VAK is derived from the accelerated learning world and seems to be about the most popular model nowadays due to its simplicity. While the research has shown a connection with modalities and learning styles (University of Pennsylvania, 2009), the research has so far been unable to prove the using one's learning style provides the best means for learning a task or subject. This is probably because it is more of a preference, rather than a style.

Learners use all three modalities to receive and learn new information and experiences. However, according to the VAK or modality theory, one or two of these receiving styles is normally dominant. This dominant style defines the best way for a person to learn new information by filtering what is to be learned. This style may not always to be the same for some tasks. The learner may prefer one style of learning for one task, and a combination of others for a different task.

Classically, our learning style is forced upon us through life like this: In grades kindergarten to third, new information is presented to us kinesthetically; grades 4 to 8 are visually presented; while grades 9 to college and on into the business environment, information is presented to us mostly through auditory means, such as lectures.

According to the VAK theorists, we need to present information using all three styles. This allows all learners the opportunity to become involved, no matter what their preferred style may be.

While there is some evidence for modality specific strengths and weaknesses (Rourke, et al. 2002), what has has not been established is matching the instructional style to individual learning strength improves their learning abilities. For example, one study (Constantinidou and Baker, 2002), found that visual presentation through the use of pictures was advantageous for all adults, irrespective of a high or low learning-style preference for visual images. Indeed, it was especially advantageous for those with a strong preference for verbal processing.

$ Hints for Recognizing and Implementing the Three VAK Styles

Auditory learners:

Auditory learners often talk to themselves. They also may move their lips and read out loud. They may have difficulty with reading and writing tasks. They often do better talking to a colleague or a tape recorder and hearing what was said. To integrate this style into the learning environment:

Begin new material with a brief explanation of what is coming. Conclude with a summary of what has been covered. This is the old adage of “tell them what they are going to lean, teach them, and tell them what they have learned.”

·       Use the Socratic method of lecturing by questioning learners to draw as much information from them as possible and then fill in the gaps with you own expertise.

·       Include auditory activities, such as brainstorming, buzz groups, or Jeopardy. Leave plenty of time to debrief activities. This allows them to make connections of what they leaned and how it applies to their situation.

·       Have the learners verbalize the questions.

·       Develop an internal dialogue between yourself and the learners.

Visual learners:

Visual learners have two sub-channels—linguistic and spatial. Learners who arevisual-linguistic like to learn through written language, such as reading and writing tasks. They remember what has been written down, even if they do not read it more than once. They like to write down directions and pay better attention to lectures if they watch them. Learners who are visual-spatial usually have difficulty with the written language and do better with charts, demonstrations, videos, and other visual materials. They easily visualize faces and places by using their imagination and seldom get lost in new surroundings. To integrate this style into the learning environment:

·       Use graphs, charts, illustrations, or other visual aids.

·       Include outlines, concept maps, agendas, handouts, etc. for reading and taking notes.

·       Include plenty of content in handouts to reread after the learning session.

·       Leave white space in handouts for note-taking.

·       Invite questions to help them stay alert in auditory environments.

·       Post flip charts to show what will come and what has been presented.

·       Emphasize key points to cue when to takes notes.

·       Eliminate potential distractions.

·       Supplement textual information with illustrations whenever possible.

·       Have them draw pictures in the margins.

·       Have the learners envision the topic or have them act out the subject matter.

Kinesthetic learners:

Kinesthetic learners do best while touching and moving. It also has two sub-channels: kinesthetic (movement) and tactile (touch). They tend to lose concentration if there is little or no external stimulation or movement. When listening to lectures they may want to take notes for the sake of moving their hands. When reading, they like to scan the material first, and then focus in on the details (get the big picture first). They typically use color high lighters and take notes by drawing pictures, diagrams, or doodling. To integrate this style into the learning environment:

·       Use activities that get the learners up and moving.

·       Play music, when appropriate, during activities.

·       Use colored markers to emphasize key points on flip charts or white boards.

·       Give frequent stretch breaks (brain breaks).

·       Provide toys such as Koosh balls and Play-Dough to give them something to do with their hands.

·       To highlight a point, provide gum, candy, scents, etc. which provides a cross link of scent (aroma) to the topic at hand (scent can be a powerful cue).

·       Provide high lighters, colored pens and/or pencils.

·       Guide learners through a visualization of complex tasks.

·       Have them transfer information from the text to another medium such as a keyboard or a tablet.

 B. Recreational activities: games, puzzles, riddles, quiz in mathematics:

Recreational activities in mathematics are creative and enjoyable tasks designed to make learning mathematics fun, engaging, and less stressful. They go beyond traditional teaching methods by incorporating play, puzzles, and exploration, which stimulate curiosity and deeper understanding among students. 

 PUZZLES/ QUIZ:

Administering puzzles/quizzes is essential for teachers to find out what their students are learning or are not learning. When you organize a math puzzles/quiz for your students, it's also important to include a variety of sample questions to ensure that they've learned all that you've taught them.

 Instructions :

o   Brainstorm with the students all of the mathematical information that you taught them prior to the puzzles/quiz.

o   Review samples of each type of mathematical problem so that your students are fully aware of what you plan to present on the math puzzles/quiz.

o   Create the quiz using the same type of sample problems that you reviewed with the students.

o   Include some challenging questions on the math puzzles/quiz. These questions can be sample problems from chapters that you taught weeks or months ago. Organize these questions in no particular order; otherwise, the students can sense that the easiest questions are first.

o   Administer the math puzzles/quiz during class. If the students are allowed to use sample problems to look at, provide them with the samples.

o   Take down any relevant information in the classroom that you don't want the children to see. For example, if you are giving a multiplication puzzles/quiz, take down the multiplication table posters that you posted on the walls.

o   Correct the math puzzles/quizzes. Watch for problems the children had the most difficulty with. Re-teach the material that the students did not do well in.

Tips & Warnings :

Ø  Don't include information on the math quiz that you didn't review or teach.

Ø  Organize the math quiz so that it makes sense to the students.

Math Puzzles

Every kid deserves to be successful and confident in school. Math Puzzles are great for that.  Kids love games and puzzles, so learning math while working puzzles makes learning math fun. Is your math should be fun and interesting. Math puzzles are just one of the many ways to enjoy all of what math has to offer. 

Example: Take a look at the three circles below. Look at the pattern in the top two, and to determine what number should replace the question mark?.

What number goes in the box that has the question mark in it?
Hint: The logic to this puzzle is vertical instead of horizontal.

More math puzzles below and you can also go to the main math puzzles page by clicking link near bottom of this page.

Math Word Search Puzzles

         If they can have fun at it, they can learn to love it. Math word search puzzles are a simple and fun way to help students active in learning. Use them to make sure kids know and understand important math terms!

You can print them off and they're good for use at home or in the classroom.

You can use these puzzles for almost any age group...from elementary all the way though high school.

Whatever they are learning in math at the time, those words can be used in the puzzle. It's very helpful to get students familiar with math terminology.

. Do you notice that all the rows add up to 15.

For example, adding each of the three numbers in the top row, we get,

8 + 1 + 6 = 15

Likewise, adding the three numbers in the second row, we get,

3 + 5 + 7 = 15

And finally the last row, we get,

4 + 9 + 2 = 15

Pretty Cool, huh. But wait, there's more....

Do you notice the sum of each of the columns is also 15? Let's have a look...

Column 1: 8 + 3 + 4 = 15

Column 2: 1 + 5 + 9 = 15

Column 3: 6 + 7 + 2 = 15

But wait, there's is still more...

If we add the three numbers on the diagonals, their sum will also equal 15.

8 + 5 + 2 = 15

6 + 5 + 4 = 15

Kids enjoy magic squares because they're like a fun puzzle to figure out. Teachers and parents like them because while they are fun for students, they also provide practice in mental arithmetic and operations with numbers.

Benefits of Math Puzzles Using math logic puzzles can help foster a student's creativity and imagination. And it helps to build their problem-solving skills, enabling them to become better math students.

GAMES: 

When we're having fun, we're more open to learning. When we're having fun, we want to keep doing whatever we're doing. So if you’re a parent, teacher, or student and want to make math more user-friendly, come and explore our site where you'll find lots of fun math activities and other cool math stuff!

You'll find fun games and math activities on this site for just about any topic students are learning in math...

Imagine having a child beg to practice some aspect of Math! Pull out a great Math Activity and kids of all ages lose their Math inhibitions and happily engage in even complex mathematical tasks. Talk about motivation!

Math activities are for everyone. Whether a student does well or struggles with Math, Mathematical games teach new concepts and provide lots of opportunity to practice. A good game allows people with all levels of skill to participate together.

MATH RIDDLES:

 Short riddles are a statement or a question that has a double meaning which is presented as a solvable puzzle. There are two riddle types that you will come across:

Enigma: These types of riddle are presented as either a metaphor or allegorical language which requires careful thinking and ingenuity in order for a solution to be found.

Conundrum: These riddles rely on the questions effects on punning the answer or the question itself.

Examples:

1.Why should you never mention the number 288 in front of anyone? Because it is too gross (2 x 144 - two gross).

2. Which weighs more?  A pound of iron or a pound of feathers?  Both weigh the same.

3. How is the moon like a dollar? They both have 4 quarters.

4. What is alive and has only 1 foot? A leg.

5. When do giraffes have 8 feet? When there are two of them.

C. Mathematics laboratory and Mathematics club

Meaning:

A Mathematics Laboratory is a dedicated space designed for students to explore, experiment, and engage with mathematical concepts in a hands-on, practical manner. It is equipped with tools, manipulatives, models, and technology that help students understand abstract mathematical ideas by visualizing and experiencing them in a concrete way.

Purpose:

The main purposes of a Mathematics Laboratory are:

• Experiential Learning: To provide students with opportunities to learn through doing, experimenting, and exploring mathematical ideas.

• Conceptual Clarity: It helps students visualize abstract mathematical concepts, making them easier to understand.

• Problem Solving: Encourages critical thinking and problem-solving skills by allowing students to approach mathematical problems in different ways.

• Collaborative Learning: Promotes teamwork and cooperative learning, as students often work in groups to solve problems or conduct experiments.

• Innovative Approach: Introduces a creative, engaging way to approach learning math, moving beyond traditional textbook methods.

Importance:

1. Improves Understanding: Mathematical concepts like geometry, algebra, trigonometry, and arithmetic can be better understood through visualization and practical experience.

2. Increases Interest in Math: Hands-on learning can make math more enjoyable and engaging, helping students develop a positive attitude towards the subject.

3. Develops Mathematical Thinking: Enhances logical thinking, reasoning, and decision-making skills.

4. Boosts Retention: By experiencing concepts practically, students are more likely to remember them in the long run.

5. Encourages Self-Learning: Students can explore and discover mathematical principles on their own, fostering curiosity and independence.

Example of Equipment in a Mathematics Laboratory:

1. Geoboards: Used to explore concepts in geometry such as area, perimeter, and the properties of shapes.

2. Tangrams: A puzzle consisting of flat pieces that can be arranged to form various shapes, helping students understand geometry and fractions.

3. Algebra Tiles: Visual aids that help students solve algebraic equations and understand concepts like factoring and expanding.

4. Abacus: An ancient counting tool, still used to teach arithmetic operations.

5. Graphing Calculators: Allow students to plot graphs and explore the relationships between variables in functions.

6. Measurement Tools: Includes rulers, protractors, and compasses for measuring and drawing geometric shapes.

7. Models of Solids: 3D models like cubes, spheres, pyramids, and cylinders help students understand volume, surface area, and properties of solids.

8. Interactive Software: Computer programs that allow dynamic visualization of mathematical concepts, such as geometry or calculus.

A Mathematics Laboratory enhances the learning experience by making abstract mathematical ideas more tangible and approachable, supporting various learning styles.

Mathematics Club: Meaning, Purpose, Importance, and Example of Equipment

Meaning:

A Mathematics Club is an extracurricular group or organization within a school, college, or community where students gather to explore mathematical concepts, puzzles, problems, and activities outside of the regular classroom curriculum. It fosters a collaborative and engaging environment where students can share their interest in math, discuss challenging problems, and participate in math-related activities and competitions.

Purpose:

The primary purposes of a Mathematics Club are:

• Enhance Mathematical Knowledge: To deepen students' understanding of mathematical topics through activities, discussions, and competitions.

• Encourage Creativity and Innovation: Promotes innovative thinking by solving non-standard and complex mathematical problems.

• Develop Problem-Solving Skills: Helps students improve their logical reasoning and problem-solving abilities.

• Promote Teamwork: Encourages collaboration among students to tackle group challenges and projects.

• Prepare for Competitions: Prepares students for math contests such as Math Olympiads, quiz competitions, and other mathematical events.

• Cultivate Interest in Mathematics: Provides an informal setting for students to discover the beauty of mathematics and enjoy learning without the pressure of grades.

Importance:

1. Builds Mathematical Confidence: Participating in club activities helps students build confidence by tackling and solving complex problems in a supportive environment.

2. Improves Critical Thinking: It nurtures analytical skills and promotes a logical, systematic approach to solving problems.

3. Fosters a Positive Math Culture: By participating in fun and challenging activities, students can develop a positive attitude toward math, even if they find it difficult in formal classroom settings.

4. Provides Peer Learning Opportunities: Students can learn from each other, share different strategies for solving problems, and engage in healthy competition.

5. Enhances Academic Performance: The skills and techniques learned in the club can often help students perform better in their academic studies.

6. Promotes Leadership and Teamwork: Involvement in organizing club events and leading activities can develop leadership skills, while teamwork enhances collaboration and communication skills.

Example of Equipment and Resources in a Mathematics Club:

1. Puzzles and Brain Teasers: These challenge students’ problem-solving abilities and improve logical reasoning. Examples include Sudoku, KenKen, and mathematical riddles.

2. Math Games: Board games like Set, Prime Climb, or Math Bingo can make learning math fun.

3. Whiteboards and Markers: For group problem-solving sessions, quizzes, or explanations of complex problems.

4. Graphing Calculators: Helpful for solving higher-level problems and exploring functions, graphs, and statistics.

5. Geometry Sets: Includes rulers, protractors, compasses, and 3D models for activities related to geometry and measurement.

6. Math-related Software or Apps: Programs like GeoGebra, Desmos, and Mathematica can be used for dynamic learning of algebra, calculus, and geometry.

7. Books and Journals: A library of math-related books, problem-solving guides, and academic journals can be a useful resource for students to explore beyond the curriculum.

8. Math Manipulatives: Items like algebra tiles, fraction bars, or base ten blocks can be used for hands-on learning and exploring different mathematical concepts.

9. Computers or Tablets: To access online resources, apps, and simulations that support math learning.

10. Competition Kits: Materials and resources required for math competitions, such as practice papers for Olympiads or quiz buzzers.

A Mathematics Club creates an enriching environment for students to enjoy math, develop their skills, and explore the subject beyond the boundaries of the classroom, promoting both personal and academic growth.

D. VEDIC MATHEMATICS:

Introduction:

         The most important contribution of ancient India not only for India but also for the world is in the field of education. It may also be remembered that education is not an abstract term. It is manifested in the cultural economic, individual, philosophical, scientific, social and spiritual advancement. In other words, education is the means for developing the mind for the betterment of the individual and society. Seen from this perspective, the following views of great scholars and thinkers deserve mention.

Albert Einstein:-

“We owe a lot to the Indians who taught us how to count without which no worthwhile scientific discovery could have made.”

Mark Twain, an American Writer:-

“India is the cradle of the human race. Most valuable and the most instructive materials in the history of man are treasured up in India only.”

Lancelot Hagen, in his publication Mathematics for the Millions:-

“There has been no more revolutionary contribution than the one which the Hindus made when they invented zero.”

Aims, Ideals and Objectives of Vedic Education:

1. Ultimate objective as moksha or self-realisation:- Ancient Indians believed that education should prepare and individual in such a way as to prepare him to attain the objective of liberation, i.e. to be one with the almighty and to be free from the cycle of births & deaths.

1. Infusion of Piety & Religiousness:- In ancient India religion played a prominent part. Education aimed at the infusion of piety and religiousness in the minds of the pupils.

2. Education for worldliness:- Vocational aim :- Happiness in other world was given more stress than the happiness in this world. This world according to them, was unreal & full of fetters. The highest wisdom was a release from these betters.

3. Character formation:- Education must from character. Mere intellect was not of worth if the person was devoid of not much morality. Morality or the right behavior was the higher “Dharma”. Education was regarded as a means of inculcating values such as strict obedience to elders, truthfulness, honesty and temperance.

4. Development of all round personality:- Ancient Indians believed that personality should be developed through education. Personality was developed through the following methods:-

(a)    Self-restraint

(b)   Self-confidence

(c)    Self-respect

(d)   Discrimination and judgement

5. Stress on Social duties:- A student was not to lead self-centered life. He was to perform his duties as a son, as a husband, as a father & many other capacities conscientiously and efficiently in the society. His wealth was not for his own sake as for his family, he must be hospitable and charitable. All professions laid stress on civil responsibilities.

6. Promotion of Social Efficiency and Welfare:- The promotion of social efficiency & welfare was an equally important aim of education. Education was not imported simply for the sake of culture or for the purpose of developing mental powers but for the purpose of training every member of society in the profession which he expected to follow. Society had accepted the theory of division of work which was later on governed by the principle of heredity. Each family trained its children in its own profession. The purpose was to make each individual society efficient.

7. Preservation and promotion of culture:- the preservation and promotion of national culture and heritage was also stressed. “The services of the whole community were conscripted for the purpose of the preservation of the Vedic literature. Every person had to learn at least a portion of his sacred literacy heritage.” A section of Brahman as had to devote the whole of their life to the cause of learning to commit the Vedas to memory in order to ensure preservation.

Education of Women: The Vedas give a very honorable & respectable status to women. They were eligible for higher education for the study of the Vedas and the performance of administrative and other important jobs mostly performed by men even today.

Boys should go to the schools meant for boys and girls should go to the schools where there are women teachers. The women should have opportunity to attain knowledge of the Vedas from all the four concerns.

Role of Mother in Education: A mother should impart education to her children so as to broaden their horizon. At this stage good manners are to be taught so that the children behave properly with the elders and in assemblies.

Teachers as Spiritual as well as Intellectual Guide: Teacher occupied a pivotal position in the Vedic System of education. The teacher was a parent surrogate (Parent Substitute), a facilitator of learning, exemplar and inspirer, confident, detector friend and philosopher moral educator, reformer, evaluator, character and personality builder, importer if knowledge & wisdom and above all a guru, religious & spiritual guide. The relationship between the teachers and pupil was regarded as filial in character. Teacher was the spiritual father of his pupils. In addition to imparting intellectual knowledge to them, he was also morally responsible. He was always to keep a guard over the conduct of his pupils. He must let them know what to cultivate and what to avoid. He must instruct them as how to sleep and as to what food they may take and what they may reject. He should advise them as to the people whose company they should keep and as to which of the villages and localities they should frequent. During the Vedic period learning was transmitted orally from one generation to another. Great importance was attached to the proper accent and pronunciation in the Vedic recitation & these could be correctly learnt only from the lips of a properly qualified teacher. The spiritual solution depended almost entirely upon the proper guidance of a competent teacher.

Short Cut Methods (Vedic Mathematics):

         Vedic Mathematics is the name given to the ancient system of Mathematics which was rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960). According to his research all of mathematics is based on sixteen Sutras or word-formulae. For example, 'Vertically and Crosswise` is one of these Sutras. These formulae describe the way the mind naturally works and are therefore a great help in directing the student to the appropriate method of solution.

         Perhaps the most striking feature of the Vedic system is its coherence. Instead of a hotch-potch of unrelated techniques the whole system is beautifully interrelated and unified: the general multiplication method, for example, is easily reversed to allow one-line divisions and the simple squaring method can be reversed to give one-line square roots. And these are all easily understood. This unifying quality is very satisfying, it makes mathematics easy and enjoyable and encourages innovation.

         In the Vedic system 'difficult' problems or huge sums can often be solved immediately by the Vedic method. These striking and beautiful methods are just a part of a complete system of mathematics which is far more systematic than the modern 'system'. Vedic Mathematics manifests the coherent and unified structure of mathematics and the methods are complementary, direct and easy.

         The simplicity of Vedic Mathematics means that calculations can be carried out mentally (though the methods can also be written down). There are many advantages in using a flexible, mental system. Pupils can invent their own methods, they are not limited to the one 'correct' method. This leads to more creative, interested and intelligent pupils.

         Interest in the Vedic system is growing in education where mathematics teachers are looking for something better and finding the Vedic system is the answer. Research is being carried out in many areas including the effects of learning Vedic Maths on children; developing new, powerful but easy applications of the Vedic Sutras in geometry, calculus, computing etc.

But the real beauty and effectiveness of Vedic Mathematics cannot be fully appreciated without actually practicing the system. One can then see that it is perhaps the most refined and efficient mathematical system possible.

 Examples:

i) To Subtract 357 from 1000. We simply take each figure in 357 from 9 and the last figure from 10.

ii) Just put a decimal in front of the numerator:

1/10 = .1

2/10 = .2

3/10 = .3

4/10 = .4

iii)11th are easy in a similar way, assuming you know your multiples of 9:

1/11 = .090909...

2/11 = .181818...

3/11 = .272727...

4/11 = .363636...

5/11 = .454545...

iv) VERTICALLY AND CROSSWISE formula for multiplication.
23 below 21:

REFERENCES:

1. Rourke, B., Ahmad S., Collins, D., Hayman-Abello, B., Hayman-Abello, S., and Warriner, E. (2002). Child clinical/pediatric neuropsychology: some recent advances.Annual Review of Psychology, 53, 309Ð339.

2. University of Pennsylvania (2009). Visual Learners Convert Words To Pictures In The Brain And Vice Versa, Says Psychology Study. ScienceDaily. Retrieved July 10, 2011, from http://www.sciencedaily.com/releases/2009/03/090325091834.htm

3. ·       Burns, M. (2007). About teaching mathematics: A K–8 resource (3rd ed.). Math Solutions Publications.

4. ·       Reys, B. J., Lindquist, M. M., Lambdin, D. V., & Smith, N. L. (2014). Helping children learn mathematics (11th ed.). Wiley.

5. ·       National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Author.

6. ·       Natarajan, C., & Anitha, V. (2005). Mathematics laboratory in schools: Towards joyful learning. National Council of Educational Research and Training (NCERT).

7. ·       Kapur, J. N. (1992). Mathematics education: From classroom environment to laboratory environment. Arya Book Depot.

8. ·       Singh, M. (2013). Teaching of mathematics. PHI Learning Pvt. Ltd.

9. ·       Ghosh, S. (2016). Mathematics laboratory manual. Laxmi Publications