Teacher Manual Mathematics Curriculum Development
Maths is a unique and universal approach to an understanding of the physical universe. The utilization of mathematical methods promotes human knowledge and understanding and develops the ability to think and reason. Mathematics provides the possibility, through modeling real phenomena and problems, to transform them into the language of figures, pictures and symbols, and thus to understand them better
The main goal of Maths is to promote the learners’ mental abilities through solving mathematical problems and exercises and to work with mathematical concepts in order to develop higher order thinking skills, which will allow learners to make better judgments and will provide them with the tools to resolve a wide range of problems.
Purpose of the teacher manual
Read the purpose of this manual well, make notes if necessary.I
n every country, at all times, mathematics has been treated as one of the essential educational subjects in schools. This is because mathematics helps develop the thinking power of students as well as playing an important role in solving practical problems.
The value of mathematics is universally recognised not only for its daily and professional necessity and for its supportive role for the development of various branches of science and technology, but also for the development of human qualities. The irrefutable logic of mathematics, its clarity of expression and creativity in problem solving and proof dependency helps develop the desired qualities in a student’s mind.
This teacher resource manual is designed to help teachers implement the mathematic curriculum grade 1-4. It will help the teacher also how to read and use the curriculum in the classroom. The new curriculum is basic document that wants to help the teacher to be creative in his classroom. The document is competency based what means:
In outcome-based education, the learning process ensures achievement of the set goals expressed in form of competencies. Competency is individual’s ability for active, responsible life action performed on the basis of personal identity and attitudes, ability to actively interact with environment and to change oneself and the environment in the course of this interaction.
Competencies are built in the course of learning process, not only in educational institution, but also under influence of family, friends, work, politics, religion, culture, etc. In this regard, realization of competency-based approach is dependent upon educational and cultural situation in which a student lives and develops.
Competency is capability of an individual for active, responsible life action performed on the basis of individual’s value system, ability to actively interact with the environment, to understand and change oneself and environment during this interaction.
Defeniton and function of the curriculum
The Curriculum defines the main educational policy guidelines, establishes the general principles behind the development of the state standards for secondary education, pre-school and special education and the subject standards for general education, as well as the main requirements specified for learners and teachers.
The main functions of the Curriculum are:
1. To ensure uniform policy throughout the education system;
2. To ensure continuing improvement in the quality of education provided;
3. To regulate the relationships between central and local self-government authorities, educational institutions, society and individuals in the system of general education;
4. To ensure the conformity of the education system with the objectives established by the state and society, the needs of individuals and internationally recognized standards;
5. To ensure the sustainability of the main educational projects implemented in the Republic of Armenia;
6. To establish a foundation for the development and implementation of professional educational programs.
Try to find two more functions of the curriculum, think about your classroom
activities
General aims of curriculum development
· Help develop inquisitiveness and logical thinking powers of students
· Make students aware of the inherent beauty of mathematics
· Increase students’ skills in applying mathematical knowledge to develop skilled manpower for the twenty-first century
· Establish the relationship of mathematics with other subjects and to master skills in applying mathematical knowledge in real life situations
· Develop students’ skills in inventing ways to solve practical and mathematical problems
· Help students attain virtue through reaching a realistic proof by applying mathematical logic.
4. Specific objectives of mathematics:
Through selected units and common school activities, the secondary level curriculum has been prepared to achieve the following objectives:
Intellectual
· Consolidating and expanding previously acquired knowledge, skills, outlook and ethics during the earlier academic levels.
· Enhancing the students’ capacity to acquire higher knowledge through application of mathematical knowledge, analysis, synthesis, logical sequences and problem solving
· Assisting students in acquiring the main skills in using mathematical languages
· Assisting the students in applying apply research techniques and scientific methods in both abstract and practical areas in different fields of Mathematics
· Strengthening the basic mathematical ideas of students to assist them in acquiring application skills for use in information and communication technology
Moral and Spiritual
· Developing personal qualities such as honesty, morality, responsibility, discipline, cleanliness, personal accountability, tolerance and respect towards others through mathematical knowledge
Communicative
· Ensuring student’s ability to communicate through graphs, table, symbols and charts
· Establishing relationships and improving communication between mathematics and other branches of knowledge
Social and Cooperative
· Developing understanding and brotherhood by working with others, solving mathematical problems outside school and through interaction and co-operation
Personal
· Gaining confidence, satisfaction and pleasure through achieving mathematical knowledge and skills
· Developing skills in mathematical logic and attaining skills in its application.
Find for each objective a specific classroom activity
Framework explanation
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Competencies |
Content and specific competencies |
Resources |
Assessment |
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T&L Mat |
Methods |
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- To gain basic ideas of numbers
- To be able to use these numbers
- Read and write numbers in digits and numbers
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Numbers:
1.Name, chain and designation of numbers from 1 up to 20. Reading and writing of numbers. Counting of objects.
2.Number 0
Getting and signing. .
3.Comparison of numbers.
Signs <,>, =.
4.Configuration of numbers. Numbers and dates.
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- counting materials;
-numerical cards;
-numerical line;
-models of watches / clocks
-geometrical figures;
-natural objects (buttons, beads, nuts, etc. )
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- talk, interview;
-observation;
-visual – illustrated methods;
- table;
- practice work;
- individual work;
-group work;
-frontal work;
- work in pairs;
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- portfolio;
- project defense;
- verbal assessment;
- marking assessment;
-emotional assessment;
- mutual assessment;
-individual creative works;
-thematically cards done by the student;
- self evaluation;
-presentation;
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In column 1 we have set up basic general competencies. We developed the corresponding content and transformed it in sub-subject competencies (will be done in the month of December). Link those competencies to the materials, methods and assessment.
The mathematics curriculum has five sub-subjects
Numbers
Operations
Measurement
Geometry
Problem solving
Each section is developed in every grade (1-4) and linked to the Key competencies (column 1), to the content (column 2), to the resources (column 3 and 4) and to the assessment (column 5)
Fill in the framework, choose yourself the key competency and then fill in the other parts of the framework.
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Competencies |
Content and specific competencies |
Resources |
Assessment |
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T&L Mat |
Methods |
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Competencies (Column 1)
- Key competencies are competencies related to general (meta-subject) content of education;
- General subject competencies are competencies related to a specific range of school subjects and education domains;
- Subject competencies are particular competencies having a specific description and possibility to be shaped within scope of school subjects.
Competencies development is a major part of the Primary School Curriculum. It states: Strong emphasis is placed on developing the ability to question, to analyze, to investigate, to think critically, to solve problems, and to interact effectively with others. Focusing on the development of competencies facilitates the integration of learning and provides for the coherent planning and delivery of the curriculum. Numeracy competencies including estimation, problem-solving, prediction, information handling, and so on, are developed in Mathematics.
Numeracy-what does it mean?
In practice, the term may signify any one of a number of things including basic computational arithmetic, essential mathematics, social mathematics, survival skills for everyday life, quantitative literacy, mathematical literacy and an aspect of mathematical power. These descriptions span a spectrum of personal abilities from basic skills to high-level cognitive abilities such as problem solving and interaction with, and attitudes to the society.
The research literature contains no universally accepted definition of numeracy. Its initial use in 1959 was in the UK Crowther Report where it was named as the mirror image of literacy.
Most definitions of numeracy have emphasized the use of mathematics in real-life situations, and the notion that these can be used or addressed by a person in a goal-oriented way, dependent on their needs and interests within some particular contexts (home, community, workplace, etc.), as well as on their beliefs and attitudes.
It is clear from these definitions that numeracy does not refer only to operating with numbers as the word might suggest, but to a much wider range of skills.
Competency-based Primary Education in the Kyrgyz
Republic:
In competency-based education students’ acquisition of specific competencies is the focus. Such an educational program includes a set of learning objectives that are clearly specified so that their accomplishment can be understood in the form of specific learner behaviors and knowledge.
This idea was first introduced in America in the late 1960’s in teacher education programs, and was later adapted for other professional educational, and vocational training programs in UK and Germany.
The Essential Learning Continuum (ELC) is a listing of competencies, which serves as a guide to determine what to teach and measure among the pupils at the primary level.
Competency was defined in this way ‘the acquired knowledge, ability and viewpoint when those could be applied in real life at the right time could be called competency.
These competencies are based on the age, physical capability and psychological maturity of the children, on changes happening in our society, demands for the future, existing physical facilities in schools, and on the preparation of teachers at the school level. The children are expected to acquire these competencies in the four-year long primary education, and they are referred to as the ‘terminal competencies of primary education’.
To gain the basic ideas of number and to be able to use them
To know the four fundamental operations and to be able to use them
To apply the simple methods of computing/calculating in every-day life problem solving
To know and to use the units of money, length, weight, measurement and time
To know and understand the geometrical shapes and figures
In your opinion are the competencies the same for rural or urban school
children? Explain.
Content: (Column 2)
In the column content you find “what” the teacher has to teach in every grade and what the children need to know at the end of a lesson, at the end of a term or at the end of the school year.
Teaching and learning materials: (Column 3)
The use of teaching learning materials can play a most important role in learning. People have different preferences for how they learn: some learn better by listening, others by watching, others by reading and others by doing. Traditional teaching methods mainly employ listening and reading skills in the classroom. Although many students can learn this way it is not the most efficient method for all students. For these reasons teachers should try to engage all the students’ senses in their learning as this will increase the efficiency of their learning.
Textbooks will play a prime role in classroom teaching. Besides the textbook the teacher should make use of charts, posters, models and real life examples to stimulate learning particularly as many students have difficulty translating and using mathematical symbols such as those used in algebra. Teachers will have to use their initiative in providing these materials.
How to use the Teaching-Learning Materials
1. Look through the activities until you find one that looks interesting.
2. Read the activity and try to understand how it would function.
3. Plan to teach such a lesson along the lines of the activity.
4. Note the purpose of the activity – the Learning Outcomes.
5. Note the student involvement as given in the student worksheet.
6. Try out the activity in your classroom.
7. After the lesson, make notes on the lesson and perhaps suggest modifications to the activity.
8. Look for another interesting activity. OR try creating an activity of your own.
A sample of a T&L Material:
a. Tables of Multiplication game:
Example of a ‘Bingo Game’ to practice the tables of multiplication:
For a group of 5 players, prepare 4 cards with 6 results of multiplications.
Examples:
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24 |
30 |
54 |
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60 |
45 |
18 |
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48 |
15 |
20 |
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10 |
16 |
27 |
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35 |
21 |
8 |
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14 |
72 |
32 |
Prepare 24 small cards with the multiplications corresponding to the results on the big cards.
Examples:
- One player is the leader and doesn’t have a card. The other 5 players have each a big card. The small cards are in the middle of the table, face up, so that all players can see them.
- The leader announces ‘a multiplication’. Example ‘8 X 3’, the player who has the result on his/her card announces the result ‘24’ and takes the small card with the corresponding multiplication to put it on the result on his/her big card.
- The first player who can cover all the results is the winner and shouts ‘BINGO’.
- The game continues until all players have covered the 6 results.
b.Stimulate number sense:
To help students to develop number sense it is important to analyze the regularities in a numeric system, this facilitates the understanding of the numbers as a total, and the importance of place value.
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