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"No subject is ever well understood and no art is intelligently practiced, if the light which the other studies are able to throw upon it is deliberately shut out." - RAMONT
What is correlation?
The meaning of term 'correlation' in simplest form is "connect" or "to be connected". More precisely, 'Correlation' means mutual relation of two or more items/things or Mutual relation of two or more than two items/things.

The relation may be inverse or direct. For examle if there are two variables 'a' and 'b', if there is increase or decrease in one will affect on other. It is really a brainstorming activity which involves lots of efforts to be establishing relationship between school Subjects.

In modern scenario, due to the number of innovation of 21 st century involves lots of development in the education. These involve meaningful knowledge of the concept. Here child's mind is an integrated whole, he wants to receive experiences in a fruitful manner.
Definition
"Correlation indicates a joint-relationship between two variables." Lathrop

"Correlation is concerned with describing the degree of relation between variables." Ferguson

"Correlation is an analysis of co-variation between two or more variables." A.M. Taule

"Correlation analysis deals with the association between two or more variables." Simpson & Kafka
Types of correlation

Positive correlation - when an increase in one variable, increases the value of another variable or vice versa.

Negative correlation - when an increase in one variable, decreases the value of another variable or vice versa.

Incidental correlation - It is not a planned/pre-decided, no deliberate or a systematic attempt made to correlate it. Teacher plays a leading role. E.g. If any teacher has basic knowledge of concepts/elements of versatile or different subjects, he can easily make correlation between two or more subjects. A teacher cannot establish incidental correlation without having knowledge of different subjects.

Systematic correlation - teachers can sit together with his students and how to correlate? While doing systematic correlation, the previous knowledge/content of the student should be related with the current knowledge. To relate the same is called systematic correlation. Here, the student and the teacher have to think about the application of the fact, laws, principles, and correlation of two subjects. After that knowledge becomes interesting.

No correlation - when there is no mutual relationship between the two variables. It is also known as no linear dependent.

Uses of correlation:

The aim of education is "to achieve the all round development of a child", this cannot be done by teaching only in simple classroom.

In correlation, the practical subjects like maths and science plays important role. Where the correlation with concepts is used in learning of students.

It makes learning permanent and concrete and knowledge to the learner.

It makes the lesson easy and clear for the student.

It enhances the mental abilities like problem solving, logical reasoning, imagination, and analytical power of student, because these can easily correlate acquired knowledge with the other subjects.

It strengthens the skill, complexity of practical subject and makes mastery over the practical subject.

It develops social relationship like - human and social qualities in students.

For teachers; it helps to complete the curriculum within short period of time and provides time for revision.

Knowledge is useful and is maintained so that it can be developed and used in day to day life.

Examples of dependent phenomena include the

1. Relation between parents and their offsprings.

2. The correlation between theprice and availabilty of product in the market.

3. The theoretical aspect of anything explains the practical concept.

4. Even a crime is also related to wrong addictions.

5. The negative correlation between age and normal vision.

6. The positive correlation between the incidence of lung cancer and cigarette smoking.

Correlation of Mathematics with other disciplines
Mathematics is "Science of all Sciences" and "Art of all Arts". After understanding the basic concept of mathematics, students need to correlate the importance and concept of mathematics with other subjects, so as to understand other subjects easily and establishing relationship. Mathematical knowledge plays a crucial role in understanding the contents of other subjects.

MATHEMATICS WITH GENERAL SCIENCE: Science without mathematics is totally meaningless, because chemical reactions, scientific theories and detail of elements are only generated/ counted with the help of mathematics. Mathematics is used in most of applications like in work, energy, electricity, motion, gravitation, magnetism etc.

MATHEMATICS AND PHYSICS: child should have rich knowledge of mathematics to understand physics. Generally final shape to the rules of physics is given by mathematics; it presents these rules in practically workable form. Mathematical calculations occur in every step of physical science. Charle's law of expansion of gases is based upon mathematical calculations, numerical problems on liquid, pressure,frictional force, laws of motion, gravitation, momentum etc.

MATHEMATICS AND CHEMISTRY: Molecular weights of organic compounds are calculated with mathematics. To measure the constituents of mixtures and Chemical compounds. To calculate Empirical or molecular formula. In balancing the chemical equations. In electronic configuration of atom of the element. Charle's law of expansion of gases is based upon mathematical calculations.

MATHEMATICS AND BIOLOGY: Mathematics has very high correlation with biology. The Normal Weight, Caloric value, Rate of Respiration, Nutritive Value of Food, Transpiration, is calculated by Maths. The Growth in Weight of infants' upto Nine months. To count the number of bones in human being and other different species. To measure blood pressure. To count the number of WBC & RBC in different blood groups. To count Sex chromosomes.

MATHEMATICS AND SOCIAL SCIENCES: After completion of the unit child can read, interpret, and draw the graphs. For example, to compare the Population- students can draw bar graphs, Population Density of various countries, Per Capita Income etc.

MATHEMATICS AND GEOGRAPHY: Geographical figures are explained in the terms of numbers only like seasonal conditions, temperature, humidity, degree, measurement of rain etc. the geographical conditions also defines the economy of a rich/poor country. Many countries like India have agricultural based economy due to its climate, rainfall, rivers and weather prediction.etc.

Certainly Mathematics is used for constituting the map, Formation of Nights & Days, Solar & Lunar Eclipse, Longitude Latitude, Maximum and Minimum Temperature, Barometric Pressure, Height above Sea Level, Surveying, Calculation of International, Local and Standard Time, Instruments etc. And here are also many other calculations. Punjab, Haryana and U.P are very fertile states in India, so contribute to grain stores, industries are established there but in these states there are no mines.

MATHEMATICS AND HISTORY: in history Mathematics helps in Calculation of Dates like duration of Britishers ruled in India? When Gandhi ji was born? Celebrate National Days and festivals, Cost in building of Taj-Mahal. Tenure of President in India. This gives us new information of the historical world. When the First and second world wars were fought? On account of economic considerations industrial revolution in Europe.

MATHEMATICS AND ECONOMICS: Statistical Methods are used to calculate and to know the Volume of Trade, Trend of Import and Exports, Economic Forecasts, Trade Cycles, It helps in calculating various indexes like crop production inflation, etc.

All economists, citizens and the businessmans can get the market trends & economic conditions. Through currencies market, the Current updates of currency and through stock and commodity market the current updates of the stock and commodity of different countries.

Only because of economic reasons certain empires faced liquidation. Similarly, economic events have been influenced or affectd by historical circumstances. In the current scenario the economic condition of India during UPA and NDA.

MATHEMATICS AND FINE ARTS: decides size, Ratio and Proportion while constructing the Similarity, Scale appreciation, Balance and Symmetry, Postulates, Drawing images on cloth and paper, Rhythm in Music etc.

MATHEMATICS AND LANGUAGE:

Math and Reading:- Students read about the discoveries or work of great mathematicians, and they can make poem on numbers.

Math and Writing (numbers are converted into writing):- A student makes the pie chart and interprets in his own words.

e.g. Counting of alphabet, vowel, Read About The Life History of Mathematicians. Student can draw make a bar graph of time spent in school and home the whole week and can interpret. (Interpretation of Non-Verbal Data)

MATHEMATICS WITH AGRICULTURE: Agriculture has close relationship with Maths. Agriculture has correlation with maths like area of crops, which season is suitable for which crop. How much quantity of water may be used in irrigation is also calculated in concern of agriculture by the use of mathematics. Investment, expenditure and saving in sowing specific crop, Division of land, Cost of labour, seed, fertilisers, expenditure in transportation of vegetables to the market, has the use of mathematics. As due to scientific inventions, there is lot of growth of agriculture & economy takes place.

MATHEMATICS WITH COMMERCE/ACCOUNTS: With the rich knowledge of commerce it is possible to study the economy of the country. Only by the knowledge of mathematics, Debit, Credit process & expenditure in accounts of industry, banks firm, etc are determined. The commerce teacher of should try to teachor make understand in such a way that students may relate and explain all specific terms mathematically.

MATHEMATICS AND ICT: The ICT is strongly correlated with mathematics. Computer programmes, applications, software and different languages without mathematics are impossible to operate and follow. Students are taught computers only because of knowledge of mathematics. Computer Provides important software for calculation e.g. SPSS software used in the long statistical calculations for research work. Many mathematical packages are used included Logo, dynamic geometry software, graph plotting etc., which are used in the teaching programmes.

MATHEMATICS WITH ENGINEERING: without mathematics Engineering is like sea without water. Mathematics has very strong correlation with each and every branch of engineering. Mathematics is used in every branch of engineering like Electronics, Electrical, Mechanical, Architect, Civil, Chemical, Computer etc. To get admission in any engineering stream, student must read Mathematics as a subject upto class 12.

MATHEMATICS WITH PSYCHOLOGY: Mathematics has correlation with Psychology for measuring I.Q, S.D, coefficient of correlation, Significance of difference, Measure of central tendency (Mean, Median, and Mode). "Likert Scale" used in psychology to make questionnaire. Mathematics is used in different modes of psychology like industry, army, social etc.

MATHEMATICS WITH ASTRONOMY: Counting of Stars and Planets, No. of moon/satellite of all planets. No. of stars in galaxy. Time taken in revolving at its own orbit. Formation of seasons, Life of star, galaxy etc. And Distance between two planets.

MATHEMATICS WITH PHYSICAL EDUCATION: Mathematics is used to measure structure of the body, blood pressure, the height, weight, rules of the games etc. Temperature of the normal human body, Size of playground, norm and standard of game like boot-ball, hockey, cricket, volleyball, tennis, wrestling, boxing etc.
One more important espect or field

MATHEMATICS WITH INDUSTRY: Mathematics is used in industrial work for example:- weaving, knitting, making furniture, leather work, making paints and fertilisers etc. Mathematical calculations are required to calculate all work and the cost.
References http://www.businessdictionary.com/definition/correlation.html#ixzz2RmJKiVEA http://en.wikipedia.org/wiki/Correlation_and_dependence http://www.ditutor.com/regression/types_correlation.html
PPT by Ms. Namrata Katare Saxena, Asst Prof. PCER, MES

Dr. B. Pandya; Teaching of Mathematics (2007), Radha Prakhashan Mandir, Agra

S.K. Mangal; Teaching of Mathematics, Tondon Publications, Ludhiana

Find out more

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Correlation of Mathematics With Other Subjects

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Disclaimer: This work has been submitted by a student. This is not an example of the work produced by our Essay Writing Service. You can view samples of our professional work here. Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of UK Essays.

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The exasperated sighs of students who insist that they'll never need the information they learn in math classes are so common that many teachers and parents have stock answers for the ways math functions in everyday life. But math is also relevant to a wide variety of academic subjects, which means that a student who does poorly in math could end up struggling in other subjects. Many classes in college and trade school involve measuring, weighing, drafting, understanding chemical formulas, calculating statistics and analyzing marketing data, for instance. Students' career options will be limited if they do not have a solid foundation in math.

Science and math are intimately connected, particularly in fields such as chemistry, astronomy and physics. Students who can't master basic arithmetic skills will struggle to read scientific charts and graphs. More complex math, such as geometry, algebra and calculus, can help students solve chemistry problems, understand the movements of the planets and analyze scientific studies. Math is also important in practical sciences, such as engineering and computer science. Students may have to solve equations when writing computer programs and figuring out algorithms. Nursing majors may have great bedside manner. but they also need to know how to precisely calculate dosages to pass their courses.

Literature might seem like a far cry from math, but mastering basic arithmetic can enable students to better understand poetry. The meter of poetry, the number of words to include in a line and the effect that certain rhythms have on the reader are all products of mathematical calculations. At a more mundane level, math can help students plan reading assignments in literature classes by discerning their average reading time and estimating how long it will take them to read a particular work. The linear, logical thinking used in mathematical problems can also help students write more clearly and logically.

Social studies classes, such as history, often require students to review charts and graphs that provide historical data or information on ethnic groups. In geography classes, students might need to understand how the elevation of an area affects its population or chart the extent to which different populations have different average life spans. Knowledge of basic mathematical terms and formulas makes statistical information accessible.

Students interested in pursuing careers in theater, music, dance or art can benefit from basic mathematical knowledge. Musical rhythm often follows complex mathematical series, and math can help students learn the basic rhythms of dances used in ballet and theater performances.Art thrives on geometry, and students who understand basic geometric formulas can craft impressive art pieces. Photographers use math to calculate shutter speed, focal length, lighting angles and exposure time.

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How Is Mathematics Used in Other Subjects?

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Understanding how math is important to future career aspirations can help motivate students to study and ask questions in class. Brainstorming how math is used in different occupations demonstrates that math is an essential skill. Math proficiency opens doors to exciting career options.

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Elsie Arntzen is Montana's Superintendent of Public Instruction

March 31, 2020

I want to thank Montana's students, teachers, parents, and school leaders for your tremendous leadership in these extraordinary times! The OPI is here to serve you each and every day.

COVID-19 Updates

To view the latest updates and press releases from the OPI, DPHHS, the Governor's Office, and other state agencies visit this LINK.

For education resources and updates related to COVID-19 visit this LINK.

Be sure to sign up for the OPI's newsletters at this LINK.

The U.S. Department of Education has approved the OPI's request to waive requirements for the 2019-2020 school year assessment, accountability, and reporting for states and local education agencies under ESSA. The waiver still requires the OPI to solicit public comment on the request. Any comments on this waiver should be directed to essainput@mt.gov.

Montana is projected to receive $41.3 million through the Title I formula (but with local flexibility over use) and $8.8 million for the Governor's Emergency Education Relief Fund from the federal CARES Act. The OPI will share with districts their projected allocations as soon as they are available. Districts are also able to directly apply for Project SERV funds which can be used for a variety of disaster responses: https://www2.ed.gov/programs/dvppserv/applicant.html

Superintendent's Office COVID-19 Outreach

Six calls with district and county superintendents

Phone call with the Governor

Phone call with Secretary DeVos

Phone Call with Assistant Secretary Mark Schultz on Special Education

Phone call with Deputy Education Secretary Zais and State Superintendents from ND, SD, WY, ID, and AK

Seven press releases issued on OPI's actions and waiver requests

Dozens of media interviews

Dedicated COVID-19 education webpage with resources and udpates

Constant communication with the Governor's office, education associations, Congressional offices, the Department of Education, DPHHS, and the Montana Coronavirus task force

Waiver requests to provide schools with flexibility in delivering alternative education and nutrition services

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Elsie Arntzen is Montana's Superintendent of Public Instruction March 31, 2020 I want to thank Montana's students, teachers, parents, and school leaders for your tremendous leadership in these extraordinary times! The OPI is here to serve you each and every day.

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Back to Course Home Page

Welcome to Unit 1!

Welcome to the first unit in the mini-course on Mathematical Literacy: Teaching with, developing, and utilizing Math Journals. To start off this unit, I want you to think in your head (or write out) words that come to mind when you think of Mathematics and Literacy. This can be about the two terms separately or even together as the idea of Mathematical Literacy. I imagine there are many ideas that come to mind about both. As we continue to uncover the ideas that are deeply rooted in the study of Mathematical Literacy, see how some of these words and ideas are related to the topics discussed. Perhaps the connections you see will help to better relate your current beliefs to the new ideas and understandings presented.

What is Mathematical Literacy?

Though this unit may be called "Defining Mathematical Literacy," I will not be handing you out a definition of the term. My purpose in this unit is for you to come to a conclusion on what you believe this definition truly is. Mathematical Literacy encompasses a large number of tools, skills, and understandings, as well as ways of thinking, doing, and teaching. Take a look at the following cartoon:

What does this cartoon truly communicate, beyond the student's misinterpretation of the idea of a variable? What underlying math literacy issue is at work here? By the end of this unit, you will have a better idea of what ideas and understandings impact this students ability to make sense of the term 'x.'

In order to understand and in turn define mathematical literacy, we must also make ourselves aware of the skills and methods for teaching mathematics. Mathematical literacy is about engaging in the real world conversation that surrounds mathematical thinking. For students to engage mathematical thinking and perspectives there are many skills, tools, and mathematical understandings that students must have. On the flip side of the coin, teachers must also consider how their own methods and practices impact the fostering of mathematical literacy in students, and how they can better help their students to engage in the deeper conversations that are necessary for mathematical thinking.

Mathematical Skills

A first step in understanding Mathematical Literacy is to consider the skills involved in mathematical problem solving. There are several skills identified as new and important skills for mathematical thinking, which in turn help students to become more mathematically literate. These skills help students to process and solve their way through mathematics in novel, real world situations, an important implication for the study of mathematics.

Students should be able to:

1. Apply mathematical skills in both familiar and unfamiliar situations.

2. Learn how to select and combine various skills for the purpose of solving problems.

3. Work in collaborative groups to solve problems and talk about mathematics.

4. Write about mathematics and the problem solving process (A crucial skill for mathematical literacy).

5. Use mathematical ideas and ways of thinking to communicate about the world (A second crucial skill for mathematical literacy).

6. Reflect on their own learning process (A component of Mathematics Journals).

7. Use technology to support problem solving in math.

8. Utilize their skills appropriately and effectively in combination with research.

Once students develop many of these important skills they will better be able to participate in the three major domains of mathematical literacy. These three domains are comprised of Reading, Interpreting, and Expressing. When these three modes of thinking and communicating about mathematics are combined, students will start to become more mathematically literate.

Mathematical Literacy

Reading, in the context of math, is about learning to deal with the language specific to math. Within mathematical understanding, students encounter a math-specific set of technical language that they must comprehend to work and solve their way through math. Additionally, students must learn to interpret components of a language that is very different and new. Students will encounter symbols, algebraic equations, diagrams, and graphs, each communicating about the real world in a mathematical lens. In order to be literate in mathematics, students must learn to interpret and make meaning from this new and unfamiliar language.

This leads to the next domain important for mathematical literacy of Mathematical Interpretation. In making meaning from mathematics, students must learn to transform their everyday language into mathematical language, in a way that is accurate and meaningful. This is the interpretation step for literate mathematics students. There are a number of ways that this can look as well. Students may represent the real world and situations they encounter in it through numbers, symbols, diagrams, and graphs. (Which are all components of math language).

A third domain of mathematical literacy is expressing. In expressing mathematical understandings and ideas, students must learn to use math language for means of talking to others about every day occurrences and situations. This can occur in many ways, whether it be simply talking in mathematical language, modeling a process or skill, problem solving in math, or performances, such as a math demonstration or proof. When students are able to communicate about math, they add on the third crucial component to their own mathematical literacy. In a way, the three domains are simply, Reading, Comprehending/Understanding, and Writing/Speaking about mathematics.

Try working through one of these examples in order to practice using mathematical language and for purposes of self-reflection.

Example #1: Write a story about the information shown in the graph.

Example #2: Create a new representation of the article utilizing graphs and/or tables.

(Clarke, pg. 10)

Having completed one of these exercises, how did the exercise help you to better understand the domains of Mathematical Literacy?

Mathematical Tools

There are many mathematical tools that a math literate student can use. However, more importantly, students must learn how, when, and why to use the tools that they have learned. Teachers help to shape students fluency in using tools to make meaning out of the situations that they encounter in problem solving through mathematics.

1. Tool Possession: Does the student have the tool to solve a problem? (For example, can a student take an average of a set of numbers).

2. Tool Understanding: Does the student know how to use the tool? (For example, if a student is given an average of a set of 5 numbers, can they develop a set of data that results in the same average).

3. As a Concept: Is the student able to use a real world situation to demonstrate an understanding of the concept? (For example, using a string to measure and display the average height of a group of students).

4. Tool Application: Can the student apply the tool using a real world context? (For example, finding averages related to expenses, incomes, or sales).

5. Tool Selection: Does the student know when to use a tool? (For example, if a student is given an open-ended question that can be solved using averages, can they appropriately select that tool to solve the problem).

When students are fluent in the usage of mathematical tools they can better work their way through the problem solving process. In addition, when they can do this, they will be able to better communicate and express how they solve problems and what tools they decided to use when/how to solve those problems.

Mathematical Thinking

In Mathematics, there are a many different ways for students to think about mathematics in order to create the most meaning out of what they are learning. Sometimes, it is more important for students to be aware of their own thinking about a problem then to simply attempt the problem. When students are able to think about the best way to look at a problem, they can better generate a solution pathway into working through the mathematical ideas presented.

1. Abstraction: a student's ability to decontextualize a problem; recognize the mathematical ideas outside of the situation of the problem.

2. Contextualization: a student's familiarity with mathematical ideas in a variety of contexts/situations.

3. Interconnectedness: a student's ability to change how the information is represented and still see the similarities in mathematical ideas throughout.

Explore the following example to see how you think about the problem. Is it necessary for you to identify solely the mathematical ideas? Or do you need to understand something about the situation to solve the problem? Is it necessary for you to represent the situation in a different form to make meaning of the mathematical ideas?

A photograph is 4 inches wide by 6 inches long. If an enlargement of this photo is 10 inches wide, how long is it? If the enlargement needed to fill a billboard is 8 feet wide, how long would it be? Use a graph to represent the photo's length for any width up to 12 feet. (Clarke, pg. 14)

How did your understanding of the context help you to understand the problem? How did you use that understanding in combination with the mathematical idea of proportions to solve the problem?

Good Educational Practice in Mathematics

Though many of the preceding ideas about math are very student-centered, they help teachers to better understand what is necessary for good instruction and assessment of important mathematics. Teachers must begin to think about what ideas and messages they truly want to convey about mathematics, and not just what the students need to know. Sometimes a teacher's intentions for students' learning in mathematics are not accurately matched to the way they assess. Teachers should be careful to maintain a sense of sensitivity towards how they convey ideas about math. Since each individual constructs their own personal meaning and understanding of mathematical ideas, teachers must prepare to work with and develop these meanings amongst their students. Furthermore, teachers must develop respect for diverse forms of learning existent in their classrooms. To do this teachers should utilize a form of assessment that looks at what students attach meaning to and how they use that to aide their problem solving process. This practice will be explored further in later units in the course.

Next, in order to ensure good educational practices teachers should recognize the two important messages that are conveyed when instructing and assessing students. These two messages are that the teacher is interested in what the student knows as well as that the teacher wants the student to know that what they are teaching is important mathematics. One way to do this is by monitoring the forms of questions that are asked. A teacher's questions should be more than a simple search for the right answer. The questions asked should be about conveying the importance of learning for understanding of mathematics. When this occurs, students can truly focus on the important understandings in math and become more mathematically literate.

Reflection

Unit 1 Questions for Reflection

1. Clarke, D. (1997). Constructive assessment in mathematics: practical steps for classroom teachers. Berkley, CA: Key Curriculum Press.

2. Mathematics Cartoons. (n.d.). Home. Retrieved November 16, 2012, from http:// simonsingh.net/books/fermats-last-theorem/wacky-fermat-stuff/mathematics-cartoons/

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Back to Course Home Page Welcome to the first unit in the mini-course on Mathematical Literacy: Teaching with, developing, and utilizing Math Journals. To start off this unit, I want you to think in your head (or write out) words that come to mind when you think of Mathematics and Literacy.

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Being that it's a Greek root, this lead to my Day 2 lesson.

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The Greek alphabet is the writing system developed in Greece which first appears in the archaeological record during the 8th century BCE. This was not the first writing system that was used to write Greek: several centuries before the Greek alphabet was invented, the Linear B script was the writing system used to write Greek during Mycenaean times. The Linear B script was lost around c.1100 BCE and with it, all knowledge of writing vanished from Greece until the time when the Greek alphabet was developed.

The Greek alphabet was born when the Greeks adapted the Phoenician writing system to represent their own language by developing a fully phonetic writing system composed of individual signs arranged in a linear fashion that could represent both consonants and vowels. The earliest Greek alphabet inscriptions are graffiti incised on pots and potsherds. The graffiti found in Lefkandi and Eretria, the 'Dipylon oinochoe' found in Athens, and the inscriptions in the 'Nestor's cup' form Pithekoussai are all dated to the second half of the 8th century BCE, and they are the oldest known Greek alphabetic inscriptions ever recorded.

Origin & development of the Greek Alphabet

During the early first millennium BCE, the Phoenicians, who originated in Lebanon, turned into successful maritime merchants, and they gradually spread their influence westwards, establishing outposts throughout the Mediterranean basin. The Phoenician language belonged to the Semitic branch of the Afro-Asiatic language family, and it was closely related to Canaanite and Hebrew. With them, the Phoenicians carried goods to trade and also another valuable commodity: their writing system.

Even though today the Greek alphabet is only used for the Greek language, it is the root of most of the scripts used today in the western world.

The Phoenicians had a writing system similar to those used by other Semitic-speaking peoples of the Levant. They did not employ ideograms; it was a phonetic writing system composed of a set of letters that represented sounds. Like the modern Arabic and Hebrew writing systems, the Phoenician alphabet only had letters for consonants, not for vowels. The Greeks took the Phoenician alphabet and made a few key changes: they dropped those signs for which there was no consonantal equivalent in the Greek language and used them instead for individual vowel sounds. As a result, the Greek vowel letters A (alpha), E (epsilon), I (iota), O (omicron), Y (upsilon) and H (eta), came into being as adaptations of Phoenician letters for consonant sounds that were absent in the Greek language. By using individual symbols to represent vowels and consonants, the Greeks created a writing system that could, for the first time, represent speech in an unambiguous manner.

There are some considerable advantages that result from these changes. While syllabaries, logographic, and pictographic systems can sometimes be ambiguous to represent spoken language, the Greek alphabet could accurately convey speech. In the Near East and also in the Aegean Bronze Age, writing was a skill monopolized by specialists, the scribes. All this would change in Greece after the time of the Greek alphabet: the Greek alphabet had a lower number of signs, making the writing system more accessible for those who wished to learn.

What were the reasons that motivated the Greeks to apply such changes to the Phoenician alphabet? This is not fully understood, but it seems likely that certain differences between Phoenician and Greek phonology played a role in the process. While no Phoenician word begins with a vowel (only with a consonant), many Greek words do have a vowel at the beginning. This means that unless the Phoenician alphabet was altered, it would have been impossible to write Greek accurately. The way these changes were executed is not known with certainty either. However, there are a few inferences that can be made based on the archaeological evidence available. It is believed that the innovations were performed by the Greeks in a single move. This is supported by the fact that the classic Greek vowels are all present in the earliest examples of Greek alphabetic writing, with the only exception of Ω (omega). In other words, there is no evidence of a developmental stage of the Greek alphabet as far as we can tell from the earliest recorded examples: if instead of a single move, the Greeks executed these innovations gradually, we would expect to see examples of defective, inconsistent, or incomplete vowel representations, but none of these has been identified so far. This is one of the reasons why some believe that the Greek alphabet had a single 'inventor', or at least a specific moment of 'invention'.

In the earliest versions of the alphabet, the Greeks complied with the Phoenician practice of writing from right to left and the letters had a left-facing orientation. This was followed by a period of bidirectional writing, which means that the direction of the writing was in one direction on one line but in the opposite direction on the next, a practice known as boustrophedon. In boustrophedon inscriptions, non-symmetrical letters changed their orientation in accordance to the direction of the line that they were part of. During the 5th century BCE, however, the direction of Greek writing was standardized as left to right, and all the letters adopted a fixed right-facing orientation.

Legendary Accounts on the Origin of the Greek Alphabet

The ancient Greeks were more or less aware of the fact that their alphabet was an adaptation of the Phoenician alphabet, and there were several accounts about the creation of the alphabet in ancient Greece. One famous example is reported by Herodotus:

So these Phoenicians, including the Gephyraians, came with Kadmos and settled this land [Boeotia], and they transmitted much lore to the Hellenes, and in particular, taught them the alphabet which, I believe, the Hellenes did not have previously, but which was originally used by all Phoenicians. With the passage of time, both the sound and the shape of the letters changed (Herodotus, 5.58).

The Kadmos mentioned by Herodotus is the Greek spelling for Cadmus, the legendary Phoenician of Greek folklore who was considered the founder and first king of Thebes in Boeotia. Interestingly, his name seems to be connected to the Phoenician word qadm "east". Because of the supposed involvement of Cadmus and the Phoenicians in the transmission of the alphabet, in 6th century BCE Crete an official with scribal duties was still called poinikastas "Phoenicianizer" and early writing was sometimes referred as "Kadmeian letters". The Greeks called their alphabet phoinikeia grammata, which may be translated as "Phoenician letters". Some Greeks, however, were not willing to admit the eastern influence of their alphabet, so they justified the origin of the name phoinikeia grammata with different apocryphal accounts: some said that the alphabet was invented by Phoenix, the tutor of Akhilleus, while others said that the name was linked to the leaves of phoinix "palm-tree".

Scripts derived from the Greek alphabet

There were several versions of the early Greek alphabet, broadly classifiable into two different groups: the eastern and the western alphabets. In 403 BCE, Athens took the initiative in unifying the many versions of the alphabet, and one of the eastern versions of the Greek alphabet was adopted as the official one. This official version gradually displaced all other versions in Greece, and it became dominant. As the Greek influence grew in the Mediterranean world, several communities came into contact with the Greek idea of writing, and some of them developed their own writing systems based on the Greek model. A western version of the Greek alphabet used by Greek colonists in Sicily passed into the Italian peninsula. The Etruscans and the Messapians created their own alphabet based on the Greek alphabet, inspiring the creation of the Old Italic scripts, the source the Latin alphabet. In the Near East, the Carians, Lycians, Lydians, Pamphylians, and Phrygians also created their own versions of the alphabet based on the Greek one. When the Greeks gained control of Egypt during the Hellenistic period, the Egyptian writing system was replaced by the Coptic alphabet, which was based on the Greek alphabet as well.

The Gothic alphabet, the Glagolitic alphabet, and the modern Cyrillic and Latin alphabet are all ultimately derived from the Greek alphabet. Even though today the Greek alphabet is only use for the Greek language, it is the root script of most of the scripts used today in the western world.

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The Greek alphabet is the writing system developed in Greece which first appears in the archaeological record during the 8th century BCE. This was not the first writing system that was used to write Greek: several centuries before the Greek alphabet was invented, the Linear B script was the writing system used to write Greek during Mycenaean times.

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Pythagorean Theorem

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Introduction

Most people are familiar with sports rules and terminology; however, they are not always aware of the important role that math plays in sports. A myriad of data on players, teams, divisions and leagues is provided by the media and the sports world. You have been selected to explore the numerous connections between math and sports.

You are probably familiar with professional sports and stay abreast of scores and standing for your favorite teams. In each webquest below, you will engage in web-based inquiry to answer the questions presented and to perform the tasks required. These tasks will require a computer, access to the web, graph paper (see the math resources below), paper, pencil and a ruler. Access to a printer is helpful, but not required. Links are included for each quest to help you explore. In addition, there are links to sports and math resources at the bottom of this page. It's time to "play ball!"

1. Order the batting averages in tem 3 from least to greatest.

2. Compute the batting averages for 25 players in the 2008 season.

3. Find historical player stats for 20 baseball players from the 2009 season.

4. Compute the batting average for each player.

5. Create a table for your results.

6. How does a batting average measure a player's performance?

Part II: Earned Run Average
WebQuest 1 - Baseball Stats

Part I: Batting Average

The following tasks may require some of the sports resources listed near the bottom of this page. Try our Lessons on Decimals, then do the following:

1. What is a batting average?

2. How is a batting average calculated?

3. Calculate the batting averages for the following players.

1. What is an Earned Run Average?

2. How is an ERA calculated?

3. Gather pitching stats for Earned Runs (ER) and Number of Innings Pitched (IP).

4. Calculate the ERA for each pitcher.

5. Create a table for your results.

6. How does an earned run average measure a pitcher's performance?

WebQuest 2 - Win-Loss Percentage

Win-Loss Percentage is important data for any team. For example, WL% can be computed for a baseball team. However, WL% is also used in other sports. Try our Lessons on Understanding Percent, then do the following:

1. Look at win and loss data for teams in football. For example, the NFL.

2. Compute the WL% for five teams in a league, five in a conference and five in a division.

3. Create a table for your results.

4. Look at win and loss data for teams in basketball, for example, the NBA.

5. Compute the WL% for ten teams of your choice.

6. Create a table for your results.

7. What other sports use WL%?

8. Is WL% always expressed as a percentage? Explain your answer.

WebQuest 3 - The NBA Draft Lottery

The NBA Draft Lottery is an annual event held by the National Basketball Association in which the teams who had missed the playoffs in the previous season participate in a lottery process to determine the draft order in the NBA Draft. The lottery is normally held during the fourth week of May. The non-playoff teams are often called "lottery teams".

The NBA draft lottery uses a lot of mathematics, including combinatorics and probability. To better understand how the lottery works, you need to understand factorials, combinations and outcomes. Try our Lessons on Probability, then do the following.

1. What is the formula for the number of possible combinations of r objects from a set of n objects?

2. How many different committees of 5 people can be chosen from a group of 11?

3. How many non-playoff teams participate in the Draft Lottery?

4. What kind of balls are used?

5. How many numbered balls are placed the lottery machine?

6. How many balls are randomly drawn from the lottery machine?

7. Does the order in which the balls are drawn matter?

8. How many combinations are there when the balls are randomly selected from the lot of numbered balls?

9. How many combinations are actually used in the NBA Draft?

10. What is wrong with the numbered balls shown in this image taken from this page?

In the draft lottery, numbered balls are drawn to the top of the machine to determine a combination. The team that has been assigned that combination will receive the number one pick. Non-playoff teams are then ranked in reverse order of their regular season record, and are assigned chances, as shown here. The largest number of outcomes is assigned to the team with the worst record. The team with the second worst record gets the second largest number of outcomes, and so on for each of the 14 teams in the lottery. The experiment is conducted, and the team to which the winning outcome was assigned receives the first pick in the NBA Draft. Therefore, the NBA Draft is weighted in favor of the worst lottery teams based on their season record.

1. One outcome is disregarded: it is given to no team and ignored. How many outcomes are then distributed among the non-playoff teams?

2. From a mathematical standpoint, why do you think is this done?

3. Can a team's win-loss record affect their chances of getting the first draft pick?

WebQuest 4 - Graphing Data for a Sport or Event

Tables and graphs are commonly used to summarize sports statistics. Standings for teams and leagues are often summarized in tables, and historical data about a sport or event is often summarized in graphs.

The 2010 Winter Olympics in Vancouver, British Columbia, Canada ended on February 28, and the accompanying Paralympics are being held March 12-21. The first of the modern Summer Games opened on Sunday, March 24, 1896, in Athens, Greece. The first IOC Games was hosted in the Panathenaic stadium in Athens in 1896. The Winter Games were added in 1924. Historical data about this event has been tracked for years! For example, view a bar graph of Winter Olympic medals by country.

The Super Bowl is the championship game of the National Football League (NFL), the premier association of professional American football. It was first played on January 15, 1967. The Super Bowl is a very popular football event. A great deal of historical data about the Super Bowl is available, including Super Bowl Standings.

The following tasks may require some of the math and sports resources listed near the bottom of this page. Try our Lessons on Data and Graphs, then do the following.

1. Gather historical data from the Olympics. For example, choose a country and look at the data. If you chose the United States, then you would see a table for number of participants, men, women, sport, and medal.

2. Print the Olympic data you gathered, or save it to your computer.

3. Decide which type of graph is appropriate for summarizing your data.

4. Graph your Olympic data.

5. Gather historical data from the Super Bowl. For example, Super Bowl Game-Time Temperatures can be summarized in a line graph.

6. Print the Super Bowl data you gathered, or save it to your computer.

7. Decide which type of graph is appropriate for summarizing your data.

8. Graph your Super Bowl data.

Batting Average Buddy Project Figure This! Math MLB Historical Player Stats Earned Run Average Urban Dictionary Home Run Web MLB Baseball Pitching Statistics and League Leaders Baseball Baseball Stats 101 Baseball-Reference.com
Other Topics for Further Exploration
Basketball
Topics for Elementary Students:
NBA.com Statistics Index databaseBasketball.com Football NFL Standings Super Bowl History NBA Draft Lottery

1. Students can look at the basics of football scoring and add whole numbers.

2. The Super Bowl uses Roman Numerals to identify each game. Write these Roman Numerals as numbers in standard form.

3. Have students compare and order decimals by looking at batting averages of their favorite baseball players. They can find real data for players at websites such as ESPN.com. They should be reminded that a batting average is stated as a three-digit number; however, it is actually a decimal rounded to the nearest thousandth.

As ping pong balls bounce, fates of 14 teams hang in balance
Topics for High School and College:
PROBABILITY OF GETTING A TOP-THREE PICK Olympics The 2010 Winter Olympics Olympics Statistics and History Winter olympic medals by country
Historical Player Stats (PDF)
Olympic Games WikiPedia
NBA at ESPN
Math Resources Other Resources Evaluation
Countdown to NBA Draft 2010 - 2010 Mock Lottery
Conclusion
NBA Draft Lottery Probabilities (PDF)

Olympic.org -Official website of the Olympic Movement

Instructional Math Units

1. Print or save tables, graphs and other data you gathered in these webquests.

2. Discuss your findings with a classmate or family member, and a teacher or a sports aficionado.

3. Name three formulas you learned in these webquests.

4. Create five original problems from math and sports.

5. Share your problems on Facebook.

Congratulations! You have explored the important role that math plays in the world of sports. These explorations should give you a better understanding of the numerous connections between sports, probability and statistics, and other areas of mathematics.

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Introduction Most people are familiar with sports rules and terminology; however, they are not always aware of the important role that math plays in sports. A myriad of data on players, teams, divisions and leagues is provided by the media and the sports world.

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math examples. mathematics practise and problem solving

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Pythagorean theorem - fundamentals of Physics - math problems

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Pythagorean theorem - fundamentals of Physics - solved math word problems, problem solving and knowledge review. Problems count: 10

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The beautiful color illustration of frieze patterns above is taken from Frank A. Farris' Creating Symmetry: The Artful Mathematics of Wallpaper Patterns (Princeton University Press, 2015), a math book that, unusually, makes an outstanding coffee-table book in addition to having deep mathematical content.

Lavished with many beautiful illustrations of this kind, Farris' book is a joyful yet serious exploration of how mathematics can create beautiful patterns and provide us with a deep understanding of symmetry, one of the underlying principles of great art. "Euclid alone has looked on Beauty bare," wrote the poet Edna St. Vincent Millay, and Frank Farris shows us what that means. His book uses the abstract, esoteric beauty of mathematical equations to create the universally appealing beauty of visual art. I believe our ability to find beauty in both mathematics and art reveals something deep about the human mind, a topic we may explore in the solution column. For now, let's tackle today's puzzles. They are inspired by the more elementary parts of Farris' book, which discusses different types of symmetries in wallpaper, friezes and Escher-esque morphing patterns using a host of mathematical techniques involving groups, vector spaces, Fourier series, rosette functions, wave functions and several others. The puzzles below merely skim the surface of the connection between math and art that the book explores in depth, but they are designed to encourage all of our readers to create stunning visual patterns using mathematics. ( Update: The solution is now available here.)

Question 1:

Look at the family of symmetrical curves below, one of which is featured in Farris' book as a "mystery curve":

Each of these curves has an ordered pair of numbers associated with it, shown at the lower left of the curve. These two numbers determine the type of symmetry and complexity exhibited by the curve, and a simple mathematical relationship between the two numbers is required to generate the curve's pleasant symmetry. In the second question below, we'll give you the precise way these numbers are used to generate their curve. Without looking ahead, ponder these numbers and try to get an intuitive sense of how the curves change as the numbers do. Then look at curves A and B below and see if you can match them to the correct pairs of numbers, from the 10 choices given. Give your reasons for choosing your particular pairs and describe what you think the relationship is between the two numbers.

Choices:

1. (5, -19) 2. (6, -19) 3. (7, -17) 4. (7, -12) 5. (7, -19)
6. (8, -20) 7. (8, -12) 8. (8, -13) 9. (8, -19) 10. (6, -24)

How are the numbers related to the curves, and how can we generate other similarly graceful curves? Our next two challenges arise from these questions. Question 2 requires some mathematical sophistication, but you can skip it if you wish and go straight to question 3, which only requires a willingness to explore and play, and create beauty.

Question 2:

The "mystery curve" from Farris' book is the second one (6, -14) from question 1. The curve has a fivefold symmetry, which you can clearly make out in the image at right. Here's the expression that generated this curve: (cos( t) + cos(6 t)/2 + sin(14 t)/3, sin( t) + sin(6 t)/2 + cos(14 t)/3).
Note that this is a parametric equation - the first half gives the x-coordinate and the second part the y-coordinate as the parameter t goes from 0 to 2π. The mystery is this: What do the coefficients 6 and 14 have to do with generating fivefold symmetry? Why did we use -14 instead of 14 in question 1? Can you explain how this formula works to a general audience?

Question 3:

Anyone can generate the above curve - use your favorite graphing app, or enter the above expression into Wolfram Alpha or the excellent graphic calculator Desmos. Now start playing with the parameters - change the coefficients, fiddle with the signs, do anything you want using sine and cosine terms. You can use the insights you gained from considering question 1 above - or not. Go wild! It's like having a magic Spirograph whose pen never slips. Try to come up with the most pleasing curves you can. Submit the equations for your two or three most beautiful curves as comments to this column. We will publish a gallery of the curves our panel considers the most beautiful.

Happy puzzling. And may insight and creativity be with you!

Editor's notes: The reader who submits the most interesting, creative or insightful solution (as judged by the columnist) in the comments section will receive a Quanta Magazine T-shirt.
If you'd like to suggest a favorite puzzle for a future Insights column, submit it as a comment below, clearly marked "NEW PUZZLE SUGGESTION" (it will not appear online, so solutions to the puzzle questions above should be submitted separately). Note that we will hold comments for the first day to allow for independent contributions. (Update: The solution is now available here.)

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How to Create Art With Mathematics | Quanta Magazine

# data[].attributes.attachment_link.description
The beautiful color illustration of frieze patterns above is taken from Frank A. Farris' Creating Symmetry: The Artful Mathematics of Wallpaper Patterns (Princeton University Press, 2015), a math book that, unusually, makes an outstanding coffee-table book in addition to having deep mathematical content.