An assignment on Concept Mapping, Simulation and Gradation.

Assignment prepared by

Shefsyn K.Y.

Reg. No: 13 386 006

B. Ed (Mathematics)

STTC

Concept Mapping

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Introduction to Concept Mapping

Used as learning and teaching technique, concept mapping visually

illustrates the relationships between concepts and ideas. Often represented in

circles or boxes, concepts are linked by words and phrases that explain the

connection between the ideas, helping students organize the structure their

thoughts to further understand information and discover new relationships. Most

concept maps represent a hierarchical structure, with the overall, broad concept

first with connected sub-topics, more specific concepts, following.

Concept maps are a way to develop logical thinking and study skills, by

revealing connections and helping students see how individual ideas forms a

larger whole.

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Concept maps are flexible. They can be made simple or detailed, linear,

branched, radiating or cross-linked.

Linear concept maps are like flow charts that show how one

concept or event leads to another.

Hierarchical concept maps represent information in a descending

order of importance. The key concept is on top, and subordinate concepts

fall below.

Spider concept maps have a central or unifying theme in the center

of the map. Outwardly radiating sub-themes surround the main theme.

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Spider concept maps are useful for brainstorming or at other times when

relationships between the themes need to be open ended.

Cross-linked maps use a descriptive word or phrase and identify

the relationship with a labeled arrow.

Definition of a Concept Map

A Concept Map is a type of graphic organizer used to help students

organizer used to help students organize and represent knowledge of a subject.

Concepts maps begin with a main idea (or concept) and then branch out to show

how that main idea can be broken down into specific topics.

Benefits of Concept Mapping

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Concept Mapping sires several purposes for learners.

Helping students brainstorm and generate new ideas.

Encouraging students to discover new concepts and the propositions that

connect them.

Allowing students to more clearly communicate ideas, thoughts and

information.

Helping students integrate new concepts with older concepts.

Enabling students to gain enhanced knowledge of any topic and evaluate

the information.

How to build a Concept Map

Concept maps are typically hierarchical, with the subordinate counts

stemming from the main concept or idea. This type of graphic organizer

however, always allows change and new concepts to be added. The

Rubber sheer analogy stated that concept positions on a map can

continuously change, while always maintaining the same relationship with

the other ideas on the map.

Start with a main idea, or issue to focus on.

A helpful way to determine the context of your concept map is to choose a

focus question something that needs to be solved or a conclusion that

needs to be reached. Once a topic or question is decided on, that will help

with the hierarchical structure of the concept map.

Then determine the key concepts.

Find the key concepts that connect and relate to your main idea and rank

them most general inclusive concepts come first then link to smaller more

specific concepts.

Finish by connecting concepts creating linking phrases and words.

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Once the basic links between the concepts are created, add cross – links,

which connect concepts in different areas of the map, to further illustrate

the relationships and strengthen students understanding and knowledge on

the topic.

Concept Maps in Education

When created correctly and thoroughly, concepts mapping is a powerful

way for students to reach high levels of cognitive performance. A concept map is

also not just a learning tool, but an ideal evaluation tool for educators measuring

the growth of and assessing student learning. As students create concept maps,

they reiterate ideas using their own words and help identify incorrect ideas and

concepts, educators are able to see what students do not understand providing an

accurate objective way to evaluate areas in which students do not get grasps

concepts fully.

Inspiration software , Webspiration classroom and Kidspiration

classroom service all contain diagram views that makes it easy for students to

create concept maps, students are able to add new concepts and links as they see

fit. Inspiration, inspiration and respiration classroom also come with a variety of

concept map examples, templates and lesson plans to show how concept

mapping and the use of other graphic organizer can easily be integrated into the

curriculum to enhance learning comprehension and writing skills.

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SIMULATION

May topics in mathematics that have immediate utility value can be best

introduced using the technique of simulation that is enacting a real situation in

the class. Topics that have relation with commercial concern are an example.

The functioning of a co-operative society or bank can be cited as examples. First

the students may be taken to such institutions to observe the nature and

techniques of the various activities going on there. Notes may be taken. In order

to reinforce and to make the activity more familiar the working of such

institutions may be enacted in the class. The simulation should be carefully

arranged so as to make the insight as meaningful as possible.

For example, there is a school co-operative society. The working of the

society may be observed and the salient features of how it was organized and

what the activities taken up are noted. Then imagine that the learners are

planning to start a class co-operative society. The steps such as selling of shares

to pool the capital required election of various office bearers, nature of

transaction involved (together with the related mathematical skills) the style of

keeping records concerning the various aspects including the account book the

technique of preparing a balance sheet, calculation and dispersal of dividends to

the share holders etc may be simulated.

In the same way the activates in a Bank, which special reference to the

mathematical calculations involved (Such as deposits and withdrawals,

calculation of interests at various rates other money transaction giving loans etc.)

may be simulated in a realistic matter.

This will not only help in realizing the utility value of mathematics, but

also will give realistic insights into the related commercial mathematics. Further

the roles played in simulation will create interest among the learners.

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Definitions of Simulation

1. R. Wynn (1964): ‘Simulation is an accurate representation of

realistic situation.’

2. W.R. Fritz (1965): ‘Simulation may be considered as a

dynamic implementation of a model representing a physical or

a mathematical system.’

Simulation in Education

The International Dictionary of education defines the term as ‘teaching

technique used particularly in management education and training in which a

‘real life situation’ and values are simulated by ‘substitutes’ displaying similar

characteristics.’ It also means ‘Techniques in teacher education in which

students act out or role play teaching situations’ and values are simulated by

‘Substitutes’ displaying similar characteristics. It also means “Techniques in

teacher education in which students act out or role play teaching situations in an

attempt to make theory more practically oriented and realistic”

What is its purpose?

Simulations promote concept attainment through experiential practice.

Simulations are effective at helping students understand the nuances of a concept

or circumstance. Students are often more deeply involved in simulations than

other activities. Since they are living the activity the opportunity exists for

increased engagement.

Advantages

Enjoyable, motivating activity.

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Element of reality of compatible with principles of constructivism.

Enhances appreciation of the more subtle aspects of a concept / principle.

Promotes critical thinking.

Disadvantages

Preparation time Cost can be an issue Assessment is more complex than some traditional teaching methods.

How do I do it?

Ensure that students understand the procedures before beginning. It

improves efficacy if the students can enjoy uninterrupted

participation. Frustration can arise with too many uncertainties’.

This will be counterproductive.

Try to anticipate questions before they are asked. The pace of

some simulations is quick and the sense of reality is best

maintained with ready responses. Monitor student progress.

Know what you wish to accomplish. Many simulations can have

more than one instructional goal. Developing a rubric for

evaluation is a worthwhile step. If appropriate, students should be

made aware of the specific outcomes expected of them.

Gradations

For effective teaching, concepts should be introduced step by step. This is

called Gradation. For students, to discover mathematical principles by their own,

it must be presented in a gradation way. The teaching should be proceeding from

simple to complex. This teaching technique is good for gradation.

Psychologically this is very important principle. If complex concepts introduce

from the beginning, that teaching will be ineffective. That will affect student's

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confidence level and it makes concept attainment more difficult. Moreover they

can’t understand concepts on heuristic method by their own.

Let’s look at an example. Take the lesson addition. It can be arranged different

stages according to the difficulty level.

Stage 1: Primary addition facts – Sum that does not exceed 10 e.g:4+3=7

Stage 2: Primary additions fact – Sum that is greater than 10 e.g.: 7+5=12

Stage 3: Adding 3 or 4 numbers using primary addition facts e.g.:

5+4+5=14.

Stage 4: Adding secondary addition facts using primary addition facts.

E.g. – tens place value not changing. E.g. 5+2=7, likewise

15+2=17

Stage 5: Secondary addition facts – changing tens place value e.g. 7+5 =

12, likewise 17+5=22

Stage 6: Two two digit numbers addition – those with no remainders in

both positions. E.g. 22 + 33

Stage 7: Two two digit numbers addition. Where remainder comes only in

one position e.g. 45+37

Stage 8: Two two digit numbers – where zero will come as a result in ones

place value. E.g. 35+45

Stage 9: Two two digit numbers – where remainder comes also in tens

place value e.g. 75+48

Stage 10: Adding 3 or 4 one digit numbers e.g. 7+5+8+4

Stage 11: Including one digit & 2 digit numbers. E.g. 48+7+16+6

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Stage 12: Two three digit numbers.

Stage 13: Three two digit numbers etc.

By introducing stage wise addition facts mentioned above, that will

enable the addition principles which discover by the students their own and it

will makes the teaching effective. The main thing to be notices is that we should

proceed to the next stage only after the successful completion of each stage.

Maintaining the motivation by giving reinforcement through formative

evaluation. Understanding addition facts or any other mathematical facts is very

difficult for students without gradation. Moreover, because of the difficulty from

the vague concepts, students will feel afraid of mathematics.

In mathematics, all lessons we can teach like this. Gradation will make

the teaching meaningful. After the teaching is completed, each question should

give using gradation principles. That way start with simple problems then

difficult problems, this order has to be followed when giving problems.

Gradation is not including in subjects that also include in teaching

learning process. Like, concrete to abstract, simple to complex, empirical to

rational and known to unknown etc. These all gradation principles are using in

teaching learning process. A teacher should acquire a skill to start a class by

giving familiar facts and experiences for students. Piaget’s thoughts on cognitive

domain to make it firm through accommodation & assimilation in each steps,

and Gagne’s idea on chaining put more light into these gradation theory.

These all gradation principles are also known as maxims of teaching. The

maxims of teaching are very helpful in obtaining the active involvement and

participation of the learners in the teaching learning process. They make learning

effective, inspirational, interesting and meaningful. A good teacher should be

quite familiar with them.

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1. Proceed from the known to unknown.

The most natural and simple way of teaching a lesson is to proceed from

something that the students already know to those facts which they do not

know. What is already known to the students is of great use to the

students. This means that the teacher should arouse interest in a lesson by

putting questions on the subject matter already known to the pupils.

2. Proceed from simple to complex.

The simple task or topic must be taught first and the complex one can

follow later on. The word simple and complex are to be seen from the

point of view of the child and not that of an adult.

3. Proceed from easy to difficult.

We must graduate our lessons in order of case of understanding them.

Student's standard must be kept in view. This will help in sustaining the

interest of the students. There are many things which look easy to us but

are in fact difficult for children. The interest of the child has also to be

taken into account.

4. Proceed from concrete to the abstract.

A child’s imagination is greatly aided by a concrete material. “Things

first and words after” is the common saying. Rousseau said, “Things,

Things, Things, “Children in the beginning cannot think in abstractions.

Small children learn first from things which they can see and handle.

5. Proceed from particular to general.

Before giving Principles and rules, particular examples should be

presented. As a matter fact a study of particular facts should lead the

children themselves to frame general rules. The rules of arithmetic, of

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grammar, of physical geography and almost of all sciences are based on

the principles of proceeding from particular instances to general rules.

6. Proceed from indefinite to definite.

Ideas of children in the initial states are indefinite, incoherent and very

vague. These ideas are to be made definite, clear, precise and systematic.

7. Proceed from empirical to rational.

Observation and experiences are the basis of empirical knowledge.

Rational knowledge implies a bit of abstraction and argumentative

approach. The general feeling is that the child first of all experiences

knowledge in his day to day life and after that the feels the rations bases.

8. Proceed from whole to parts.

Whole is more meaningful to the child than the parts of the whole.

9. From near to far.

A child learns well in the surroundings in which he resides. So he should

be first acquainted with his immediate environment.

10. From analysis to synthesis.

Analysis means breaking a problem into convenient parts and synthesis

means grouping these separated parts into one complete whole. A

complex problem can be made simple and easy by dividing it into units.

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References

en. wikipedia. Org / wiki / concept – map

www.inspiration .com / visual – learning / concept – mapping

Users. edte. utwente. nl / lanzing / cm-home. htm

olc. Spsd.sk.ca/De/PD/inst/r/strats/simul/index

Dark. Soman. (2010). ‘

Ganitha shastrabhodhanam’. Kerala: The state institute, of languages.

Dr. K. Soman, Dr. K. Sivarajan. (2008). ‘Mathematics Educations’. Calicut:

Calicut Universtiy.

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