Baselios Marthoma Mathews ii training college, Kottarakara

ASSIGNMENT IN MATHEMATICS

2013-2014

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ASSIGNMENT

Simulation in mathematics

Submitted by Submitted to

Renjith S. Mrs. Prinsamma K. George

13350007 Lect. In Mathematics

Education

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Mathematics B. M. M II Training College,

Kottarakara

Introduction

Education is not just about being literate enough to read and write, it is about

developing your perceptive and observational skills and constructively using

them to deduce and infer. Education is about becoming aware and making a

positive contribution to our society and the world in which we live, education

is about passing on the morals, values, literature, heritage, traditions and the

vast scientific knowledge we gather in our time to the next generation.

Technology today has become so intermingled with the fabric of our daily life

that we cannot in our wildest dreams imagine a life without it. Scientific

wonders are a useful part of our everyday life, and so it was only natural that

this science and technology enter the portals of the education realm too.

Today, all modern schools have incorporated the use of Information and

Communication Technology products as a complementary aid to effectively

teaching the curriculum content and enhancing classroom practices all over

the globe.

Simulation

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An instructional simulation, also called an educational simulation, is

a simulation of some type of reality (system or environment) but which also

includes instructional elements that help a learner explore, navigate or obtain

more information about that system or environment that cannot generally be

acquired from mere experimentation.  Instructional simulations are typically

goal oriented and focus learners on specific facts, concepts, or applications of

the system or environment.  

In the traditional classroom setting, students tend to interpret the

knowledge and ideas in terms of that setting rather than in terms of the

environment where the knowledge and ideas are needed.  Hence, a divide

exists between how students engage with the course content and how they

will need to engage and use the legal doctrine in a real-world context.  This

divide often has a negative impact on learner motivation and on the learning

process itself.  In contrast, research has shown that real-world learning

experiences have a positive impact on learner motivation and learning.  The

integration of a simulation into a course is one teaching strategy that can

bridge this divide and serve to align classroom and real-world expectations.  

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Teaching with Simulations

When students use a model of behavior to gain a better understanding of

that behavior, they are doing a simulation. For example:

When students are assigned roles as buyers and sellers of some good

and asked to strike deals to exchange the good, they are learning about

market behavior by simulating a market. 

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When students take on the roles of party delegates to a political

convention and run the model convention, they are learning about the

election process by simulating a political convention. 

When students create an electric circuit with an online program, they

are learning about physics theory by simulating an actual physical set-

up. 

The Geometer’s Sketchpad is the world’s leading software for teaching

mathematics. Sketchpad gives students at all levels—from third grade

through college—a concrete, visual way to learn mathematics that

increases their engagement, understanding, and achievement. It make

math more meaningful and memorable using Sketchpad.

Why Teach with Simulations?

Instructional simulations have the potential to engage students in "deep

learning" that empowers understanding as opposed to "surface learning"

that requires only memorization. It helps in effective transaction of any

subject, especially Mathematics. At secondary school level the most

challenging subject need to be taught is Mathematics as it demands

multiple skills and intelligence from the learning. It is every Mathematics

teacher’s challenge that, how to keep the students engaged throughout the

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classroom interactions ensuring deep learning. Deep learning means that

students: Learn scientific methods including, the importance of model

building, the relationships among variables in a model or models, data

issues, probability and sampling theory, how to use a model to predict

outcomes. Learn to reflect on and extend knowledge by, actively

engaging in student-student or instructor-student conversations needed to

conduct a simulation, transferring knowledge to new problems and

situations, understanding and refining their own though processes. seeing

social processes and social interactions in action.

What are Instructional Simulations?

What Differentiates this Teaching Method?

The key element that differentiates instructional simulation from other

pedagogies is the formal specification of a conceptual structure with which

students interact to learn about relationships between concepts. As

Mathematics demands the ability of students to relate or connect more than

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one concept to reach the finding, Simulation can prove effective in teaching

and learning Mathematics at any levels of learning.

Different Disciplines have Different Simulations

Every discipline treats the conceptual structure of the simulation

differently. To economics and Mathematics, the conceptual structure is

typically mathematical. In other words, simulation involves the specification

of a mathematical model that is solved several times with different

parameters to reveal relationships and illustrate concepts. To sociologists,

the conceptual structure is typically sets of social interactions. To political

scientists, the conceptual structure is often institutional.

Simulations Vary in Style and Complexity

Simulations may use computer programs that require only a portion of a

single class period. More commonly, computer models require that students

complete several assignments taking significant time or indeed even a large

part of a course. Simulations range from attempts to duplicate complex

social processes, such as a legislature, to very simple social interactions,

such as making eye contact. These simulations may be conducted with

computers, pencil-and-paper, or physical models of some natural

phenomenon. Some work only with small classes. Some work with all class

sizes.

Why Teach with Simulations?

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Tell me, I forget. Show me, I remember. Involve me, I understand. _

Chinese Proverb

This explains why simulations are important in teaching learning process.

Deep Learning

Instructional simulations have the potential to engage students in "deep

learning" that empowers understanding as opposed to "surface learning"

that requires only memorization. Mathematics as a subject requires deep

learning as it includes multiple skills and more than one concept in a single

content. Deep learning means that students:

Learn scientific methods including

The importance of model building. Experiments and simulations are the way scientists do their work. Using instructional simulations gives students concrete formats of what it means to think like a scientist and do scientific work.

The relationships among variables in a model or models. Simulation allows students to change parameter values and see what happens. Students develop a feel for what variables are important and the significance of magnitude changes in parameters.

Data issues, probability and sampling theory. Simulations help students understand probability and sampling theory. Instructional simulations have proven their worth many times over in the statistics based fields. The ability to match simulation results with an analytically derived conclusion is especially valuable in beginning classes, where students often struggle with sampling theory.

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How to use a model to predict outcomes. Simulations help students understand that scientific knowledge rests on the foundation of testable hypotheses.

Learn to reflect on and extend knowledge by

Actively engaging in student-student or instructor-student conversations needed to conduct a simulation. Instructional simulations by their very nature cannot be passive learning. Students are active participants in selecting parameter values, anticipating outcomes, and formulating new questions to ask.

Transferring knowledge to new problems and situations. A well done simulation is constructed to include an extension to a new problem or new set of parameters that requires students to extend what they have learned in an earlier context.

Understanding and refining their own thought processes. A well done simulation includes a strong reflection summary that requires students to think about how and why they behaved as they did during the simulation.

Seeing social processes and social interactions in action. This is one of the most significant outcomes of simulation in social science disciplines such as sociology and political science.

Examples of Simulations in Mathematics.

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As technology has swept in to different areas of education, role of

technological aspects has great importance in Mathematics education too.

There are several examples for simple simulations that are possible in

Mathematics classrooms. This ranges from activities for Kindergarten till

Secondary Education. A few of it is embedded here for reference. Teachers

can create their own simulations in accordance to their classroom

environment, if equipped with simple technological knowhow.

http://www.nctm.org/eexamples/

http://mathforum.org/pcmi/hstp/resources/cerealbox/

http://mathforum.org/escotpow/

http://www.horton.com/portfolio/MathSim/MathSim.html

http://www.mathapprentice.com/

How to Teach with Simulations

Instructor Preparation is Crucial

Lesson preparation varies with the type and complexity of the simulation. However, most expert users argue that instructional simulation work best when:

Instructors have a clear written statement in the course syllabus about the goals of the simulation and an explanation of how the simulation is tied to the course goals.

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Instructors read ALL the supporting material for the simulation.

Instructors do a trial run of the simulation before assigning the simulation to students, when possible.

Instructors make sure that university laboratory facilities support the simulation when laboratory facilities are needed.

Instructors integrate instructional simulations with other pedagogies such as Cooperative Learning or Interactive Lecture Demonstration.

Active Student Participation Is important

Students learn through instructional simulations when they are actively engaged. 

Students should predict and explain the outcome they expect the simulation to generate.

Every effort should be made to make it difficult for students to become passive during the simulation. Students must submit timely input and not rely on classmates to play for them.

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Instructors should anticipate ways the simulation can go wrong and include this in their pre-simulation discussion with the class. 

Post –Simulation Discussion is Crucial

Post-simulation discussion with students leads to deeper learning. The instructor should: 

Provide sufficient time for students to reflect on and discuss what they learned from the simulation.

Integrate the course goals into the post-simulation discussion.

Ask students explicitly asked how the simulation helped them understand the course goals or how it may have made the goals more confusing.

Conclusion

Simulations are among the most often used pedagogies in the changing concept of classrooms.

Porter et. al. (2004) summarize what is known about the learning effectiveness of simulations in their study in economics principles courses as, simulation either makes no difference or a small amount of positive difference. There are suggestions in the various economics studies, however, that instructional simulations may be more effective for some students than the general results suggest.

There is some evidence that students who think in a scientific manner apply this thinking to a simulation and benefit, while other students do not. Shute, Glaser, and Raghavan (1990), Katz and Ochs (1993).

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There is some evidence that students in a class that used simulations learned a set of concepts in less time that students in a traditional, lecture based class. Shute & Glaser (1989). 

An instructor thinking about how to improve the critical thinking of his or her students should find instructional simulations a valuable tool. The findings also suggest that upper-division courses that structure the curriculum in terms of scientific inquiry are tailor made for instructional simulations.

As Mathematics is a complex subject with many concepts and step by step process to put together with, well organized computer packages of simulation in mathematics can break down the complexity of the subject and understandable to the learner at their own understanding level and pace.

Reference

http://en.wikipedia.org/wiki/Simulation

http://net.educause.edu/ir/library/pdf/erb1003.pdf

http://www.creativeteachingsite.com/edusims.html

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http://web.stanford.edu/class/symbsys205/commentaryonsimulationineducation.htm

http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/

http://news.stanford.edu/news/2010/february15/devlin-aaas-mathematics-021910.html

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