Saturday, February 8, 2020
Friday, February 7, 2020
How to Upgrade to Windows 10 for Free Tips for Education
If you are still using Windows 7 on your PC, there is some important news for you. Microsoft is ending support for the OS on all computers and laptops. The action is taking place as the company is planning to focus more on Windows 10 going in the new decade. The support for Windows 7 will end on January 14, 2020. This means that the US tech giant will no longer be issuing patches or fixes for it, unless in very extreme circumstances.
Microsoft's support web pages have revealed that Microsoft will discontinue its support so that they can focus on supporting newer technologies and creating better experiences. As a replacement, the tech giant recommended users to install Windows 10 sometime before January 2020.
While Microsoft does not talk about providing a free upgrade to Windows 10, rather urges users to purchase the new version, users can still switch to Windows 10 for free. Of course, you need to have a legit licensed copy of Windows 7 running on your PC. Here’s how you can upgrade to Windows 10 for free:
Step 1: Visit the Windows 10 download page.
Step 2: On the page, click on ‘Download Tool now’ and download the Windows 10 Media Creation Tool.
Step 3: Now, run the Media Creation Tool and accept the licence terms.
Step 4: Next, select ‘Upgrade this PC now’ and click on ‘Next’.
Step 5: Click on ‘Keep personal files and apps’ and then click ‘Continue’.
Step 6: Once the Install option will be clicked, Windows 10 will begin to be installed. However, this will require some time.
Step 7: Once the Windows 10 finishes installing, users need to connect to the internet and open Settings > Windows Update > Activation and the computer/laptop will be activated with a digital license.
15 tricky questions with easy and difficult answers
They are known as trick questions and often lead to wrong answers or make us doubt their response. These tricky questions can lead us to think that the answer is in the same statement or that your answer will be something more complicated than it really is.
In this article we give you 45 examples of funny questions with answers , to have a fun time with your family or your friends.
45 tricky questions with easy and difficult answers
Here is a selection of cheating questions and their answers, which you can use to challenge logic or squeeze your brain.
friends
1. What color are the ‘black boxes’ of the planes?
This is one of the most popular trick questions, since the name of the box is misleading. Although they are called black boxes, they are usually orange, so they can be seen and found more easily in case of an accident.
2. If there are 12 fish in a tank and 5 of them are drowning, how many fish are left?
This is a tricky question , since by focusing on solving the mathematical calculation, we forget that fish do not drown in water. Therefore, the answer is 12, since the same remain.
3. What happened yesterday in Paris from 6 to 7?
How can we know what happened if we have not been? It is not necessary, because the only data we need is given by the same statement: what happened from 6 to 7 was one hour.
4. If a baby is born in Colombia, but when he is two years old, he goes to Ecuador, where do his teeth grow?
To answer this tricky question, it is not necessary to know when children grow their teeth or do any kind of calculation. The teeth grow in your mouth.
5. You are running in a race and you advance to the person who is in second place, in what position do you happen to be?
This question with a trap can make you think that you would be in the first position, but if you advance to the second, you stay in your position: second place.
6. The word Paris begins with “P” and ends with “T”, true or false?
It is true. The truth is that the word “Paris” begins with the letter “P” and the word “ends” begins with “T” as well. A tricky question with a lot of cheating because of the way it is formulated .
7. If an electric train moves north at 100 km / h and the wind blows west at 10 km / h, where will the smoke go?
This is another question posed with a trap in its statement. It is an electric train, which does not smoke.
8. What is the question that no one can answer in the affirmative?
The answer is “Are you asleep?”, Since if you are really asleep, you can not answer the question.
9. In what month do the Russians celebrate the October Revolution?
Many people will respond in a wrong way that is celebrated in October, given the name of the revolution, but the truth is that it is celebrated in the month of November. When the revolution took place, the Russians used the Julian calendar, in which that date was in October.
10. A father and son are on the road, until their car crashes in an accident. The father dies and the son is taken to the hospital to be operated. It is a complicated operation, so they call a medical eminence for surgery to operate it. When he enters the operating room he says: “I can not operate it, it’s my son”. Why does this happen?
This question was recently used to raise awareness about the prevailing machismo in our society. One of the answers to this trick question is that the medical eminence is the mother of the child, but many people relate “medical eminence” with a man, so they do not consider that this person can be the mother.
11. A is the father of B. But B is not the son of A. How is that possible?
This is another trick question similar to the previous one. B can not be A’s child because he is actually a girl and is his daughter.
12. What goes up and down, but still in the same place?
This is a difficult question to answer and it makes you think, but the answer is easier than it seems: it’s the stairs.
13. What word would you use to describe a man who does not have all the fingers in one hand?
This other question also makes you think, but has a trap for how it is formulated . The answer is that it is a normal man, since none has all the fingers in one hand.
14. What are camel hair brushes made of?
Although they have this name, camel hair brushes are not really made of that material. They are usually manufactured with squirrel hair, marten hair, goat hair or they can be simply made of synthetic hair.
15. How many are the months of the year that have 28 days?
It might seem that the answer is February, which only has 28 days. But the truth is that in reality every month they have 28 days.
50 essential Graduation phrases you should know to congradulate and motivate
Whether it is for a friend, brother, relative or your partner, in addition to the celebration or if you plan to deliver a gift, write or express a motivating phrase or congratulation, it is an excellent idea either during the ceremony or celebration or even if it is done In private.
1. We have struggled hard to study and graduate, but the irony of all this is that today the real struggle begins. (Fernando Antus)
The end of this stage brings with it the beginning of another where the effort, talent and ability to face the world outside of school will be put to the test.
2. It is not great who always triumphs, but he who never becomes discouraged. (José Luis Martín Descalzo)
We must remember that success is not measured by the triumphs achieved, but by the ability to get up as many times as necessary to achieve what we propose.
3. The future belongs to those who believe in the beauty of their dreams. (Eleanor Roosevelt)
A very powerful and motivating phrase to congratulate those who tried hard to pursue the dream of finishing a career and graduating.
4. The greatest encouragement to strive in study and in life is the pleasure of the work itself, the pleasure of the results and the awareness of the value of the results for that community. (Albert Einstein)
This graduation phrase is perfect to start a speech or to invite some graduate to reflect on the value of study and effort.
5. What counts is not the amount of hours we dedicate to work, but the quality of the work we perform during those hours. (Sam Ewing)
With this statement invites reflection on the importance of putting effort in the work and give value to it.
6. Formal education has its lights and shadows. Our effort, beyond being graduated today, can serve to give energy to the lights and make the shadows disappear. (Grant Smith)
A great speech in a few words to invite to do with our actions a significant change that impacts our environment.
7. The man who graduates today and stops learning tomorrow, will be uneducated the day after tomorrow. (Newton D. Baker)
This phrase is an excellent reflection on the importance of never stop learning.
8. There are no shortcuts to any place worth going. (Beverly Sills)
A short but forceful message to reflect on the effort required to get where you want.
9. You have an education. Your certification is a title. You may think of him as a ticket to a good life. Let me ask you to think of an alternative. Think of it as a ticket to change the world. (Tom Brokaw)
The graduation phrase can be used to start a speech addressed to the rest of the graduates.
10. The roots of education are bitter, but the fruit is sweet. (Aristotle)
This short but very representative message of what the sacrifice and effort of the study means in exchange for the benefits that can be enjoyed from it.
Graduates
11. We are facing a very volatile work environment. Learn every day to reinvent yourself, be creative, never let short-termism turn off your great ideas (Susan Bayle)
A reflection about the world that awaits after graduation and how to face it to continue reaching the goals.
12. You will have failures in your life, but it is what you do during those falls that determines the height at which you will arrive. (Rahm Emanuel)
Remind graduates that failures are not what define a person but how they are faced.
13. It is ironic that we spend our days wishing to graduate and the rest of the days we feel nostalgia for the days of university. (Isabel Waxman)
This graduation phrase is perfect to invite graduates to enjoy the stage they are living and what is to come.
14. You can not climb the ladder of success with your hands in your pockets. (Arnold Schwarzenegger)
The actor reminds us that to achieve what we want we must work hard for it.
15. Knowledge is learned through study. Wisdom through observation. (Arturo Torres)
The accumulation of knowledge should not be the only objective to be achieved but to take the acquired skills further and cultivate observation.
16. Your time is limited, so do not waste it by living the life of another. Do not get caught up in the dogma, which is to live according to the results of the thought of others. Do not let the noise of the opinions of others drown your own inner voice. And most importantly, have the courage to follow your heart and your intuition (Steve Jobs)
No doubt a powerful message for young people from the thinking of the genius behind Apple.
17. The obstacles are those frightening things that you see when you turn your eyes away from your goals (Henry Ford)
This reflection is very useful to give to those who are going to graduate.
18. When you finish your university studies you will notice a certain existential void. Until now, all your routine was planned, predictable. Now it’s time to face the uncertainty and come out of this struggle. (Miranda Boozer)
A graduation is also a moment of reflection on what will come in the next stage and the best way to face it.
19. The true meaning of life is to plant trees under whose shadow you do not expect to sit. (Nelson Herdenson)
Today’s hard work will not always have rewards or immediate compensation.
20. An investment in knowledge always pays the best interest. (Benjamin Franklin)
The best we can do for ourselves and for our environment is to invest in our education because a benefit is always assured.
21. Graduation is just a concept. In real life, you graduate every day. Graduation is a process that continues until the last day of your life. If you can understand that, you will make a difference. (Arie Pencovici)
A phrase to understand that graduation is the beginning of a new stage and that it never ends.
22. Education is what survives when what has been learned has been forgotten. (BF Skinner)
This great famous phrase expresses in a few words the importance of continuing to cultivate the spirit.
23. Death is probably the only good invention of life. It is the agent of change of life; erase the old to make way for the new. And now you are new. But someday, not long, you will have become the old and you will be replaced. I’m sorry for being so dramatic, but it’s the truth. Your time is limited so do not waste it living the life of another person. (Steve Jobs)
The creator of apple leaves in this speech a message that any graduate should listen to.
24. All our dreams can come true if we have the courage to pursue them. (Walt Disney)
A thought full of motivation for the day of graduation.
25. Do not judge every day by what you harvest, if not by the seeds that you plant. (Robert Louis Stevenson)
In this way you can congratulate the people who graduate by letting them know that their seed has paid off.
26. Education is the key to open the world, a passport to freedom. (Oprah Winfrey)
A perfect graduation phrase to congratulate and motivate.
27. That we succeed in transmitting to our children this grace of being simply “all-terrain” men and women, citizens of the world. (Jaime Borrás)
This small reflection is very important especially for those who are parents.
28. If you are not enthusiastic, you will be fired with enthusiasm. (Vince Lombardi)
In short, an absolute truth that those who join the labor market must take into account.
29. For a long time, the experts, the people who are supposed to be able to tell you what to do, will tell you that you are not capable of doing something even when you know that you are. And many times it will be your own friends who tell you that you can do it. (Mark Zuckerberg)
A small speech that also lived in the flesh the creator of Facebook.
30. If you think education is expensive, try ignorance. (Andy McIntyre)
Far from believing that there has been an expenditure on studies, it must be understood that ignorance is even more expensive.
Speech
31. If the opportunity does not call, build a door. (Milton Berle)
A very motivating phrase maybe to start a speech or include it and motivate the graduates to be persistent.
32. What is your great idea? What are you going to use your moral, intellectual capital, your money, beyond the walls of the University of Pennsylvania? The world is more malleable than you think and it is waiting for you to give it form. (Bond)
This speech by singer Bono at the University of Pennsylvania has a lot of energy and motivation to transmit to young people.
33. Have great thoughts but enjoy the great pleasures. (H. Jackson Brown)
It is good to remember that our dreams and ambitions should not cloud the simple pleasures we have today.
34. If you believe in what you say, if you believe in what you do, you will be more effective, more passionate and more authentic in everything you do. (Seth Goldman)
A motivating and beautiful thought about the importance of being coherent with what we do and say.
35. It does not matter how far you can go. At some point you are bound to stumble. If you are constantly pushing yourself to the top, the law of averages, not to mention the myth of Icarus, predicts that you will fall at some point. And when you do, you must remember one thing: there is nothing like failure. Failure is simply life trying to move us in another direction. (Oprah Winfrey)
A great speech perfect to give to someone in his graduation and reflect on that failure is part of life.
36. Although no one has been able to go back and make a new start, anyone can start now and make a new ending. (Jonathan García-Allen)
Sometimes there are people who regret being where they are, but this phrase is a reminder that you can always change the direction to a better one.
37. Fireworks start today. Each diploma is a lit match and you the match. (Edward Koch)
A great graduation phrase to congratulate and motivate. It can be the beginning of a speech or write it on a card for those who graduate.
38. Do not go where the road leads. Go, instead, where there is no road and leaves a trail. (Ralph Waldo Emerson)
This message is ideal to motivate those who have graduated to become a person who makes a difference.
39. Success is not a result of spontaneous combustion. You must light up in flames. (Arnold H. Glasow)
A convincing way to express the importance of doing things with passion.
40. Excellence is not a skill. It is an attitude. (Ralph Marston)
This short but profound sentence is an invitation to rethink the meaning of excellence.
41. A wise man will build more opportunities than he finds. (Francis Bacon)
This reflection is full of truth and is ideal to share with someone who is about to graduate.
42. Use the talents you have in life: the forest would be very silent if only the birds that sing best sang. (Henry Van Dike)
Sometimes people doubt about the value of their talents, this phrase will undoubtedly provide security to anyone and is perfect for anyone who graduates.
43. It is impossible to live without failing in something, unless you live so cautiously that you may not have lived at all, in which case, you will have failed by default. (JK Rowling)
Another great reflection about the importance of not running away from failure but understanding and acting proactively in front of him.
44. Shoot the moon, even if you miss the stars. (Les Brown)
A very emotional and motivating phrase that can be perfect to congratulate someone in his graduation.
45. We do not conquer the mountain, but ourselves. (Edmund Hillary)
This reflection reminds us that every achievement we achieve is not external but internal.
46. Go wherever you go, no matter the time, always carry your own light. (Anthony J. D’Angelo)
No doubt this reflection is an ideal phrase for a graduation because it is very motivating and emotional.
47. Do not try to become a successful man. Try to become a man of value. (Albert Einstein)
The famous Albert Einstein leaves in this reflection a great truth to exalt the importance of values in the face of success.
48. Learning without thinking is wasting energy. (Confucius)
An ideal absolute truth to invite reflection to someone who graduates on the importance of reflecting what they have learned beyond just storing data and knowledge.
49. They will not get very far in life if they rely on what they already know. They will advance in life through what they learn once they move from here. (Charlie Munger)
These words that were used in a graduation speech are very accurate about life after school.
50. I think that it is often easier to progress in mega ambitious dreams. I know it sounds completely crazy. But since nobody else is crazy enough to do it, you have little competition. There are very few people so crazy that I feel I know them all by name. Everyone travels like cargo dogs and sticks together like glue. The best people want to face great challenges. (Larry Page)
This passionate and motivating speech can be a great graduation phrase that inspires whoever reads it.
How to Automatically Create PDFs with Google Form Responses for Education
Types Will Be the best Instrument for creating Surveys, Surveys, surveys, and questionnaires. The form submissions are saved which makes it more easy for you to analyse the entries, along with your forms can obtain an unlimited number of answers.
When Your Google Type is submitted by An individual, a row has been inserted with the replies to the destination Google Sheet. The tutorial describes how you also have it emailed to one or more recipients through Gmail and can save your Google Form answers.
For This instance, we’re constructing an event registration form. The attendees fill out the form, choose the session(s) that they want to attend an email confirmation is delivered to them immediately. There is A PDF file connected and it includes a QR Code which may be scanned in the event place in addition to the kind responses.
Please try the workflow so that you’ve got a clearer idea of what we’re building before we get into the implementation information.
And, in just a couple of seconds, you will be given a email with a PDF attachment. It comprises a QR code plus a special registration ID that’s created automatically with all the =QRCODE() formulation .
Make a Google Form to begin at which the answers would get and select a destination Google Spreadsheet stored.
Next, Produce a template in Google Sheets Slides or Google Docs. In your template, the areas ought to be included within double curled braces and the query title should be just matched by the domain .
For Instance, If your Google Form query is”Full Name”, the mark On your file template will be undefined and it’s going to be automatically replaced with the response filed by the form submitter.
Then set up Document Studio to Google Sheets and authorize The add-on. Open the Google Spreadsheet which is currently keeping your Google Type answers, Visit the Add-ons menu, then select Document Studio and start The workflow to be built by The sidebar.
My ambition Essay
My ambition
Ever since I was very young and saw perhaps a child cut and bleeding or an old woman suffering from an incurable disease.
I have always hated pain and the human suffering that it causes. It has, therefore, always been my ambition to become a doctor and to be able to cure diseases and to ease pain. Many count riches, power and glory among their ambitions, but for me, to serve humanity through medicine is the highest ambition of all.
The training is long and expensive and I shall need to work very hard. After passing the right examinations in school. I shall then need to take a University examination, which will enable me to enter the medical school, which is part of our University life in Singapore.
At University, there will be many lectures to attend. Physiology and Anatomy are two of the most important subjects during the first year. The different organs of the body such as the heart, the kidneys and the liver, together with their functions and disorders have to be studied. As well as this, there will be lectures on the many different diseases to which man is subject, with the various ways of diagnosing them and dealing with them. Lectures are given by highly qualified specialists.
As well as this theoretical work, there will be a practical course during the five years training. A new medical student has to begin by 'walking the wards' in a hospital. He accompanies doctors in charge of patients and watches what they do. He has to study patients being examined and listen tot he conclusions reached. he has intricate operations being performed by skilled surgeons. He had to make his own reports from his own diagnoses, at the same time, as the qualified doctor. All of these are checked and corrected, so that the student can learn from his mistakes. When he has passed this practical course, which lasts for about four years, he is then called a 'House man'.
Written examinations are taken at different stages. At the end of the first year, there is the first M.B. This is the first part of a Bachelor of Medicine degree and is a very difficult hurdle. Many students fail it. Then, there is the second M.B. and at the end 'finals' which include both a written, and oral and a practical examination. When 'finals' are safely behind me, I will really by a qualified doctor and be able to add this style to my name.
It will then be my ambition to obtain a grant from the authorities to travel abroad for further studies and I would like to go to Australia to do this. At a post-graduate course there, I would be able to study different methods, to see new techniques and to obtain even higher qualifications like a Doctor of Medicine degree.
Finally, I would return to Malaysia where I want to work as an assistant medical officer in one of our busiest cities. There, I would gain more practical experience than I ever could in a small village. All types of illness would, among a large population, most certainly come my way. The ailments of children, of young mothers and of the very old could all be studied. I would learn to recognize an appendicitis of tonsillitis very quickly. In a very large city, it is not always possible to have the services of a gynecologist and so I would have practice in delivering babies myself.
During this time, I would try to save money. Doctors are rightly well-paid and I would live moderately. After some years, therefore, I hope to be not only experienced as a general practitioner, but also comfortably rich as well.
Finally, then I would realize my ultimate ambition, which is to do the medical practice in my own village and to return here. I have never had any desire to specialize and to become a pathologist, a surgeon, a gynecologist or an ear, nose and throat specialist. To be a good general practitioner here, in my own home is the end of my dream and, although not a specialist in any particular sphere, I shall know enough to deal with the common ailments of life and to call in the right specialists a once if they are needed. I shall then be able to serve the village I love so well.
Importance of Education In Society Essay
Zeal study shares you the composition for second term 2 new syllabus Importance of Education In Society
First of all, Education helps in spreading knowledge in society. This is perhaps the most noteworthy aspect of Education. There is a quick propagation of knowledge in an educated society. Furthermore, there is a transfer of knowledge from generation to another by Education.
Education helps in the development and innovation of technology. Most noteworthy, the more the education, the more technology will spread. Important developments in war equipment, medicine, computers, take place due to Education.
Education gives us a knowledge of the world around us and changes it into something better. It develops in us a perspective of looking at life. It helps us build opinions and have points of view on things in life. People debate over the subject of whether education is the only thing that gives knowledge. Some say education is the process of gaining information about the surrounding world while knowledge is something very different. They are right. But then again, information cannot be converted into knowledge without education. Education makes us capable of interpreting things, among other things. It is not just about lessons in textbooks. It is about the lessons of life.
Education is the most element in the evolution of the nation. Some people across the world would think that money is an important factor, but it is wrong because without education, no money. Learning is the major factor which is related to education if you learn new things, then you will educate more and more. Without the education you will not explore the new ideas it means you will not able to develop the world because without ideas there is no creativity and without creativity, there is no development. Across the world, we saw that some country is more germinate and some are not. The country which is more growing the more educated people ratio compares to the country which is less developed. Education is the tool which provides people require knowledge, skill, technique, and information and enables them to know their rights and duties toward their family, society, and obviously nation. Education expands the vision, outlook to see the world. Education develops the capabilities to fight the injustice, violence, corruption and other factors. Just as a face is the mirror of the heart, level of education develops the status of the nation. Our system is like that rich students get more and more education and poor will not. Education in nowadays becomes more costly such that poor parents of the most talented student cannot even think of getting their wards admitted into such institute. We need a system that will provide equal opportunity to both rich and poor students that can contribute to the development of the country. By providing education, we remove the poverty and every person in the country will become successful and provides their contribution to developing their country. Hence we can easily conclude that for an evolution of a country, there is need of education, we have to change the person's mind and make a country a developed country.
Conclusion:
Education is a ray of light in the darkness. It certainly is a hope for a good life. Education is a basic right of every Human on this Planet. To deny this right is evil. Uneducated youth is the worst thing for Humanity. Above all, the governments of all countries must ensure to spread Education.
The importance of water
Introduction
Life, both animal and plant, is impossible without water. Without water men die of dehydration About 70% of the human body is water. Of the total surface of the earth, 75 % is water and just below the surface of the land in most areas there is a saturated layer known as the water table. Animals and plants have large percentages of water in their make-up and some animals regulate their movements according to the water sources.
Water:
If there is no water there can be no life. The moon is a sterile desert because there is no water in it. It is to be remembered that it was water that determined the location of human settlements and without the Nile the Egyptian Civilization would not have developed The Nile provided the Egyptians facilities for irrigation and transport. As Herodotus said, Egypt is the "Gift of the Nile".
Importance of water:
The urban man rarely thinks of the importance of water. When he needs water, all he has to do is to turn on the tap. The only time the urban folk become aware of the importance of water is when there is a drought and their water supply is regulated. If water rationing becomes too drastic. they may find themselves in a worse position than the rural man who may have a steady supply of water from his well.
Imagine a day when the taps ran dry: Mr. Townsman would have found life intolerable. He could not brush his teeth, have his shave or could he have his bath in the morning. After lunch, he would have had a very difficult time trying to wash up. He might have used cloth to wipe his crockery. He could not wash his car. At the end of the day, however, our Mr. Townsman would have realized that water is precious and he should not be a water-waster.
Scientists find water the most fascinating fluid in the world because of its versatility and usefulness. Electricity is generated by the force of running water. Unlike other substances, water expands when freezing takes place. In ancient Rome snow was used to pack prawns and meat. Ice is used for refrigeration. Water is converted into steam and used as power.
Whatever man eats is dependent on water for its growth. Water can convert whole, barren tracts of land into luxurious, rich and fertile regions, through the use of irrigation. In parts of Spain, diminishing quantities of rain have caused fertile land to dry up in the past years, creating barren deserts. This is turn has caused many men and their families to move to new places.
Conclusion :
Most of us who take our daily supply of water for granted. may not be able to fully appreciate the importance of water. Many have perished through lack of water.
Military men know that the most effective way of subduing any city or fortress is to cut its water supply.
The importance of forests
Man has been cutting down forests indiscriminately and today the trend is not only to save natural forests but to create artificial ones. Deserts are made to bloom! The Imperial Valley of the Sonoran desert in southern California has been converted into a green patch which yields crops all the year round. Forests are not to be considered merely as a direct source of wealth; they are to be considered in relation to the national economy and geography.
Forests serve many purposes. They hold together the soil and prevent or minimize soil erosion. The oxygen in the air is replenished by forests and plankton in the sea. Trees and plants, during photosynthesis, absorb carbon dioxide and release oxygen. Scientists fear that if forests are destroyed indiscriminately, there will be an increase in carbon dioxide and eventually the sun's rays will become hotter, the polar caps will melt and the ocean level rise and submerge much of our land. Vegetable mould that forests supply increases the fertility of the soil. Forests influence climate. The roots suck up sub-soil water and it is expelled as moisture by foliage. Forests provide sanctuary for animals and birds. It is to he remembered that the rich and varied wild life vanishes in proportion to the forest we destroy.
Industries like paper, rayon. straw-boards, matches, insulation boards and wood-panel products are dependent on forests. Indian forests are said to yield 2,500 species of wood, about 18% of which are commercially valuable. Forests are a source of essential oil and medicinal herbs. The lignin and cellulose found in wood are chemically treated to produce valuable drugs like sulfonamide and chloroform. Spruce and fur are used for making airplane and glider parts. Ash and mulberry woods are used for making many sports goods.
Governments all over the world have taken steps to conserve forests: President Franklin Roosevelt of the USA, alarmed by the massive destruction of forests by man, created a conservation corps of two million men to plant trees, dig lakes and build forest roads and in the course of ten years saved the country's forests. Today the trend is not only to save the existing forests but to create artificial ones. Israel is the classic example of a country where a desert has been converted into a garden. The success of this experiment shows that land can be reclaimed and thus increase the food supply of the world. It stands to Israel's credit that within twenty-five years it has doubled the area of its arable land.
My Plans for the Holidays
The final examinations for the year are over and everyone is waiting impatiently for the start of the six-week school holidays. Now that the pressure of the examinations are over and the periods of intense study are behind me, I plan for the well-deserved break till the end of the year.
First, I would like to read all the latest best-sellers that have been released. Busy with my studies, here have been quite a number of new books that I have not read. Novels from Sidney Sheldon and Lawrence Block, two of my favorite authors, have been released recently. Then, there are also some issues of National Geographic and Readers' Digest magazines that I have bought in recent months which I have not had the time to read.
Then, I would have to watch the numerous television programs that I have recorded on video cassettes. I have missed out many episodes of "E.R." and "X-Files", not to mention the critically acclaimed "Desperate Housewives". Television programs are not the only ones that I have missed out. There have also been a few good movies which I have not yet watched. I would have to rent DVDS to watch those as well.
Finally, I plan to organize some fun activities with my classmates. I intend to go fishing by the stream and go trekking through the nearby woods with them. And if there is keen interest, we might even go camping for a week. We would, of course, have to bring the necessary camping items like tents, sleeping bags, insect repellents, cooking utensils and sufficient food.
I look forward in earnest to the activities I have planned for the holidays. I am sure that the coming holidays will be a time of cheery rest and cheerful recreation.
English essays Topic: Global Warming Effects
Global Warming refers to the observation that the atmosphere near the Earth’s surface is warming. This warming is one of many kinds of climate change that the Earth has gone through in the past and will continue to go through in the future. It is reasonable to expect that the Earth should warm as the amount of greenhouse gases in the atmosphere dramatically due to human activity. It is less well known exactly how the increases in these green house gases factor in the observed changes of the Earth’s climate and global temperatures.
There are many misconceptions about global warming. Some believe that pollution causes global warming, but the fact is global warming is the result of burning fossil fuels, coal and oil that release carbon dioxide. Another misconception is nuclear power causes climate change. Nuclear power actually reduces emissions of carbon dioxide when used in place of coal. Some believe that global warming means that it will become warmer all over. The name is misleading because in some places, it will actually become colder. The majority of scientists add to the levels of these gasses, causing more problems. The increase in agriculture, deforestation, landfills, industrial production, and mining contribute a significant share of emissions too. The gases released into the atmosphere are tracked by emission inventories. An emission inventory counts the amount of air pollutant discharged into the atmosphere. These emission inventories are used by many organizations.
Global warming can affect our future ability to obtain food. As climate change, plants and animals will change, leading to a change in the eating patterns of humans. An increase in precipitation is one result of global warming that could have devastating effects. First, the quality of crops would be affected by an increase in precipitation. Second, increasing rains could lead to an increase in soil erosion.
There are ways that you can help prevent global warming. Car-pooling, auditing the energy in your home buying fuel-efficient cars, and reducing the electricity in your home are ways to help prevent global warming. You can also write to your local congress representative or your loyal newspaper in response to stories, which say global warming, does not exist. Government authorities can help by passing laws to reduce emissions from factories. They can also form a treaty with other countries to legally bind limits on emissions of heat trapping gases.
The future of emissions damage depends on several factors, demographics, economics, technology, policies and institutional development. Future predictions do not look good for this planet if nothing is done. Without the help of emissions control policies, CO2 levels are projected to be 30-150% higher in 2100. Our renewable resources will be very limited. With cooperation from citizens and government officials, we can slow the effect of global warming by reducing greenhouse gas emissions.
How to rectify the issues releated to writing in mathematics
Teaching writing numbers/numerals involves several skills and various physical and cognitive actions:
(a) teaching and correcting pencil grip, paper position, body position, location of the other hand, etc.;
(b) teaching and correcting poorly established letter and number construction; and
(c) teaching a new handwriting form or shaping the old handwriting form, for example, print or cursive.
It is easier to learn these skills, but difficult to correct when they are poorly taught and poorly learned. Therefore, effective initial instruction is critical. Preventive teacher is always important than corrective teaching. If preventive teacher is absent or poor then corrective teaching has to be effective and efficient. For example, after fourth grade, the items in (a) are tough to correct, but not impossible.
A correction to type (a) habit is difficult, but it can be done and it is worth it. There are definite physical reasons for this. For example, proper finger and thumb overlaps, the left-hand hook (sometimes right, but often left), and other grips are difficult to overcome and require a great deal of patience, practice, consistency, and often the use of corrective aids, such as pencil grips.
It is always a great challenge to correct error of type (b). Only if (a) is already in place, (b) and (c) are not as difficult to correct/introduce as many assume. Many immigrant children who come with proper (a) and (b) easily learn to write in English, even cursive, with little teaching.
In my private practice and in lesson demonstrations in schools, in classrooms from Kindergarten to high school, I have found many students have problems writing numbers, letters, and mathematics symbols correctly. Whenever, I find poor writing of numbers and symbols, I always help them to write them properly. I correct pencil grips, paper positions and demonstrate how to write numbers and mathematics symbols. I have even introduced cursive writing to many high school students, successfully, and eventually, they have gained automaticity.
I strongly believe we should correct writing with persuasion, with humor, with challenge, with reason, and always seeking their cooperation in this effort. I have found with effort, on my and student’s part, it is possible to correct poor handwriting. It is, of course, much easier earlier (in the early grades). However, even later, under right circumstances—when it is supported by school, parents, and other teachers, one can improve it.
I find that many students are not consistently encouraged and supported during elementary, middle, and high school to become proficient in legible and accurate writing. Writing is not an isolated activity. It is part of any academic work; it should be emphasized during all academic instruction. It is a means of learning new concepts and cognitive skills and gain new information and acquire new knowledge.
There are high school students, who have never written a complete sentence, during their entire schooling. They only fill blank spaces with words and numbers on the worksheets provided by special and regular education teachers alike. And, high school is a bit late to realize that there is something called writing.
I always make pleas to teachers/schools to have consistent handwriting instruction that focuses proper strategies and methods for writing that should include pencil grip, paper position, posture, proper use of writing equipment, and so on. Poor handwriting instruction is detrimental to learning. Both students and teachers are affected by poor handwriting instruction. For example, high school and middle school teachers pay a big price for students’ poor handwriting. It is difficult even to read an equation where the variables x, t, y, and z are involved.Mathematics expressions withfractions, exponents, trigonometric functions, radical expressions and groupings are impossible to decipher.
When I am teaching, whether one-to-one, small groups, or whole class, from Kindergarteners to graduate students, I closely observe students writing mathematics. I ask them to write a lot of mathematics. Without writing you do not develop “language containers” for mathematics concepts and the ability to communicate mathematics. Without the language containers one does not hold information in the memory. Conceptual schemes emerge from the interaction of language and models.
Writing is the recording of the abstractions and processes resulting from these interactions. Without writing them clearly, succinctly, legibly, and precisely using mathematics terminology, a student may not remember the processes and outcomes from a lesson. The writing process also helps students to connect ideas. When we do not focus on the writing process, in a mathematics lesson, problems occur.
Here are some of my observations about handwriting issues and problems from the mathematics classrooms, collected over years. These are not isolated examples. When I have observed something happening consistently, I have included it on my list.
Most students have poor grip on their pencils and their usage.
Many students, even in high school, do not know their left from right.
Most students begin writing in the middle of the page, middle of the line.
Few mathematics teachers insist students to write on graph paper.
Even when they are given graph paper, many students and teachers alike do not respect the lines on the graph paper. No instructions are given how to write on a graph paper and how s graph is an asset for writing, learning, and doing mathematics.
There is no correspondence between the numbers representing dimensions of figures and the student’s drawings. The idea of drawing a figure according to some kind of meter, scale, or unit is absent from their training.
Shapes and sizes (heights, spacing, orientation, etc.) of letters and numbers, in the same word, line, or equation are uneven. Sometimes the same variable (i.e., a) is written in the same equation, formula or expression as a, A, or looks like a 9 or q.
Most students cannot draw a decent rectangle even on a graph paper.
Writing fractions, exponents, variables and operational signs is very poor. Unfortunately, no or little instruction is given in how to write a mixed fraction or a newly introduced mathematics symbol:
(i.e, ±, <, ∏, 𝚽, &, 𝜎, @, %, ∑, etc.)
Hardly any teacher gives feedback on student handwriting or spelling with the excuse that: “I am not teaching spelling or handwriting. I am teaching mathematics.” Mathematics is an alpha-numeric language. It is not just a collection of symbols. Even in Principia Mathematica some language is used. Teaching mathematics means teaching the mathematics language: How to learn it? How to read it? How to write it? How to use it? How to use it for communicating ideas?
Most students, from Kindergarten to high school and even in my college classes, when they want to correct an error, they change the pencil to the eraser side by handing the pencil to the other hand. The other hand reverses it and hands it over to the dominant hand. The dominant hand erases it and hands the pencil back to the other hand. The other hand reverse it and hands it over to the dominant hand. One small activity becomes such a production. Some drop the pencil on the table, pick it up erase and then drop it on the table and then pick it up to do the writing. I am able to correct this problem it in one session.
And, many more ….
Students with poor grip, often have some of the sloppiest handwriting in the class or the neatest, but arrived at laboriously. Often these students write less than most of the other students in their classes. Because of poor grip, poor organization, and little practice in writing, their hand fatigues easily. A middle school student whose hand throbs when s/he writes a single paragraph is in need of effective writing instruction.
Best practices in handwriting instruction are about reducing fatigue, increasing legibility and accuracy, and achieving automaticity with comprehension. It is about activating reading/writing/spelling/concept links. It is about giving students the opportunity to communicate mathematics effectively in writing.
4. Writing Process
Writing, just like all learning, is the interaction of multiple brain systems:
• Sensory Motor and Visual Perceptual and Spatial systems
• Socio-Linguistic Systems
• Cognitive Processes and Executive Systems
• Social-Emotional Systems
It begins with the reception and comprehension of visual and auditory information. Then, one retrieves the corresponding orthographic representations to the auditory and visual information. Once an orthographic representation has been retrieved from long-term memory, assembled through sound–spelling conversion, or visual representations (information on the board, book, or paper) additional processing is required to produce an overt written response in handwritten, typed, or key-boarded form.
First, the abstract letter representations, in the working memory, must be converted to a form appropriate for the chosen output format or modality. For handwritten output, letter-form representations (e.g., a representation of lower-case print f) must be activated, whereas for oral spelling letter name representations (e.g., /εf/) are required. For other forms of output (e.g., typing) different representations (e.g., keystroke representations) would need to be computed. Here. we focus on the processes required for handwritten output only.
Some theorists assume that in generating a handwritten response, abstract letter representations are first converted to allograph (letter shape) representations corresponding to the chosen form of written output (e.g., lower-case print). The allograph representations in turn activates effector-independent graphic motor plans, which are learned representations specifying the movements (i.e., the sequence of writing strokes, the letter ‘b’ has a stick and a ball attached to the bottom right) required to write the letter in the chosen form. The graphic motor plans are effector independent in the sense that they are not tied to particular effectors (e.g., the right hand, pencil or pen, etc.), and do not specify movements with respect to specific muscles or joints. These are not innate, these are learned behaviors. They depend on earlier experiences. For example, immigrants bring the experiences of their first language in writing the English alphabets and Hindu Arabic numerals. But, the nature of writing (sloppy or neat, small or large letters, scrawls or properly form letters, etc.) are carryover in handwriting into English from their mother-tongue. They are also learned behaviors, but automatized and internalized. Hence, the graphic motor plan for upper-case print B could mediate writing of that letter with the right hand, left hand, left foot, or so forth.
Although the assumption of a progression from abstract letter identities to allographs to graphic motor plans is common, some theorists have proposed instead that abstract letter representations are mapped directly to graphic motor plans.
Regardless of how graphic motor plans are activated, the final steps in the writing process involve the conversion of the graphic motor plans to effector-specific motor programs, and the use of these plans by the motor system to execute the appropriate writing movements with the chosen effector. For example, when writing on a page, when we come to the end of the line and it is close to the end of paper, we automatically begin to write smaller or bigger depending on whether we want to finish there or go to the next line or page. There is a host of decisions being made when we write, therefore, the close relationship between executive function and writing. Ultimately, writing is a means of learning and problem solving.
During the writing process visual feedback plays a significant role, not only in ensuring appropriate orientation and spacing of letters and words across the page, but also in monitoring and controlling the shapes of individual letters. The feedback is of two kinds: first, self-monitoring/self-evaluation of one’s own work and choice. Second, a timely, supportive, constructive, and corrective feedback from a caring and knowledgeable adult. When the feedback is absent or minimal, the handwriting may become sub-standard and illegible. Most of the time, this is one of the most important contributing factor in the developing of effective handwriting.
The writing involves the integration of visual, motor, as well as cognitive and perceptive components. The perception allows one to remember and then recognize the shape of the letters and numbers that are written while sight and motor skills of the hand enable the writing. It is a continuous flow from input (visual and perception) to output (visual, tactile). Brain imaging studies show that the nerves and then a bundle of neurons are connected to these three components and then definite new neural connections are taking place or being reinforced in the writing process. In the actual act of writing, by hand with pen or pencil on paper, one must use motor skills to copy or produce a letter/number graphically, although a slower process (compared to typing), but, that motor action actually aids in a child’s cognitive development. For example, with practice, the quality and keenness of perception improves. With better perception the flow from input to output become more smooth. Perceptual improvement makes us better observers, therefore, better learners.
(a) Fine Motor Skills and Writing
Fine motor skills involved in writing letters and numbers by hand are referred to as grapho-motor skills. Fine motor skills in naming numerals by mouth are referred to as oro-motor skills. We use oro-motor skills when we speak and identify and say the number. A complex of grapho-motor skills are involved in gripping and using tools—pencil, paper, stylus, iPad, eraser, and to produce number, symbols, and letter strokes, stylus strokes, and for pressing keys when typing on keyboards. These subtle and fine motor finger and hand skills draw on executive functions: planning and control, organization, judgment, and production of motor processes in different regions of the brain.
I have observed that many middle and high school students have difficulty forming special mathematical symbols and letters in lower case and cursive form even after occupational therapy. It is understood that hand writing letters may be an important exercise to facilitate children’s early letter understanding. At that time, many occupational therapists (OT) and handwriting specialists work on the improvement of generalized motor skills rather than specific fine motor skills related to numbers and letters. The question is: What type of intervention is most effective: specific or general—whether this effect is general to any visual–motor experience or specific to handwriting letters and numbers and specific symbols and forms.
Recent research has addressed this issue of letter knowledge using key precursor academic skill measures in preschool children before and after a school-based intervention. Children practiced letter or digit (numeral) writing or only viewing letters or digits. In an intervention of six weeks, results demonstrated that the writing (letters and digits) groups improved in letter recognition—one component of letter knowledge—significantly more than the viewing groups. And, digit-writing group performed significantly better on letter recognition than the letter writing group.
These results suggest that visual–motor practice with any symbol could lead to increases in letter recognition. This result can be interpreted as suggesting that any handwriting exercise, particularly digit writing, will increase letter recognition in part because it facilitates gains in visual–motor and visual-perception coordination.
(b) Cognitive Skills and Writing
Cognitive skills such as: following directions, identification of spatial orientation/space organization, pattern recognition, comparing and contrasting—comparing shapes, assessment of work, visualizing, doing task analysis, supporting one’s work with reasoning, etc. are involved when we learn and use the components of the visuomotor tasks in forming numbers—where to start, go left or right, up or down, make small or bigger, lower or higher, full circle or half circle, vertical or horizontal, in numerator or denominator, super-script or sub-script, etc. Students who write mathematics have a larger mathematics vocabulary, remember more, and receive and perceive more information during instruction.
(c) Role of Equipment in Writing
The writing equipment also plays an important role in the writing process. Few studies have explored the implications of the change of writing devices. On a very simple level, when students write on graph paper, with sharp pencils and effective erasers, in organized fashion, under guidance, their work is much better and they express that they have done better work.
The question is: what will be the nature of change in handwriting and learning as move from traditional pen or pencil on paper to computer keyboards, digital stylus, pens, and fingers on writing tablets, and speech to print software? Results from analysis of previous literature on various writing methods, devices and their implications have shown that there is a significant difference (particularly on neural activation, formation of connections, and on the myelanization process) between handwriting and the use of mechanized devices. Neuroscientists have noted that the shift from handwriting to mechanized or technical writing has serious implications on cognition and skill development—and the whole learning process. However, there is not enough research in this area. However, we can extrapolate some of the implications from the available research.
For example, typewriting involves both hands actively while handwriting involves, one active hand and the other as an aide (holding paper, maintaining balance, holding the book or another device from which information may be copied, cleaning and straightening paper), and handwriting is slower and more laborious than typing. In handwriting, one may focus on the word as a whole—the gestalt. Handwriting needs a person to shape and organize a letter, where typing does not. Some Japanese studies have shown that repeated handwriting aids in remembering the shape of the letters and numbers better. One study showed that when children learned words and numbers by writing, they remembered them better than if they learned them by typing. There are some observational studies to show that because of the topological nature of the written information (spatial location on the page), when we read that information from the book, or write it in a particular part of the paper, we remember better. I still remember many passages from the books and their particular places on the page, I had read in high school or even earlier.
Handwriting makes a person focus on one point alone–the tip of the pen—and a particular stroke (part and component) of the letter or number and we look at it longer than we look at it when we type. Expert typists do not even look at the paper. I have asked many typists, if they remember the material they typed. Their answer is: no! The focus on the written letter or number heightens perception and visual motor integration. This helps focus on the task—an important component of executive function. However, mechanized writing makes a writer oscillate between the keypad, the monitor, and the source of the information— this involves constant shifting of attention. Handwriting is a better aid in developing the different components of the executive function, particularly, inhibition control, organization, and spatial/orientation.
(d) Role of Cursive Writing
Many schools do not teach cursive writing because they think it is no longer important or it is too difficult to teach. Today, the emphasis is on keyboarding. Yes, all students should learn keyboarding. It is necessary and it has an important role in the highly technological society. It is a means of acquiring new knowledge, new skills, a new avenue to empowerment. Through keyboarding, they develop many cognitive skills and other content skills.
However, the goal of writing instruction in the information age should be developing hybrid scribes who are adept with multiple writing methods, using multiple tools including pens, stylus, and keyboards. Keyboarding and print writing, alone, do not help students develop other particular cognitive skills that cursive writing, whether on paper or iPad, develops. On the other hand, a certain level of cursive writing is essential for mathematics as there are many variables that need to be written in cursive and in lower case.
Cursive writing is an important part of learning. It is a multi-sensory, multi-function activity; it is more than just a writing activity. The presence of dysgraphia and poor letter formation are two important reasons to address handwriting. Dysgraphia does exist. But, just like reading problems exist without dyslexia, mathematics learning problems exist without dyscalculia, similarly, there are many whose writing problems exist without dysgraphia. Without training in writing, writing cursive, organization, visual perceptual activity, many children show signs/symptoms of dysgraphia, without really having dysgraphia. It is acquired dysgraphia. These students, with poor handwriting, are not truly dysgraphic, they never learned organization and visual-perceptual skills—tracking, copying, structure, form, discipline, and task analysis of visual tasks. Students learn great deal of organization and structure through proper handwriting instruction.
Weak spellers and students whose letters and numbers look good but are painful or laborious to produce are two other groups who need instruction in cursive writing skills. It is worth the time to make interventions in handwriting, at any grade. Every year, I get at least five to ten students in this category, and I am happy to say that, with help and guidance, they all change for good. Their issues about writing of numbers vary from dysgraphia to poor handwriting because of: poor handwriting teaching, lack of feedback to the writing, processing speed, lack of organization, slow speed of letter and number formation, perfectionist attitude—compulsive erasing/correcting, obstinate behavior, poor grip, and no or limited experience in writing.
How to develop Math vocabulary among students
For effective communication of mathematics ideas, children need robust and rich images and vocabularies (language containers). Without appropriate language containers, children cannot retain and communicate mathematics ideas. Vocabulary—words, expressions, phrases—are the language containers for mathematics concepts.
Learning mathematics, then, is using, creating, extending, and modifying language containers—the vocabulary of mathematics. Students’ proficiency in mathematics is directly related to the size of the set of their vocabulary. Rote memorization of a collection of words is not enough to master the language of mathematics. Instead, one has to acquire the related schemas with understanding. Language proficiency refers to the degree to which learners exhibit control over their language.
The introduction of mathematics vocabulary and terminology should be contextual, but even direct study of quantitative and spatial vocabulary contributes significantly to improved mathematics conceptualization—learning new concepts, creating deeper and robust conceptual schemas, and more effective communication.
When children create and encounter a language container for a mathematics concept, they also create and invoke the related conceptual model in their minds. Each word and expression such as sum, product, rational number, least common multiple, denominator, rectangular solid, conic section, and asymptotic represents a concept with its related schema. For example, if a person understands the definition of multiplication as ‘repeated addition’ or ‘groups of’, then these expressions invoke the conceptual schema. The expression 43 ´ 3, will invoke: 43 repeated 3 times (43 + 43 + 43) or 3 groups of 43 (43 + 43 + 43). If multiplication is learned as the ‘area of a rectangle’, then 3 ´ 43 will invoke an image of a rectangle with dimensions 3 (vertical side) and 43 (horizontal side).
The development and mastery of mathematical vocabulary are the result of a long and continuous interactive process between native language, mathematics language and symbols, and their quantitative and spatial experiences. This begins with play and concrete experiences in children’s environment. Experiences are represented through pictorial and visual forms and means, which then may result in abstract mathematics formulations and problems that students solve. This mathematics formulation—devising of abstract symbols, formulas, and equations, is then applied to more problems, and the result of this process is communicated. Successful communications demonstrate that the child has mastered a concept. The process can be summarized as:
Understanding the environment (concrete experiences and use of native language).
Translation (native language to pictorial and linguistic forms).
Representation (in the native language).
Description and verbalization (in the native language).
Discussion (in the native language).
Mathematical formulation of the problem (in the mathematical language).
Manipulation of mathematical language.
Communication of the outcome of mathematics operations (in mathematics and native languages).
This communication furthers not only children’s mathematics achievement but also their language development.
Building the Vocabulary of Mathematics
Many of children’s mathematics difficulties are due to their limited vocabulary—its size, level, and quality. A child’s size and level of vocabulary is the intersection of three language sets:
The level and mastery of the native language and background the child brings to the mathematics task.
The level and sophistication of language that the teacher uses and the questions she asks to teach mathematics.
The language set of the mathematics textbook being used.
The intersection of these three language sets is the available language the child has to learn mathematics. A small intersection means the child has a limited vocabulary. The objective, then, is to increase the size of this intersection. A child’s limited mathematics vocabulary may be for many reasons.
The mathematics problems of the child with English as a second language in a classroom where the medium of instruction is other than the child’s native language.
The child’s and teacher’s economic, cultural, and geographical backgrounds differ. For example, the linguistic problems that many urban black children and immigrant children face are an example of a linguistic/cultural mismatch and the assumptions teachers make in instructing children.
Textbook language sets differ from the language sets of the children and the teacher.
Whatever the reasons for limited language sets, we need to help children acquire a robust mathematics vocabulary. Properly acquired and used in context, a mathematics vocabulary has a profound effect on children’s mathematics achievement and their thinking. Planned activities for developing, expanding, and using vocabulary contribute significantly to better mathematical word problem-solving ability and support learning new concepts, deeper conceptual understanding, and more effective communication.
Although more textbooks are emphasizing the language of mathematics, there is still little attempt to develop a coherent and comprehensive mathematics vocabulary in school mathematics teaching. In one textbook, the expression “find the sum” is introduced quite early. In another series, the expression is introduced much later, and then the words “find the sum” and “add” are used interchangeably. In another text, the word “sum” is used sparingly. Consequently, a child may face different language sets from grade to grade and from school to school. Although the textbooks have a large number of common language terms and vocabulary, many words are not in common. Further, some textbooks use so much language without properly introducing the terms that many children find textbooks frustrating. Exercises do not provide enough practice in basic skills, which prevents children from automatizing the language or the conceptual skills associated with them.
Strategies for Enhancing the Mathematics Vocabulary
Ways in which children’s failure to develop mathematical vocabulary may manifest as:
(1) children have difficulty conceptualizing a mathematics idea;
(2) they do not respond to questions in lessons;
(3) they cannot perform a task; and/or
(4) they do poorly on tests, particularly on word problems.
Their lack of conceptualization of a mathematical idea may be because they do not have the language for the concept to receive it, comprehend it or express it, such as ‘find the sum of’, ‘union of two rays…,’ ‘evaluate…’
Their lack of response may be because they do not understand spoken or written instructions such as ‘draw a line between…’, ‘touch the base of the triangle’, ‘place a positive sign next to the numeral,…’ or ‘find two different ways to…’
They are not familiar with the mathematics vocabulary words such as ‘difference’, ‘subtract’, ‘quotient’, or ‘product.’
They may be confused about mathematical terms such as ‘odd’ or ‘table’, which have different meanings in everyday English and have more precise meanings in mathematics.
They may be confused about other words and symbols like ‘area’ and ‘perimeter’, ‘factor and multiply’, ‘and’.
To enhance children’s vocabulary, every school system should have a minimal mathematics vocabulary list at each grade level. Mastery of words from such lists will prepare children to communicate mathematics. This list can also be used to assess students’ grade level language of mathematics. This list should indicate the grade of introduction of words, terms, and definitions and the level where they are mastered. It should be developmentally and linguistically appropriate. The teacher should constantly identify, introduce, develop, and display the words and phrases that children need to understand and use.
The teacher should use the same techniques to introduce mathematics words as she teaches native language. She should have a Math Word Wall for every mathematics concept she teaches. When a new word related to the concept emerges in discussion, it is added to the Word Wall. With the introduction of each word, students are exposed to several words and concepts that contain it. Then students use it in their own words, with as many examples as they can. The teacher selects a word and then asks children to use it in mathematics context. The following exchange illustrates this process.
“Give me a sentence that uses the word ‘add.’”
“You have $5 and I have $14. Let us add both amounts.”
“That is great! Now use the word ‘sum’ in a sentence.”
“That is easy. If we add our monies, what is the sum of our monies?”
“That is great! Now I am going to write some words on the board. I want you to first to tell me and then write a sentence or two using each word. If you want, you can use more than one word in a sentence.”
The concepts are then reviewed in circular fashion, built upon, and tied into new ideas. This helps children construct a working vocabulary that is constantly augmented, and they are also learning skills to build it.
Once the key root words have been introduced to children, the teacher can begin to extend the mathematics vocabulary words. Among the easiest sets are the words formed with prefixes, suffixes and derivative words. The process is to introduce the math prefixes and roots casually and then formally. In a casual manner, parents and teachers can remark, “You know a tricycle has 3 wheels. Tri- means 3 and cycle means wheels.”
Teacher: What will be the name of the object that has three angles?
Student: A triangle.
Teacher: Why?
Student: A triangle has 3 angles and tri- means 3.
Teacher: Now draw a triangle on your paper.
Children draw triangles on their papers.
Teacher: The word ‘lateral’ means a side. What will you call an object that has three sides?
Student: A trilateral.
Teacher: Now draw a trilateral on a paper.
Children draw a trilateral on their papers.
Teacher: If the word ‘gon’ means a corner, what will you call an object that has three corners?
Student: A trigon.
Teacher: If ‘octo’ means eight, what does ‘octagon’ mean?
Student: A figure with eight corners.
As with all language development, there is a sequence in moving from speech ability to writing ability: the input is auditory in its foundation (the child is immersed in oral linguistic experiences), then followed by speech ability (the child produces language) and later by reading and writing ability. When young children have this kind of foundation, they avoid the anxiety of making sense of key foreign words later on in a formal setting. They will be able to generalize and relate math concepts to their daily experiences.
Instructional Suggestions for Language Proficiency
There are practical reasons children need to acquire rich and appropriate vocabulary for them to participate in classroom life—the learning activities and tests. There is, however, an even more important reason: vocabulary, as part of mathematical language, is crucial to children’s development of thinking not only in mathematics problem solving but in general problem solving. Once children have control over their language usage, they begin to have control over the meta-cognitive skills that produce insights into their learning and their interactions with learning tasks. Language and thinking are interwoven in reasoning, problem solving, and applications of mathematics in multiple forms—intra-mathematical, interdisciplinary, and extracurricular. If children do not have the vocabulary to talk about a concept, they cannot make progress in understanding its applications—therefore solving word problems.
Teachers often use informal, everyday language in mathematics lessons before or alongside technical mathematical vocabulary. This may help children’s initial grasp of the meaning of words; however, a structural approach to the teaching and learning of vocabulary is essential to move to higher mathematics using the correct mathematical terminology. This also applies to proficiency. The teacher needs to determine the extent of children’s informal mathematical vocabulary and the depth of their understanding and then build the formal vocabulary on it.
It is not just younger children who need regular, planned opportunity to develop their mathematical vocabulary. All students and adults returning to education need to experience a cycle of concrete work, oral work, reading, writing, and applications.
The teacher needs to introduce new words through a suitable context, for example, with relevant, real objects, mathematical apparatus, pictures, and/or diagrams. Referring to new words only once will do little to promote the learning of mathematics vocabulary. The teacher should use every opportunity to draw attention to new words or symbols with the whole class, in small groups or with individual students. Finally, the teacher should create opportunities for children to read and write new mathematics vocabulary in diverse circumstances and to use the word in sentences.
Concrete work: Concrete materials/models develop images and the language for mathematics ideas. The concrete materials/models help children (a) generate the language, (b) understand the concept, and (c) arrive at an efficient procedure. Students should be encouraged to explore and solve problems using manipulative materials and asked to discuss and record the activity using pictures and symbols. The teacher or a student can also act the word out.
Writing work: The teacher should explain the meanings of words carefully. The teacher should refer to a similar word; give the history and the derivation of the word and write it on the board. Children should copy it in their Math Notebook. The teacher should ask the children to say the word clearly and slowly. They should rehearse the pronunciation of the word. The teacher should ask them to spell the word and ask a child to say the word and spell it with eyes closed.
Oral work: Students describe the work done at the concrete level, using mathematics words and expressions based on the visual and tactile experience of the meaning of mathematical words in a variety of contexts. This oral work may be facilitated in different contexts by
listening to the teacher or other students using words correctly
acquiring confidence and fluency in speaking, using complete sentences that include the new words and phrases, in chorus with others or individually
discussing ways of solving a problem, collecting data, organizing data and discussing the properties of the data for a variety of reasons: to generate hypotheses, develop conjectures or make predictions about possible results or relationships between different elements and variables involved in the problem
presenting, explaining, communicating, and justifying methods, results, solutions, or reasoning, to the whole class, a group, or partner
generalizing or describing examples that match a general statement
encouraging the use of the word in context and helping sort out any ambiguities or misconceptions students may have through a range of open and closed questions.
Because students cannot learn the meanings of words in isolation, I believe in the centrality of reading and conversation in mathematics lessons. Shared reading is a valuable context for learning and teaching not only mathematics language but also mathematics content. Strategies such as using children’s books, stories, DVDs, and videos as a vehicle for communicating mathematical ideas develops mathematical language. Reading word problems aloud and silently, as a whole class and individually, is equally important. During these readings, the teacher should ask questions involving mathematics concepts. This develops strong mathematics language and understanding. Students can be asked to read and explain:
numbers, signs and symbols, expressions and equations in blackboard presentations
instructions and explanations in workbooks, textbooks, and other multi-media presentations
texts with mathematical references in fiction and non-fiction books, books of rhymes, children’s books during the literacy hour as well as mathematics lessons
labels and captions on classroom displays, in diagrams, graphs, charts, and tables
definitions in illustrated dictionaries, including dictionaries that the children have made themselves, in order to discover synonyms, origins of words, words that start with the same group of letters (e.g. triangle, tricycle, triplet, trisect…), words made by coding pre-fixes or suffixes, words derived from other words.
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