Misconceptions
The Family of misconceptions that I will examine is the following; multiplication and division always produces larger and smaller values respectively. This is related to the order in which children are taught the concepts of multiplication, Division and extending the set of numbers from integers to non integers and fractions. Misconception| Demonstration of why this is incorrect|

Multiplication always makes a number larger or it stays the same stays the samesolution larger than original number (5)| Multiplication can make numbers smaller multiplication by a decimal less than 1 multiplication by a fraction less then 1multiplication by a negative| Division always makes numbers smaller or they stay the same.solution smaller than original number (12)stays the same| Division can make a number larger division by a decimal less than 1 division by a fraction less than 1division of a negative number by another negative number| The primary reason that children have this misconception is when they first encounter the functions multiplication and division, they are only being exposed to positive integers, thus the examples that they will have been given and the examples they practiced will all have followed the pattern that multiplication makes numbers larger and division makes numbers smaller. The misconception persists when they individual does not draw a connection to the extension to the numbers space and the implications on the functions. Extension of the number space to decimals and fractions should dispel this misconception, as they should then be exposed to counterexamples to their misconception. In some cases the individual will see the examples they are asked to do as exceptions to their rule rather than a change in the way they perceive multiplication and division. If the individual is familiar with fractions then multiplication by positive numbers less than 1 can be couched in terms of fractions, When an individual is familiar...

...History of mathematics
A proof from Euclid's Elements, widely considered the most influential textbook of all time.[1]
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.
Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available arePlimpton 322 (Babylonian mathematics c. 1900 BC),[2] the Rhind Mathematical Papyrus (Egyptian mathematics c. 2000-1800 BC)[3] and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-calledPythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.
The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greekμάθημα (mathema), meaning "subject of instruction".[4]Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning andmathematical rigor in proofs) and expanded the subject matter of mathematics.[5] Chinese...

...The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction, which is shared by many animals,[19] was probably that of numbers: the realization that a collection of two apples and a collection of two oranges (for example) have something in common, namely quantity of their members.Evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have also recognized how to count abstract quantities, like time – days, seasons, years.[20]
More complex mathematics did not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy.[21] The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time.
In Babylonian mathematics elementary arithmetic (addition, subtraction, multiplication and division) first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have been many and diverse, with the first known written numerals created by Egyptians in Middle Kingdom texts such as the Rhind Mathematical Papyrus.[citation needed]
Between 600 and 300 BC the Ancient Greeks began a systematic study of...

...UNIVERSITY Of ZIMBABWE
FACULTY OF COMMERCE
TOURISM, LEISURE AND HOSPITALITY STUDIES DEPARTMENT
ROOMS DIVISION MANAGEMENT THM208
YEAR 2012
LECTURER: MRS. D ZENGENI
Time table
Monday 11.00-13.00hrs
Tuesday 11.00-12.00hrs
Preamble
This course is designed to introduce students to the principles of accommodation management in hospitality industry. Emphasis will be placed on Rooms Divisions’ traditional role as the best generator of the hotel’s revenue as well as its principal operational functions.
Objectives
By the end of the semester the students should have an understanding of:
The housekeeping division and its operations.
The guest cycle and the operational and managerial activities for each stage.
They should also be able to come up with reports on evaluating operations in the rooms division.
Communication between houseking and other Hotel departments.
Human resources in the rooms division department and its importance.
Course Outline
1. The Rooms Division
Introduction
Organization of the Rooms Division
Organization of rooms division department
Interrelationship and communication within rooms Division department with other departments
2. Housekeeping
The role of the housekeeping department
Management theory and the housekeeper
Housekeeping operations
Liaison of Housekeeping and Front Office
Automated...

...mother of Europe's languages. India was the mother of our philosophy, of much of our mathematics, of the ideals embodied in Christianity... of self-government and democracy. In many ways, Mother India is the mother of us all."
- Will Durant, American Historian 1885-1981
Mathematics is an important field of study. Mathematics is essential as it helps in developing lots of realistic skills, in fact study of mathematics itself include the concepts related to the routine lives of human. It not only develops mathematical skills and concepts, it also helps in developing the attitudes, interest, and appreciation and provides opportunities to develop one’s own thinking. So, mathematics is undoubtedly a discipline which is imperative to know and study. Figure 1 clearly specifies all the skills that are developed by the mathematics. Mathematics starts from simple things and linear thinking that lead towards the more complex things and higher order thinking skills. Mathematics has taken centuries to develop in its present form and that’s why it will be really fruitful to know about its development.
Fig. 1, Importance of MathematicsC:\Users\naveen\Desktop\Untitled.png
Mathematics has played a very significant role in the progress and expansion of Indian culture for centuries. Mathematical ideas that originated in the Indian subcontinent have had a...

...Week 5
Final Exam
Continuous schedule from Friday , November 1st. 9am until Saturday , November 2nd., 23:59pm.
Monday, November 4, 2013
20%
100%
To obtain the opportunity to take your final exam you should have delivered at least 6 activities.
Please keep this Agenda at hand so that you can deliver you assignments on time.
Greetings,
Blanca Alanís
Posted by: BLANCA HILDA ALANIS PENA
Posted to: CEL.HI09107V.343.13320 Inglés VII
Bibliography
Posted on: Thursday, October 3, 2013
Hello guys,
The books we are going to use are:
Text book:
Richards, Jack C. & Sandy, Chuck (2009). Passages 2 (2nd ed.). New York, N.Y. Cambridge University Press.
ISBN 978-0-521-68391-3
Workbook:
Richards, Jack C. & Sandy, Chuck (2009). Passages 2 (2nd ed.). New York, N.Y. Cambridge University Press.
ISBN 978-0-521-68393-7
Make sure they are the 2nd. edition, because the 1st. edition is completely different.
In your course, in the Bibliography Section you have a link of a bookstore where you can buy the books. You can try other bookstores in your city, of course, but they don't usually have the book in stock.
Greetings,
Blanca Alanís
Posted by: BLANCA HILDA ALANIS PENA
Posted to: CEL.HI09107V.343.13320 Inglés VII
Grading in the courseWeek 5
Final Exam
Continuous schedule from Friday , November 1st. 9am until Saturday , November 2nd., 23:59pm.
Monday, November 4, 2013
20%
100%
To...

...Level 1/Level 2 Certificate
Mathematics
Specification
Edexcel Level 1/Level 2 Certificate in Mathematics
(KMAO)
First examination June 2012
Edexcel, a Pearson company, is the UK’s largest awarding body, offering academic
and vocational qualifications and testing to more than 25,000 schools, colleges,
employers and other places of learning in the UK and in over 100 countries
worldwide. Qualifications include GCSE, AS and A Level, NVQ and our BTEC suite of
vocational qualifications from entry level to BTEC Higher National Diplomas,
recognised by employers and higher education institutions worldwide.
We deliver 9.4 million exam scripts each year, with more than 90% of exam papers
marked onscreen annually. As part of Pearson, Edexcel continues to invest in
cutting-edge technology that has revolutionised the examinations and assessment
system. This includes the ability to provide detailed performance data to teachers
and students which help to raise attainment.
Acknowledgements
This specification has been produced by Edexcel on the basis of consultation with
teachers, examiners, consultants and other interested parties. Edexcel would like to
thank all those who contributed their time and expertise to its development.
References to third-party material made in this specification are made in good faith.
Edexcel does not endorse, approve or accept responsibility for the content of
materials, which may be subject to...

...A critic paper on the thesis
Use of Manipulatives to Develop Second Year High School Students’ Understanding
of Equality and Linear Equations
by Melanie Rivera
Mary Grace Sinfuego
Adrian Paul Tudayan
This thesis aimed to study and analyze the students’ understanding of equality and their skills in solving Algebraic Equations specifically Linear Equations. The researchers wanted to find out the misconceptions of selected 2nd Year students regarding the said topic. Moreover, they also wished to find out if using manipulatives such as counters and rectangles could help in correcting these misconceptions and provide a better understanding on the concept of equality and their skills in solving.
It was clearly stated in the first part of the paper the concern researchers would like to address. Moreover, the objectives of the study were also given in order to provide a clear idea of what the paper is all about. The idea was further supported by background concepts regarding the definition of equality and equivalence and how is it important in solving Algebraic Equations.
The understanding or perception of students regarding equality was limited into 4 different categories: operational, relational, other alternative or no knowledge at all. These understandings are known to interfere with the ability of the student to solve and analyze linear equations. We classify someone’s understanding as operational if he thinks that the equal sign...

...HISTORY OF MATHEMATICS
The history of mathematics is nearly as old as humanity itself. Since antiquity, mathematics has been fundamental to advances in science, engineering, and philosophy. It has evolved from simple counting, measurement and calculation, and the systematic study of the shapes and motions of physical objects, through the application of abstraction, imagination and logic, to the broad, complex and often abstract discipline we know today.
From the notched bones of early man to the mathematical advances brought about by settled agriculture in Mesopotamia and Egypt and the revolutionary developments of ancient Greece and its Hellenistic empire, the story of mathematics is a long and impressive one.
Prehistoric Mathematics
The oldest known possibly mathematical object is the Lebombo bone, discovered in the Lebombo mountains of Swaziland and dated to approximately 35,000 BC. It consists of 29 distinct notches cut into a baboon's fibula. Also prehistoric artifacts discovered in Africa and France, dated between 35,000 and 20,000 years old, suggest early attempts to quantify time.
The Ishango bone, found near the headwaters of the Nile river (northeastern Congo), may be as much as 20,000 years old and consists of a series of tally marks carved in three columns running the length of the bone. Common interpretations are that the Ishango bone shows either the earliest known...

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