At the start of Year 1, children are enthusiastic ‘beginning’ mathematicians. They have an understanding of the basic concepts of number, shape and measurement, and see mathematics as an exciting and practical element of the curriculum. They develop their knowledge, skills and understanding through a balance of wholeclass activity. This involves, for example, counting, direct teaching, problem solving in groups and independent work, where children apply and practise their learning. A mix of mental, practical and informal written work engages and motivates children and fosters purposeful attitudes to mathematics. Home–school mathematics links are an important part of children’s experiences.

Children solve problems in a variety of practical contexts. They talk about the problem that they are going to solve and use practical materials, numbers and diagrams to represent and organise the problem. For example, to find the total number of children seated at five tables of four, they use toys or tally marks to represent the children at each table before recording the numbers involved. They solve the problem then place the answer back in the context of the problem: ‘There are 20 children sitting down.’

Children understand how to represent number stories by number sentences. For example, they represent the number story ‘Eleven people are on a bus and three get off; there are eight people left on the bus’ by the number sentence 11 – 3 = 8. They use the +, – and = signs to write number sentences to record mental calculations. They begin to find the unknown number represented by a symbol in number sentences such as 17 – 10 = , + 2 = 6 and 3 = 7 – .

Children solve problems involving ‘paying’ and ‘giving change’. For example, they work out different ways of paying for an apple costing 6p using 1p and 2p coins. As they work with numbers and shapes, they identify and use patterns and properties. For example, they notice that all shapes with three sides have three...

...Focus on the LearnerLearner Characteristics
Learner characteristics are difference between learners which influence their attitude to learning a language and how they learn it. These differences influence how they respond to different teaching styles and approaches in the classroom and how successful they are at learning a language. The differences include the learner’s motivation, personality, language level, learning style, learning strategies, age and past language learning experience.
Learning style: they are the ways in which a learner naturally prefers to take in, process and remember information and skills. Our learning style influences how we like to learn and how we learn best. Some of commonly mentioned learning styles are:
Visual
The learner learns best through seeing
Auditory
The learner learns best through hearing
Kinaesthetic
The learners learns best through using the body
Group
The learner learns best through working with others
Individual
The learner learns best through working alone
Reflective
The learner learns best when given time to consider
Choices
Impulsive
The learner learns best when able to respond immediately
Learning Strategies: they are the ways chosen and used by learners to learn language.
Repeating new words in your head until you remember them...

...The Teaching of mathematics should focus on conceptual understanding of the learner
By Shanecia Gordon
620043076
UWI - Mona
Mathematics is an area that is widely known and studied. It is the foundationof many subject areas and is a subject that equips one with skills and knowledge suitable for the real world.
Mathematics is defined as a reasoning activity that involves observing, representing and
Investigating relationships in the social and physical world, or between mathematical
Concepts themselves (BOS NSW, 2002). The Britannica Online (Academic Edition) also defines mathematics as a science that deals with logical reasoning and quantitative calculation, its development involves an increasing degree of idealization and abstraction of its subject matter. Mathematics consists fundamentally of concepts, which are abstract generalised ideas. Mathematics therefore is the application of physical and mental operation to concepts. Mathematics as a subject can be learnt two basic ways. Its understanding can either be procedural (understanding the process) or conceptual (understanding the concept). Teaching of mathematics should therefore be focused on the development of conceptual understanding as this involves seeing the connections between concepts and procedures, and being able to apply mathematical principles in a variety of contexts....

...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
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...

...2011, Vol. 56, No. 1, pp. 138-143
LEARNERS STRATEGY AND KEY STEPS OF TEACHING
NEW STRATEGY OF SARA COTTERALL AND HAYO REINDERS
TO 1ST YEAR STUDENTS OF ENGLISH
Hoang Thi Giang Lam
Hanoi National University of Education
E-mail: gianglam76@yahoo.com
Abstract. This study attempts to present what the author has experienced
and applied in teaching new strategies to 1st year students of English at
HNUE with an example of application into reading strategies for example
reading for main idea according to ﬁve key steps by Sara Cotterall and
Hayo Reinders (2004). These brieﬂy introduced key steps are: (1) raising
learners awareness of the strategy, that is to make them see the importance
and the need to study the strategy; (2) modelling the strategy, the step
in which a teacher tries to show how to use the strategy as they read the
text for example; (3) trying out the strategy: at this stage a teacher has to
design several activities for students to practice using the new strategy; (4)
evaluating the strategy to see if the students ﬁnd the strategy useful or if they
have any diﬃculties in using it to solve all arising problems; (5) encouraging
transfer of the strategy to new contexts: regular practice and revision should
be given to make students work independently in any situations they may
have in their lifetime learning process.
Keywords: learner’s strategy, learning...

...2012-The Year of Mathematics
P.Bhattacharyya
[pic] [pic]
(GH Hardy , Ramanujan and Littlewood)
The great Indian mathematician Srinivasa Ramanujan was born on the 22nd of December 1887 in Erode, Tamilnadu.
In a function held in the Centenary Hall of Madras University on the 26th of December 2011 marking the 125th birth anniversary of Srinivasa Ramanujan, the Prime Minister of India Dr. Manmohan Singh proclaimed:
“Our government has decided to declare his birthday, that is December 22nd, as the National Mathematics Day and the year 2012 as a whole as the National MathematicsYear”.
He said that India has a long and glorious tradition of mathematics that we need to encourage and nurture. “I hope these steps will help in providing additional impetus to the study of mathematics in our country and make our people more aware of the work of Ramanujan”.
The last part of the Prime Minister’s statement: “... to make our people aware of the work of Ramanujan” is very significant. The actual work of Ramanujan and its significance is known only to a handful of very high level mathematicians. However, one need not be surprised at this owing to the very nature of the subject of mathematics itself.
In a survey conducted amongst educated Indians in 1987, the centenary...

...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...

...EDP136 Mathematics Education
Assessment 1: Planning for mathematics teaching
Due: Weeks 3and 10
10% (Week 3) and 40% (Week 10)
The purpose of this assessment task
This assessment task is focused on developing your capacities to be an effective mathematics teacher. Key aspects of these capacities are: attitudes towards mathematics; mathematics knowledge; knowledge of how children learnmathematics; and knowledge of resources that can support children’s mathematics learning.
The weekly learning activities of this unit are designed to provide opportunities for you to develop these aspects of your professional capacities. In this regard the weekly learning activities will engage you in a variety of learning experiences, including: textbook readings; readings of scholarly and research documents; examination of classroom videos and lessons; examination of mathematics curriculum documents; critiquing of online and other resources for mathematics learning and teaching; reflections upon your own mathematics learning experiences; development of your own mathematics knowledge; answering key questions concerning mathematics education; and sharing and discussing your ideas.
What this assessment task will contain
For this assessment you are required to draw upon your learning as recorded in...