The document discusses using simulations in mathematics education. It begins by defining instructional simulations and how they can bridge the gap between classroom and real-world learning. It then provides examples of simulations used in different disciplines like economics and various types of simulations from simple to complex. The document emphasizes that simulations can engage students in deep learning and understanding over simple memorization. It also provides guidance on how to effectively teach with simulations, including instructor preparation, active student participation, and post-simulation discussion.

1. Baselios Marthoma Mathews ii training college,
Kottarakara
ASSIGNMENT IN MATHEMATICS
1
2013-2014

2. 2
ASSIGNMENT
Simulation in mathematics

3. Submitted by Submitted to
Renjith S. Mrs. Prinsamma K. George
13350007 Lect. In Mathematics Education
Mathematics B. M. M II Training College, Kottarakara
3
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

4. 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
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.
4

5. 5
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:

6.  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.
 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 classroom
6

7. 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 one concept to reach the finding, Simulation can prove
effective in teaching and learning Mathematics at any levels of learning.
7

8. 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?
Tell me, I forget. Show me, I remember. Involve me, I understand. _
Chinese Proverb
This explains why simulations are important in teaching learning process.
8
Deep Learning

9. 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:
9
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.
 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

10. 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.
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/
10
http://mathforum.org/escotpow/
http://www.horton.com/portfolio/MathSim/MathSim.html
http://www.mathapprentice.com/
How to Teach with Simulations

11. 11
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.
 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

12. Students learn through instructional simulations when they are actively engaged.
 Students should predict and explain the outcome they expect the simulation to
12
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.
 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

13. 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).
 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.
13

14. 14
Reference
http://en.wikipedia.org/wiki/Simulation
http://net.educause.edu/ir/library/pdf/erb1003.pdf
http://www.creativeteachingsite.com/edusims.html
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