__Unit
II: Teaching of Mathematics and Science __

__2.1
Role of Mathematics & Science in day to day living. __

__2.2
Objectives of teaching Mathematics & Science __

__2.3
Different approaches and techniques of teaching mathematics & Science. __

__2.4
Number concept: Teaching of basic concepts like quantity, shape, size, money
and measurement. __

__2.5
Number system & basic Mathematics calculations, addition, subtraction,
place value, multiplication, divisions and fractions. __

__2.6
Teaching environment, health, nutrition, living and non living__

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__2.1
Role of Mathematics & Science in day to day living__

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**Role of
Mathematics **

Mathematics is a study of measurements, numbers, and space, which is one of the first sciences that humans work to develop because of its great importance and benefit.

The origin of the word "mathematics" is in Greek, which means tendencies to learn, and there are many branches of mathematics in science, that are related to numbers, including geometric forms, algebra, and others.

Mathematics plays a vital role in all aspects of life, whether in everyday matters such as time tracking, driving, cooking, or jobs such as accounting, finance, banking, engineering, and software. These functions require a strong mathematical background, and scientific experiments by scientists need mathematical techniques. They are a language to describe scientists' work and achievements.

Mathematics is the pillar of organized life for the present day. Without numbers and mathematical evidence, we cannot resolve any issues in our daily lives. There are times, measurements, rates, wages, tenders, discounts, claims, supplies, jobs, stocks, contracts, taxes, money exchange, consumption, etc., and in the absence of these sports data, we have to face confusion and chaos.

Thus, mathematics has become the companion of man and his helper since the beginning of human existence on earth. When man first wanted to answer questions such as "How many?" he invented math. Then algebra was invented to facilitate calculations, measurements, analysis, and engineering.

The science of trigonometry emerged when humans wanted to locate high mountains and stars.

Therefore, the knowledge of this article arose and developed when humans felt the need and mathematics are necessary for the long planning of life and also the daily planning of any individual.

**Benefits and Importance Of Mathematics in
Everyday life And The Modern World**

1.
**Managing
time:** Keeping
a track of time is very important to do all you love to do

2.
**Budgeting:** Managing money,
understanding discounts, and buying for the best price

3.
**Sports:** Score, Time,
Strategizing to win

4.
**Cooking:** Measuring the
ingredients to add to a recipe, kitchen inventory planning

5.
**Exercising
and Dieting**

6.
**Driving:** Distance
traveled, the shortest route to take to reach a destination

7.
**Home
Decorating**

8.
**Stitching:** Measurements to
stitch a dress

9.
**Critical
Thinking**

**10.****The base of other
Subjects**

**Math Is A Universally Understood Language:** Math
is a subject that almost everyone understands. A math equation does not need to
be translated into another language to be understood by someone on the other
side of the planet. A mathematical law does not change because someone has a
different faith or speaks a different language than you. 2 + 2 equals 4
anywhere on the planet. Math’s universality is one of the many factors that
makes it such a powerful tool and, therefore, a crucial life skill.

** **

**Role of
Science**

*Science is a systematic and logical study towards how the universe
works. Science is a dynamic subject. Science can also be defined as the
systematic study of the nature and behavior of the material and physical
universe, based on observation, experiment, and measurement, and the
formulation of laws to describe these facts in general terms.*

*Science is one of the greatest blessings to the mankind. It has
played a major role in improving the quality of living of the man. Science is
omnipresent and omnipotent in every walk of our life. In every inch of our
body, science is the protagonist.*

*There are different types of science:*

1. **Physical Science**: Physics, Chemistry, Astronomy and
Earth science are branches of physical sciences.

2. **Life Science**: Biology and Social sciences are
branches of life sciences.

3. **Applied Science**: Engineering and Health care are
branches of applied sciences.

Science is involved in cooking, eating, breathing, driving, playing, etc. The
fabric we wear, the brush and paste we use, the shampoo, the talcum powder, the
oil we apply, everything is the consequence of advancement of science. Life is
unimaginable without all this, as it has become a necessity.

Examples of the use of science in everyday life are as follows:

· We use cars, bikes, or bicycles to go from one place to another; these all are inventions of science.

· We use soaps; these are also given by science.

· We use LPG gas and stove etc., for cooking; these are all given by science.

· Even the house in which we live is a product of science.

· The iron which we use to iron our clothes is an invention of science even the clothes we wear are given by science.

Observing the magic and importance of science, we can say that it has a vast use in all fields of human life. It is of great importance to make our life easier. It gives an answer to all curiosities related to life. It gives wings to our imagination by its facts and theories.

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__2.2
Objectives of teaching Mathematics & Science __

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**Objectives
of teaching Mathematics**

Aims are the general targets we wish to achieve through teaching the subject. Objectives are the ways of achieving the aim by bringing desired changes in the behavior of the person. Aims of teaching may be broken down into smaller achievable objectives. These objectives act as steps in reaching the aim.

The aims of teaching and learning mathematics are to encourage and enable students to:

- recognize that mathematics permeates the world around us
- appreciate the usefulness, power and beauty of mathematics
- enjoy mathematics and develop patience and persistence when solving problems
- understand and be able to use the language, symbols and notation of mathematics
- develop mathematical curiosity and use inductive and deductive reasoning when solving problems
- become confident in using mathematics to analyse and solve problems both in school and in real-life situations
- develop the knowledge, skills and attitudes necessary to pursue further studies in mathematics
- develop abstract, logical and critical thinking and the ability to reflect critically upon their work and the work of others
- develop a critical appreciation of the use of information and communication technology in mathematics
- appreciate the international dimension of mathematics and its multicultural and historical perspectives.

**Objectives**

Knowledge and understanding are fundamental to studying mathematics and form the base from which to explore concepts and develop problem-solving skills. Through knowledge and understanding students develop mathematical reasoning to make deductions and solve problems.

At the end of the course, students should be able to:

- know and demonstrate understanding of the concepts from the five branches of mathematics (number, algebra, geometry and trigonometry, statistics and probability, and discrete mathematics)
- use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations including those in real-life contexts
- select and apply general rules correctly to solve problems including those in real-life contexts.

Investigating patterns allows students to experience the excitement and satisfaction of mathematical discovery. Mathematical inquiry encourages students to become risk-takers, inquirers and critical thinkers. The ability to inquire is invaluable in the MYP and contributes to lifelong learning.

Through the use of mathematical investigations, students are given the opportunity to apply mathematical knowledge and problem-solving techniques to investigate a problem, generate and/or analyse information, find relationships and patterns, describe these mathematically as general rules, and justify or prove them.

At the end of the course, when investigating problems, in both theoretical and real-life contexts, student should be able to:

- select and apply appropriate inquiry and mathematical problem-solving techniques
- recognize patterns
- describe patterns as relationships or general rules
- draw conclusions consistent with findings
- justify or prove mathematical relationships and general rules.

Mathematics provides a powerful and universal language. Students are expected to use mathematical language appropriately when communicating mathematical ideas, reasoning and findings—both orally and in writing.

At the end of the course, students should be able to communicate mathematical ideas, reasoning and findings by being able to:

- use appropriate mathematical language (notation, symbols, terminology) in both oral and written explanations
- use different forms of mathematical representation (formulae, diagrams, tables, charts, graphs and models)
- move between different forms of representation.

Students are encouraged to choose and use ICT tools as appropriate and, where available, to enhance communication of their mathematical ideas. ICT tools can include graphic display calculators, screenshots, graphing, spreadsheets, databases, and drawing and word-processing software.

MYP mathematics encourages students to reflect upon their findings and problem-solving processes. Students are encouraged to share their thinking with teachers and peers and to examine different problem-solving strategies. Critical reflection in mathematics helps students gain insight into their strengths and weaknesses as learners and to appreciate the value of errors as powerful motivators to enhance learning and understanding.

At the end of the course students should be able to:

- explain whether their results make sense in the context of the problem
- explain the importance of their findings
- justify the degree of accuracy of their results where appropriate
- suggest improvements to the method when necessary.

** **

**Objectives
of teaching Science**

The aims of the teaching and study of sciences are to encourage and enable students to:

· develop inquiring minds and curiosity about science and the natural world

· acquire knowledge, conceptual understanding and skills to solve problems and make informed decisions in scientific and other contexts

· develop skills of scientific inquiry to design and carry out scientific investigations and evaluate scientific evidence to draw conclusions

· communicate scientific ideas, arguments and practical experiences accurately in a variety of ways

· think analytically, critically and creatively to solve problems, judge arguments and make decisions in scientific and other contexts

· appreciate the benefits and limitations of science and its application in technological developments

· understand the international nature of science and the interdependence of science, technology and society, including the benefits, limitations and implications imposed by social, economic, political, environmental, cultural and ethical factors

· demonstrate attitudes and develop values of honesty and respect for themselves, others, and their shared environment.

** **

**Objectives**

The
objectives of sciences listed below are final objectives and they describe what
students should be able to do by the end of the course. These objectives have a
direct correspondence with the final assessment criteria, A–F (see “Sciences
assessment criteria”).

A One world

This objective refers to enabling students to understand the interdependence
between science and society. Students should be aware of the global dimension
of science, as a universal activity with consequences for our lives and subject
to social, economic, political, environmental, cultural and ethical factors.

At the end of the course, and within local and global contexts, students should be able to:

· describe and discuss ways in which science is applied and used to solve local and global problems

· describe and evaluate the benefits and limitations of science and scientific applications as well as their effect on life and society

· discuss how science and technology are interdependent and assist each other in the development of knowledge and technological applications

· discuss how science and its applications interact with social, economic, political, environmental, cultural and ethical factors.

B Communication in science

This objective refers to enabling students to develop their communication
skills in science. Students should be able to understand scientific
information, such as data, ideas, arguments and investigations, and communicate
it using appropriate scientific language in a variety of communication modes
and formats as appropriate.

At the end of the course, students should be able to:

· communicate scientific information using a range of scientific language

· communicate scientific information using appropriate modes of communication

· present scientific information in a variety of formats, acknowledging sources as appropriate

· demonstrate honesty when handling data and information, acknowledging sources as appropriate

· use where appropriate
a range of information and communication technology applications to access,
process and communicate scientific information.

C Knowledge and understanding of science

This objective refers to enabling students to understand the main ideas and
concepts of science and to apply them to solve problems in familiar and
unfamiliar situations. Students are expected to develop critical and reflective
thinking and judge the credibility of scientific information when this is
presented to them.

At the end of the course, students should be able to:

· recognize and recall scientific information

· explain and apply scientific information to solve problems in familiar and unfamiliar situations

· analyse scientific information by identifying components, relationships and patterns, both in experimental data and ideas

· discuss and evaluate scientific information from different sources (Internet, newspaper articles, television, scientific texts and publications) and assess its credibility.

D Scientific inquiry

This objective refers to enabling students to develop scientific inquiry skills
to design and carry out scientific investigations.

At the end of the course, students should be able to:

· define the problem or research question to be tested by a scientific investigation

· formulate a hypothesis and explain it using logical scientific reasoning

· design scientific investigations that include variables and controls, material/equipment needed, a method to be followed, data to be collected and suggestions for its analysis

· evaluate the method, commenting on its reliability and/or validity

· suggest improvements
to the method.

E Processing data

This objective refers to enabling students to record, organize and process
data. Students should be able to collect and transform data by numerical
calculations into diagrammatic form. Students should be able to analyse and
interpret data and explain appropriate conclusions.

At the end of the course, students should be able to:

· collect and record data using appropriate units of measurement

· organize and transform data into numerical and diagrammatic forms, including mathematical calculations and visual representation (tables, graphs and charts)

· present data in a variety of ways using appropriate communication modes and conventions (units of measurement)

· analyse and interpret data by identifying trends, patterns and relationships

· draw conclusions
supported by scientific explanations and a reasoned interpretation of the
analysis of the data.

F Attitudes in science

This objective goes beyond science and refers to encouraging attitudes and
dispositions that will contribute to students’ development as caring and
responsible individuals and members of society.

This objective is set in the context of the science class but will pervade
other subjects and life outside school. It includes notions of safety and
responsibility when working in science as well as respect for and collaboration
with others and their shared environment.

During the course, students should:

· carry out scientific investigations using materials and techniques safely and skillfully

· work effectively as members of a team, collaborating, acknowledging and supporting others as well as ensuring a safe working environment

· show respect for themselves and others, and deal responsibly with the living and non-living environment.

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__2.3
Different approaches and techniques of teaching mathematics & Science__

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**Teaching
Mathematics**

__INDUCTIVE METHOD__

Inductive method is advocated by Pestalozzi and Francis Bacon. Inductive method is based on induction. Induction is the process of proving a universal truth or a theorem by showing that if it is true of any particular case, it is true of the next case in the same serial order and hence true for any such cases. Thus it is a method of arriving at a formula or a rule by observing a sufficient number of particular instances. If one rule applies to a particular case and is equally applicable to different similar cases, it is accepted as a general rule or formula. Therefore, inductive method proceeds from,

i) Particular cases to general rules or formulae.

ii) Concrete instance to abstract rules.

iii) Known to unknown.

iv) Simple to complex.

This method has been found to be very suitable for the teaching of mathematics because many mathematical formulae and generalizations are the results of induction.

For example: If we wish to frame the
formula (a-b)^{2} =a^{2} – 2ab + b^{2}. Let
the students actually multiply

(a-b) x (a-b) and find out the product.
They may then be asked to find the answers for (p-q)^{2}, (l-m)^{2} etc.
by actually multiplication. After this they be asked to observe results and be
helped to make generalization to get the required formula.

__Steps in Inductive Method__

1. Selection of a number of cases.

2. Observation of the case under given conditions.

3. Investigation and analysis.

4. Finding common relations.

5. Arriving at generalization.

6. Verification or application.

__Merits of Inductive method__

1. It helps in understanding.

2. It is logical method and develops critical thinking.

3. It encourages active participation of the students in learning.

4. It provides ample opportunities for exploration and observation.

5. It sustains the students’ interest as they proceed from known to unknown.

6. It curbs the tendency to rote learning as it clears the doubts of the students.

7. It facilitates meaningful learning.

8. It enhances self-confidence.

9. It is helpful for beginners as it provides a number of concrete examples.

10. It encourages experimentation, observation, analytical thinking and reasoning.

11. It facilitates fixation and retention of mathematical concepts, rules and formulae.

12. It helps in increasing the pupil-teacher contact.

13. It does not burden the mind. Formula becomes easy to remember.

14. It discourages cramming and also reduces home work.

__Demerits of Inductive method__

1. This method is limited in range and is not suitable for all topics. Certain complex and complicated formula cannot be generalized in this manner.

2. It is lengthy, time consuming and laborious method.

3. Inductive reasoning is not absolutely conclusive because the generalization made with the help of a few specific examples may not holds good in all cases.

4. We don’t complete the study of a topic simply by discovering a formula but a lot of supplementary work and practice is required for fixing the topic in learner’s mind.

5. This method is not suitable for higher classes because higher order mathematical principles cannot be generalized through the observation of concrete cases.

6. It is not suitable for mathematically gifted students as unnecessary details and too many examples make the teaching dull and boring.

__Applicability of Inductive method__

Inductive method is most suitable where

· Rules are to be formulated.

· Definitions are to be formulated.

· Formulae are to be derived.

· Generalizations or laws are to be arrived at.

__DEDUCTIVE METHOD__

Deductive method is based on deductive reasoning. Deductive reasoning is the process of drawing logical inferences from established facts or fundamental assumptions. Contrary to inductive method, in deductive method we begin with the formula, or rule or generalization and apply it to a particular case. In this method, the teacher presents the known facts or generalization and draws inferences regarding the unknown, following a network of reasoning. Therefore, deductive method proceeds from:

i) General rule to specific instances.

ii) Unknown rule to known case.

iii) Abstract rule to concrete instance.

iv) Complex rule to simple example.

__Steps in Deductive method__

Deductive method of teaching follows the steps given below for effective teaching.

1. ** Clear
recognition of the problem**: A clear recognition of the problem
statement provides the basic link for the thinking process and the solution to
the problem.

2. ** Search
for a tentative hypothesis**: The second step in deductive method is the
search for tentative hypothesis, a tentative solution to the problem.

3. ** Formulation
of tentative hypothesis**: The search for the solution leads to the
formulation of a tentative hypothesis that appears to have promise as a
possible or probable solution to the problem. The tentative hypothesis has its
basis on certain axioms or postulates, or propositions or rules and formulae
that have been accepted to be true.

4. ** Verification**:
Finally the hypothesis that has been formulated is to be verified as the right
solution to the problem at hand.

__ANALYTIC METHOD__

The word ‘analytic’ is derived from the word ‘analysis’ which means ‘breaking up’ or resolving a thing into its constituent elements. This method is based on analysis and therefore in this method we break up the problem in hand into its constituent parts so that it ultimately gets connected with something obvious, or already known. In this process we start with what is to be found out (unknown) and then think of further steps and possibilities which may connect with the known and find out the desired result. Hence in this method we proceed from unknown to known, from abstract to concrete and from complex to simple. This method is particularly useful for solving problems in arithmetic, algebra, geometry and trigonometry.

__Merits of Analytic Method__

1. It leaves no doubts in the minds of the students as every step is justified.

2. It is a psychological method.

3. It facilitates clear understanding of the subject matter as every step is derived by the student himself.

4. It helps in developing the spirit of enquiry and discovery among the students.

5. No cramming is necessitated in this method as each step has its reason and justification.

6. Students take active role in the learning process resulting in longer retention and easier recall of what they learn.

7. It develops self-confidence in the students as they tackle the problems confidently and intelligently.

8. It develops thinking and reasoning power among the students.

__Demerits of Analytic Method__

1. It is a lengthy, time consuming method and therefore not economical.

2. With this method it is difficult to acquire efficiency and speed.

3. This method may not be suitable for all topics of mathematics.

4. In this method information is not presented in a well-organized manner.

5. This method may not be very effective for below average students who would find it difficult to follow the analytical reasoning.

__Applicability of Analytic Method__

Analytic Method, though it has got certain limitations, is very effective for teaching how to solve complex mathematical problems, in proving theorems and riders and teaching many topics from algebra. This method is particularly useful for solving problems in arithmetic, algebra, geometry and trigonometry.

__SYNTHETIC METHOD__

‘Synthetic’ is derived from the word ‘Synthesis’. Synthesis is the complement of analysis. To synthesise is to combine the constituent elements to produce something new. In this method we start with something already known and connect it with the unknown part of the statement. Therefore, in this method one proceed from known to unknown. It is the process of combining known bits of information to reach the point where unknown information becomes obvious and true. In synthetic method the reasoning is as follows “Since A is true, B is true”.

The usual forms of statements of proofs found in textbook are examples of synthetic method. Beginning with known definitions, assumptions and axioms, the sequence of steps are deducted and conclusions (unknown) are arrived at.

Synthetic method is best suited for the final presentation of proofs of theorems and solutions to problems in a logical and systematic manner. However, it is advisable to adopt synthetic method following analytic method.

__Merits of Synthetic Method__

1. This method is logical as in this method one proceeds from the known to unknown.

2. It is short and elegant.

3. It facilitates speed and efficiency.

4. It is more effective for slow learners.

__Demerits of Synthetic method__

1. It leaves many doubts in the minds of the learner and offers no explanations for them.

2. As it does not justify all the steps, recall of all the steps may not be possible.

3. There is no scope for discovery and enquiry in this method.

4. It makes the students passive listeners and encourage rote memorization.

5. If the students forget the sequence of steps, it could be very difficult to reconstruct the proof/Solutions.

__Application of Synthetic method__

Synthetic method is best suited for the final presentation of proofs of theorems and solutions to problems in a logical and systematic manner. Many teachers prefer this method for teaching mathematics. However it is advisable to adopt synthetic method following analytical method.

__GUIDED DISCOVERY APPROACH__

Guided discovery has emerged as a valuable strategy of teaching mathematics. In teaching, the teacher exercises some guidance over the learner’s behaviour. If this guidance is limited, them guided discovery can take place. In this strategy of teaching, the pupils is encouraged to think for himself and to discover general principles from situations, which may be contrived by the teacher if necessary.

True discovery teaching is a process, which focuses on the learner. The pupils have a tendency to jump conclusions quickly to generalize on a very limited data, moreover how many students are sufficiently brilliant to discover everything they are to know in mathematics.

Bruner says discovery is a process, a way of approaching problems rather than the product of the knowledge. It is his contentions that process of discovery can become generalized abilities though exercise of solving problems and the practice.

Basically it is a process that presents mathematics in a way that makes some sense to the learner. It is an instructional process in which the learner is placed in a situation where he is free to explore, manipulate materials, investigate and concluded. The teacher assumes the role as a guide. He helps the learner to draw upon ideas, concepts and skills that have already been learnt in order to conclude new knowledge asking appropriate questions will do a great deal to encourage the situation.

__CONCEPT ATTAINMENT MODEL__

__Concept Attainment__

Concept attainment is an indirect instructional strategy that uses a structured inquiry process. It is based on the work of Jerome Bruner. In concept attainment, students figure out the attributes of a group or category that has already been formed by the teacher. To do so, students compare and contrast examples that contain the attribute. They then separate them into two groups. Concept attainment, then, is the search for and identification of attributes that can be used to distinguish examples of a given group or category from non-examples.

__Purpose of Concept attainment model__

Concept attainment is designed to clarify ideas and to introduce aspects of content. It engages students into formulating a concept through the use of illustrations, word cards or specimens called examples. Students who catch onto the idea before others are able to resolve the concept and then are invited to suggest their own examples, while other students are still trying to form the concept. For their reason, concept attainment is well suited to classroom use because all thinking abilities can be changed throughout the activity. With carefully chosen examples, it is possible to use concept attainment to teach almost any concept in all subjects.

** **

**Teaching
Science**

All science teaching methods come down to either teacher-centred or student-centred instruction. Both types of instruction have their place, however in practice have very different dynamics in the classroom.

In this approach, it is the teacher that is the focus. Students either passively take notes or ask questions through the teacher’s presentation. Handy for large groups of students or for when you need to get through a large body of information. The key to this lesson style is to keep it lively by inserting graphics, video snippets, animations, science demonstrations, audio grabs or guest appearances via video conference. To help increase the engagement during a lecture, try incorporating student polling using Poll Everywhere, Plickers, Quizizz or Kahoot. The advantage of getting active student feedback is that this formative assessment can help shape your lecture and future lessons to fit the student’s needs.

Break out the experiment materials! Whether the students work in small groups or by themselves, the lesson has a clear question that students need to find an answer to with the teacher acting as a facilitator. There are a few variations here;

- Students follow an experimental procedure with a clear set of instructions and scaffold for their scientific report.
- Students explore the materials themselves to design and test their own fair experiment, keeping variable testing in mind. This version is better for students who already have a clear understanding of the scientific method and are now ready for independent thinking
- Station-based rotations. Here the students rotate around the classroom to explore a variety of hands-on materials that all cover an aspect of your lesson topic. The trick here is to ensure that there is enough time for the students to complete each activity and that there are no bottlenecks in terms of access to resources or one particular activity taking too long to complete. A fun way to link all the stations together to pull together a scenario such as a forensics investigation; some students will enjoy the role-play!

This teaching method draws on the hands-on nature of the activities above and extends this to involve students in a deep dive into a given topic. Time is the key here, as students will be engaged over an extended period of time in researching their topic, designing their experiment or model, writing a scientific report or creating a poster and presenting their findings in a short talk. When planning this in your scope and sequence, consider access to resources both within and beyond your school and how the students might be able to involve the community in their research or as an audience for the final presentation at a school science fair.

Peer-led team learning (PLTL) is about empowering the students to teach the other students. Often employed in undergraduate studies, this approach also works in schools where it is most effective when connecting older students with younger students. Alternatively, PLTL can also be used when pairing students with a high subject aptitude with students needing help. Guidance is important here as you need to ensure that what is being covered is correct and safely performed. With supervision, this approach can be effective for students to learn leadership skills and can create a positive atmosphere around scholarship.

Flipped learning has gained a lot of popularity in recent years. The idea is that the instructional content is given to the students outside of normal school time, with the intention that students can then come to school with deeper questions for teacher clarification. you can present this content via a series of videos, articles and books to read, podcasts to listen to, investigating a problem and so on. There is much debate on how to best implement this in the classroom; in essence, you need to consider how your students will respond to flipped learning and how you can motivate them to trial it.

Differentiation is all about ensuring that students of all levels can be involved in your lesson. You may want to create worksheets with different tasks or levels of difficulty, perhaps have a variety of activities for students to choose from or creating a variety of job roles for students when running PBL. Of course, with differentiation comes a time requirement to prepare the lesson, however it can help with students being more on task as they can choose tasks that they can achieve. You can differentiate tasks as both extension activities as well as design activities for students who need more support.

Whether you know it or not, science is a huge part of our daily lives, from technology to transportation to medicine to legal issues and government decisions. And the pace of research and discovery is quickly accelerating. That makes it more important than ever to understand science, for in doing so, students can better understand the world.

Teaching science requires critical thinking, effective communication, collaboration and creativity. Real-life scenarios, peer-to-peer teaching, hands-on activities, science projects and field research journals are effective teaching techniques in the science curricula. Instruction in science often can foster greater interpersonal skills and independent thought.

__2.4
Number concept: Teaching of basic concepts like quantity, shape, size, money
and measurement__

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As a teacher of mathematics, remember these fundamental beliefs as you develop early number concepts in your students.

1. Thinking about the problem, not just the answer, is what is most important.

2. The teacher should be the facilitator, not the one with all the answers.

3. Process is more important than product. Mathematics is not just “facts” to be memorized. The concepts children learn are of utmost importance; and then the memorization will come. Children must experience through play and using manipulatives and “reinvent” the concepts of mathematics in their own minds.

To help children develop early early number concepts, use activities that focus on verbal counting, one-to-one correspondence, cardinality, and subitizing.

**Verbal counting** is critical in developing quantitative
thinking in young children. A focus on counting in context is one way to build
a child’s mathematical abilities, therefore it is critical to count with
children every day. Some activities include:

· Practice counting words and written numerals with pictures or representations of objects.

· Count aloud as a class.

· Use a number chart so children can see what number symbols look like visually.

**One-to-one correspondence** is
a developmental skill for young children that we take for granted. When a child
touches each toy and says the number name out loud, “one, two, three…,” he/she
demonstrates the ability to count with one-to-one correspondence. To develop
this skill in young children, you can point to objects as you say the number
word, or move each object as you say the number word out loud.

To be successful in mathematics, students must understand **cardinality** by
counting various objects and hold that number “in their head.” A child who
understands the cardinality concept will count a set once and not need to count
it again.

To develop this skill, students need constant repetition of counting and teaching through modeling. Children learn how to count (matching counting words with objects) before they understand that the last word stated in a count indicates the amount of the set. Counting should be reinforced throughout the day, not just during “math time.”

Next in the progression of counting is **subitizing**, the
ability to quickly identify the number of items in a group without counting the
items. Developing the ability to subitize is critical to the success of early
number concepts. Subitizing allows children to see groupings, and these
groupings are foundational to addition, subtraction, multiplication and
division.

Number sense is defined as a “good intuition about numbers and their relations. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms” (Howden, 1989). When students consider the context of a problem, look at the numbers in a problem, and make a decision about which strategy would be most efficient in each particular problem, they have number sense. Number sense is the ability to think flexibly between a variety of strategies in context.

Building on subitizing, composing and
decomposing numbers, using ten-frames, and the hundreds chart will help develop
number sense in your students. When students have number sense, they gain **computational
fluency**, are **flexible** in their thinking, and are able to
choose the most efficient strategy to solve a problem.

Number sense is a foundational idea in mathematics; it encourages students to think flexibly and promotes confidence with numbers. According to Marilyn Burns (2007), “students come to understand that numbers are meaningful and outcomes are sensible and expected.” And “just as our understanding of phonemic awareness has revolutionized the teaching of beginning reading, the influence of number sense on early math development and more complex mathematical thinking carries implications for instruction” (Gersten & Chard, 1999).

Number sense is a skill that allows students to work with numbers fluently and efficiently. This includes understanding skills such as quantities, concepts of more and less, symbols represent quantities (8 means the same thing as eight), and making number comparisons (12 is greater than 9, and three is half of six). Students must

1. Understand numbers, ways of representing numbers, relationships among numbers, and the number system,

2. Understand the meanings of operations and how they related to one another, and

3. Compute fluently and make reasonable estimates (NCTM, 2000).

Teachers must give students many opportunities to develop number sense through activities with physical objects, such as counters, blocks, or small toys. Most children need that concrete experience of physically manipulating groups of objects. After these essential experiences, a teacher can move to more abstract materials such as dot cards.

Here are 8 easy to do activities to promote shape and measure

1. Shape hunt in the environment – Children are natural investigators and love to hunt for things. Practitioners can support this interest alongside promoting shape recognition. Using some large cut out 2D shapes explain to the children that you are looking for things in the environment that are shaped as a square, circle, triangle etc. Allow the children to try out different items against the cut out shapes to compare.

2. Potato shape printing – This creative activity is a great way to get children talking about shapes. Raw potatoes can be cut in half and used for printing. Simple shapes such as squares and triangles can be cut into the potato and used to make marks with the paint. The children will enjoy looking at and talking about the marks that they are making.

3. Car races – This is a great activity to promote measuring. Simply place a long cardboard tube at an angle to provide a slope and measure out a long strip of paper to add to the bottom. Encourage the children to take turns releasing small world cars at the top of the slope and watch them roll down the tube and out onto the paper. Practitioners can add numbers to the paper for children to measure how far their car rolled.

4. Measuring bodies – Bodies are a fun and easy way to practise measuring. This activity can be carried out inside using large sheets of paper and pens or outside using the ground and chalks. Children can take it in turns to lie on the ground and draw around each other. They can then use rulers or tapes to measure the different parts of their body such as their arms, legs, feet etc. The children can then compare their measurements with their friends or the practitioners.

5. Size sorting – This activity can be adapted to use a variety of resources, for example shells, buttons or bears. Give the children a group of different sized objects and three sorting bowls. Ask them to sort the objects into small, medium and large using the bowls. The children will need to compare and contrast the items against one another in order to sort them into the correct bowl.

6. Masking tape shapes – Masking tape can be used to mark out large shapes on the floor. The children can then use construction items such as lego or wooden bricks to cover the tape and build along the lines. This will enable the children to develop shape recognition and support measuring skills.

**Money**

Before students can count money, they have to be able to correctly identify the most common denominations: pennies, nickels, dimes, and quarters. For low-function students, this may be a long but worthwhile process. Do not use fake plastic coins for low-functioning students with intellectual or developmental disabilities. They need to generalize coin use to the real world, and the plastic coins do not feel, smell, or even look like the real thing. Depending on the student's level, approaches include:

- Discrete trial training: Present only two coins at a time. Ask and reinforce correct responses, i.e. "Give me a penny," "Give me a nickel," "Give me a penny," etc.
- Use errorless teaching: Point to the correct coin if the student picks up the wrong coin or seems to waffle. Collect data and don't introduce a new coin until the child is at least 80 percent accuracy.
- Coin sorting: After the child has succeeded with discrete trial training, or if the child quickly seems to be distinguishing the coins, you can give them practice by sorting coins. Place a cup for each denomination, and place the mixed coins on the table in front of the child. If the child recognizes numbers, put the coin value on the outside of the cup, or place one of the coins in the cup.
- Matching coins: A variation of sorting coins is to match them to the values on a cardstock mat. You could add a picture if it helps.

The following math activities for 2nd grade and 1st grade will make counting money easier for students.

1. Focus on Skip Counting (before counting money)

2. Teach Stop and Start Counting

3. Introduce Counting Money with Coins Slowly

4. Provide Visual Reminders

5. Practice with Money Games

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__2.5 Number
system & basic Mathematics calculations, addition, subtraction, place
value, multiplication, divisions and fractions__

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Number System is a method of representing Numbers on the Number Line with the help of a set of Symbols and rules. These symbols range from 0-9 and are termed as digits. Number System is used to perform mathematical computations ranging from great scientific calculations to calculations like counting the number of Toys for a Kid or Number chocolates remaining in the box. Number Systems comprise of multiple types based on the base value for its digits.

- A number system is a way to represent number.
- Base ten or the decimal system is one common number system.
- Other number systems are Binary (base 2), Hexadecimal (base 16), and Octal (base 8).
- Early elementary grades study numbers and operations in base ten usually in whole numbers and some.
- By the time a student reaches 3rd grade fractions are included in the study of numbers.
- Once in middle school students work with the Number System includes the study of positive and negative number, and rational number and irrational numbers.
- In high school students learning is extended from rational and irrational numbers to imaginary numbers to form complex numbers.
- As students advance through the grades they apply and extend their understanding of the number system.
- Studying the number system enables the student to do mathematics; calculate, solve equations and represent measurements.

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**Addition,
subtraction, division and multiplication**

To perform any calculation in mathematics, it is essential to understand four operations, namely addition, subtraction, division and multiplication. Knowing these operations is essential for handling money:

**Addition:** It involves adding two or more numbers together. For
instance, if you and your friends purchase an ice cream costing ₹50 each,
the total amount you pay to the ice cream parlour is ₹50 + ₹50 +
₹50 = ₹150.

**Subtraction:** It involves subtracting two numbers from each other.
For instance, if your colleague owes you ₹200 and they pay you back
₹125, the money your colleagues owe is ₹200 – ₹125 =
₹75.

**Multiplication:** It involves multiplying two or more numbers together.
For instance, if you and your colleagues want to purchase a pizza and each has
₹100 in their pocket, the price of a pizza you all can afford is
₹100 x 3 = ₹300.

**Division:** It is the inverse of multiplication. For instance, if
you and two of your colleagues eat a burger costing ₹450, each person's
share would be 450/3 = ₹150.

**Fractions
and decimals**

A fraction is a portion of a whole number, and it has two equal parts, namely a numerator and denominator. The numerator is the total number of parts you count, and the denominator is the total number of equal parts that comprise the whole number. A decimal is a numerical representation of a fraction and comprises two parts, namely a whole number part and a fraction part, separated by a decimal point. For instance, 2/9 is a fraction where 2 is the numerator and 9 is the denominator. 4.5 is a decimal where 4 is the whole number and 5 is the fraction part.

BODMAS is a very important rule of mathematics. It is used in the simplification of mathematical expressions and equations involving basic operations of mathematics. BODMAS stands for the bracket, Of, Division, Multiplication, Addition, and Subtraction. It explains the sequence and order of operations to solve the expression.

According to it, if an expression contains brackets ((), {}, []) we have to first solve these brackets followed by “of” i.e. powers, then division, multiplication, addition and subtraction from left to right. The order of brackets for the simplification (), {}, [].

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__2.6
Teaching environment, health, nutrition, living and non-living__

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Students tend to think of organisms as being only animals that interact with the physical environment and plants, without appreciating the complex interdependence between members of and across species.

Their ideas of ecosystems are usually only associated with natural and wilderness areas rather than their own environments. This concept of an ecosystem also influences their ideas about how humans interact with ecosystems, which is often in terms of the destruction or collapse of natural and wilderness ecosystems rather than those systems that are part of their more immediate environments.

Classifying everything around us as living and non-living is one
of the first concepts we teach in early elementary science because it is so
fundamentally important. Many skills are used as students inquire about
characteristics of **living
and non-living things**. Such as classification, naming
attributes, etc.

Nutrition education has a broad vision which encompasses educational strategies and environmental supports to encourage adoption of healthier, sustainable food choices and eating patterns. It goes beyond information-giving to foster critical thinking, attitudinal change and practical skills, as well as integrated actions to facilitate and enable health-conducive food behaviors and environments.

It’s great to see that so many educators are interested in teaching about food and nutrition! The following tips and resources support educators with using a student-centered approach to promote long-term, positive eating attitudes and behaviors.

**Build food skills and curiosity about food.**Describe food using the senses. Explore where food comes from, how it gets to our plates, and the different ways it can be prepared and eaten.**Apply a trauma-informed approach.**Offer neutral exposure to food, without pressure. Pressure includes persuading or rewarding student to choose or avoid certain foods “to be healthy”. Students have diverse experiences and home contexts that will impact their food access, preferences, culture, supports, and nutritional needs.**Talk about all food neutrally.**Avoid labeling foods as “good or bad”, “healthy or unhealthy” or “sometimes or everyday” foods. These labels do not help students accept foods and can lead to feelings of guilt or shame.**Hold off on teaching about nutrition until middle or high school.**Abstract concepts such as nutrients (carbohydrates, protein, fat, vitamins, etc.) are difficult for young learners to understand or apply.**Talk about food as more than fuel or nutrients.**Explore how food provides pleasure and connects to the self, family, history, culture, nature, community and food systems.**Use the concept of “variety” to teach about food in an inclusive way.**There are many different ways to eat that can give us what we need to grow, learn and play.**Aim to be a positive role model.**Show students that you enjoy a variety of foods. Consider how your school can create a supportive food and eating environment.**Avoid calorie counting activities, food tracking assignments, or talking about weight loss diets.**These activities can be unsafe for students and do not support positive eating attitudes and behaviors.**Support listening and trusting our bodies to eat what we need.**Canada’s food guide no longer recommends numbers of serving of food groups. It promotes mindful eating and enjoying a variety of food.**Promote critical inquiry.**Support students to spot diet fads, find reliable sources of nutrition information, critically think about food marketing, and make connections between food and social justice issues.

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