, we can say that every Boolean ring arises from a Boolean algebra, and vice versa. Furthermore, a map f: A → B is a homomorphism of Boolean algebras if and only if it is a homomorphism of Boolean rings. The categories of Boolean rings and Boolean algebras are equivalent.

An ideal of the Boolean algebra A is a subset I such that for all x, y in I we have x lor y in I and for all a in A we have a land x in I. This notion of ideal coincides with the notion of ring ideal in the Boolean ring A. An ideal I of A is called prime if I ≠ A and if a land b in I always implies a in I or b in I. An ideal I of A is called maximal if I ≠ A and if the only ideal properly containing I is A itself. These notions coincide with ring theoretic ones of prime ideal and maximal ideal in the Boolean ring A.

The dual of an ideal is a filter. A filter of the Boolean algebra A is a subset p such that for all x, y in p we have x land y in p and for all a in A if a lor x = a then a in p.

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Posted: Jun 28, 2008                                                           I have observed that one of the main reasons that children hate math is they have not mastered the foundation of math, surprisingly the root of problems can be traced to the basics they learned in the elementary grades such as addition, subtraction, multiplication or division. When elementary students are asked why do we have math? Lots of these children can relate math to our daily life such as shopping, cooking, measuring, driving, time, shapes etc. and most of the time they think math is important because it has something to do with counting and numbers.

It is very good these youngsters realize that math has relations to our daily life but does the traditional way of doing of math worksheets such as 2 + 3 reflect the environment today our youth lives? It certainly does not. Math is not just about counting numbers. Apart from teaching the basics of addition, subtraction, multiplication or division, math is supposed to teach our next generation on how to solve problems and be creative. Part of the problems why some children hate math worksheets is simply because these traditional worksheets do not represent the world they are living now.

Many "things" or "toys" our generation play already start to reflect what the society would be like in the future, things such as internet searching and browsing, image viewing, cell phones, roaming, instant messages, downloading and uploading information, compressed files, file formats etc. all of these will simply become part of their life and basic living skills. How do math worksheets reflect the way children are living now or will be in the future? Most school math textbooks still use the same style of worksheets to teach children basic math that is basically number crunches in straight top to down or left to right fashion. There is very little convergence of numbers, images, patterns, comparisons, searching, matching, sorting, classifying between one numbers is operated with another number. This "old" way of manipulating numbers does not represent what our children are doing in today's society. This may have explained why most young children still only think math as counting numbers, but not related to the way on how they process a variety of information in their daily living.

Ho Math and Chess simply uses international chess as a tool to converge the information of images, patterns, sorting, comparison, matching, tables, etc. all together with numbers to better reflect what children are facing or already doing today. We have achieved this learning in a fun way. 

Is there such a thing that math worksheets can be created so they will be fun-oriented that children can play with numbers and be rewarded with satisfying and with great fun? How can the dreaded drill style of math worksheets be improved such that they encourage whole-brain learning? How can math basics computations such as addition, subtraction multiplication or division be incorporated with fun gamed-based approach? Is it possible that children can improve their memory and problem solving skill in a gamed-based learning environment? Ho Math and Chess has created a math and chess integrated worksheets to give positive answers to all the above questions. So how does Ho Math and Chess put math, fun, thinking, creativity, and memory improvement all together?

Chess is a strategy game and it invigorates the thinking ability and has been around for thousands of years. Many organizations and schools have set up chess lessons and often math and chess are taught under the same roof but with no real integrated math and chess curriculum. The reason of why math and chess have traditionally been taught separately is there is really no existing connection mechanism between math and chess teaching. However, this has since changed after Frank Ho, founder of Ho Math and Chess invented the patent applied Symbolic Chess Language (SCL). Ho Math and Chess has successfully created the world’s first math and chess integrated workbook by using its proprietary intellectual product (SCL).

The future belongs to a generation who understands how to process information and the information might include digits, bytes, numbers, graphics, images, languages, symbols, equations etc.  How
these different nature of information processing can be taught to kindergartners or primary students when they are learning arithmetic? It is not an easy task that is why there are so many different types of stand alone worksheets, namely logic, patterns, mazes, or crosswords.  These worksheets are created without interrelations to each other. This kind of isolated information processing is no longer reflecting the real world the young generation is facing today or they will be living in the future.

The computing world children are facing today is a much like a rich tapestry, where a diversified fabrics and colours are integrated. Children today are absorbing not just numbers but an array of information like images, sound, music, symbols, spatial information, or even abstract ideas all bundled together and delivered through many types of media. Children today are not happy just working on pure number drill without any other stimulus or motivator.  Realizing the importance of having fun while learning, Ho Math and Chess has been embarked on an important teaching philosophy that is to integrate chess into math worksheets so that children can learn math while having fun.

Ho Math and Chess created a special synergetic effect by integrating arithmetic basics, chess, mazes, and information processing all on one worksheet. This is accomplished through its own proprietary technologies (patents pending) such as SCL, Frankho Chess Mazes, and an innovative Ho Math and Chess Teaching Set.

With the new invention of Ho Math and Chess worksheets, a child is acting as a data warehouse manager and sorts data through a variety of tools namely chess, symbols, spatial relation, logic, comparison, tables, patterns, mazes, computing etc. by networking all kinds of information together. Only when children have successfully followed through instructions (SCL) and, as a result, created a question themselves, can a solution be found at last.

In Ho Math and Chess worksheets, the questions are not written out for children but must be mined (after children observing how data is moving) through data warehouse (mazes), and answers must be computed after conducting a series of logic thinking process which might include spatial relations, sorting, comparing, matching, classifying, tabling look-ups etc.

Ho Math and Chess trains children not only their basic computing ability but also train them to be an astute data warehouse manager or an excellent data miner by developing their problem solving ability and critical thinking skills.

Ho Math and Chess provides education and also entertainment value to get young children involved in the future world they will be facing.
At Ho Math and Chess, math learning is fun.
  

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