Concept of Real-World Problem

Introduction
In the Apollo 13 space mission, astronauts together with ground control had to overcome
several challenges to bring the team safely back to Earth. One of these challenges was
controlling carbon dioxide levels onboard the space craft: “For 2 days straight they had
worked on how to jury-rig the Odysseys canisters to the Aquarius’s life support system.
Now, using materials known to be available onboard the spacecraft—a sock, a plastic bag,
the cover of a flight manual, lots of duct tape, and so on—the crew assembled a strange
contraption and taped it into place. Carbon dioxide levels immediately began to fall into the
safe range”.
The success of Apollo 13’s recovery from failure is often cited as a glowing example of
human resourcefulness and inventiveness alongside more well-known inventions and
innovations over the course of human history. However, this sort of inventive capability is
not restricted to a few creative geniuses, but an ability present in all of us, and exemplified
in the following mundane example.
Consider a situation when your only suit is covered in lint and you do not own a lint
remover. You see a roll of duct tape, and being resourceful you reason that it might be a
good substitute. You then solve the problem of lint removal by peeling a full turn’s worth of
tape and re-attaching it backwards onto the roll to expose the sticky side all around the roll.
By rolling it over your suit, you can now pick up all the lint.
In both these examples, historic as well as everyday, we see evidence for our innate ability
to problem-solve in the real world. Solving real world problems in real time given
constraints posed by one’s environment are crucial for survival. At the core of this skill is our
mental capability to get out of “sticky situations” or impasses, i.e., difficulties that appear
unexpectedly as impassable roadblocks to solving the problem at hand. But what are the
cognitive processes that enable a problem solver to overcome such impasses and arrive at a
solution, or at least a set of promising next steps?
A central aspect of this type of real-world problem solving, is the role played by the solver’s
surrounding environment during the problem-solving process. Is it possible that interaction
with one’s environment can facilitate creative thinking? The answer to this question seems
somewhat obvious when one considers the most famous anecdotal account of creative
problem solving, namely that of Archimedes of Syracuse. During a bath, he found a novel
way to check if the King’s crown contained non-gold impurities.
The story has traditionally been associated with the so-called “Eureka moment,” the sudden
affective experience when a solution to a particularly thorny problem emerges. The bath
was not only a passive, relaxing environment for Archimedes, but also a specific source of
inspiration. Indeed, it was his noticing the displacement of water that gave him a specific
methodology for measuring the purity of the crown; by comparing how much water a solid
gold bar of the same weight would displace as compared with the crown. This sort of
continuous environmental interaction was present when the Apollo 13 engineers discovered
their life-saving solution, and when you solved the suit-lint-removal problem with duct tape.
There are open questions of what role the environment plays during real world problem-
solving (RWPS) and how the brain enables the assimilation of novel items during these
external interactions.
Real world problem
United nations has highlighted that informally, a global issue is any issue that adversely
affects the global community and environment, possibly in a catastrophic way, including
environmental issues, political crisis, social issues and economic crisis. Solutions to global
issues generally require cooperation among nations. Hite and Seitz emphasize that global
issues are qualitatively different from international affairs and that the former arise from
growing international interdependencies which makes the issues themselves
interdependent. It is speculated that our global interconnectedness, instead of making us
more resilient, makes us more vulnerable to global catastrophe.
UN has focused major real-world problems as;
 Climate change
 Artificial general intelligence
 Biotechnology risk
 Ecological collapse
 Molecular nanotechnology
 Nuclear holocaust
 Overpopulation
 Global pandemic
In addition to these real problems, other real problems are given below:

 Food insecurity
 Violence
 Homelessness
 Sustainability
 Education
 Sanitary, drinking water supply
 Sexuality, teen pregnancy,
 Mental health and suicide

Mathematic in real world problem solving

A mathematical problem is agreeable to being signified, analysed and possibly solved, with
the mathematics is known as real-world problem. Example; calculating the speeds of various
air planes in sky, calculating the orbits of the planets in the solar system, making the sizes of
various vehicle tyres, designing and testing the functions of mobile phone applications,
fashion design, study on suicide, home decoration, building management, study routine and
following time, time management, operating home kitchen, boot polishing method, ironing
cloth and more.
Real-world mathematical problems are inquiries related to actual setting, such as Madan
has 10 mangoes and gives 6 to Nikita. How many he has left? This question is usually more
difficult to solve than regular mathematical way like 10-6 = 4, even if one knows the
mathematics needed to solve the problem. Mathematical equation is needed to connect the
real-world situation to solve this problem.
We have to use mathematics for solving a real – world problem where, we have to develop
a mathematical model to this problem. This method needs seeking the detail of the problem
and the modeller have to be very careful not to lose essential aspects in formulating and
translating the original problem in mathematical form. Some problems are out of easy
mathematical real-world problem such as squaring the circle. In this situation, we use new
idea to solve the problem; is called language game. In language game the real-world
problems are solved with logical aspect.
A mathematical problem that is not related with the real-world problem is proposed or
attempted to solve by mathematician and it may be that interest of studying mathematics
for the mathematician himself (or herself) made much than newness or difference on the
mathematical work, if mathematics is a game.
What Is Real World Problem-Solving?
Archimedes was embodied in the real world when he found his solution. In fact, the real
world helped him solve the problem. Whether or not these sorts of historic accounts of
creative inspiration are accurate, they do correlate with some of our own key intuitions
about how problem solving occurs “in the wild.” Real world problem solving (RWPS) is
different from those that occur in a classroom or in a laboratory during an experiment. They
are often dynamic and discontinuous, accompanied by many starts and stops. Solvers are
never working on just one problem. Instead, they are simultaneously juggling several
problems of varying difficulties and alternating their attention between them. Real world
problems are typically ill-defined, and even when they are well-defined, often have open-
ended solutions. Coupled with that is the added aspect of uncertainty associated with the
solver’s problem-solving strategies. As introduced earlier, an important dimension of RWPS
is the continuous interaction between the solver and their environment.
Like discovery events, there’s typically never one singular impasse or distraction event. The
solver must iterate through the problem-solving process experiencing and managing these
sorts of intervening events including impasses and discoveries.
Analytical Problem-Solving
In psychology and neuroscience, problem-solving broadly refers to the inferential steps
taken by an agent that leads from a given state of affairs to a desired goal state. The agent
does not immediately know how this goal can be reached and must perform some mental
operations.
The problem-solving literature divides problems based on clarity well-defined vs. ill-defined
or on the underlying cognitive processes, analytical, memory retrieval, and insight. While
memory retrieval is an important process.
Problem Definition and Representation
An important initial phase of problem-solving involves defining the problem and forming a
representation in the working memory. If the problem is familiar and well-structured, top-
down executive control mechanisms are engaged. The problem representation requires
encoding problem information for which certain visual and parietal areas are also involved,
although the extent of their involvement is less clear.

Planning
The central executive network, particularly the top-level management is largely involved in
plan formation and in plan execution. Planning is the process of generating a strategy to
advance from the current state to a goal state. This in turn involves retrieving a suitable
solution strategy from memory and then coordinating its execution.
Creativity
In a research at 1930s, it is noted that “most instances of “real” problem solving involves
creative thinking”. Researcher performed several experiments to study mental fixation and
insight problem solving. This close tie between insight and creativity continues to be a
recurring theme, one that will be central to the current discussion. If creativity and insight
are linked, then it is reasonable to turn to the creativity and insight literature for
understanding the role played by the environment.
A large portion of the creativity literature has focused on viewing creativity as an internal
process, one in which the solvers attention is directed inwards, and toward internal stimuli,
to facilitate the generation of novel ideas and associations in memory. Focusing on
imagination, a number of researchers have looked at blinking, eye fixation, closing eyes, and
looking nowhere behaviour and suggested that there is a shift of attention from external to
internal stimuli during creative problem solving. The idea is that shutting down external
stimuli reduces cognitive load and focuses attention internally. Other experiments studying
sleep behaviour have also noted the beneficial role of internal stimuli in problem solving.
The notion of ideas popping into ones’ consciousness, suddenly, during a shower is highly
intuitive for many and researchers have attempted to study this phenomenon through the
lens of incubation, and unconscious thought that is internally-driven. There have been
several theories and countertheories proposed to account specifically for the cognitive
processes underlying incubation but none of these theories specifically address the role of
the external environment.
Insight Problem Solving
Analytical problem solving is believed to involve deliberate and conscious processing that
advances step by step, allowing solvers to be able to explain exactly how they solved it.
Inability to solve these problems is often associated with lack of required prior knowledge,
which if provided, immediately makes the solution tractable. Insight, on the other hand, is
believed to involve a sudden and unexpected emergence of an obvious solution or strategy
sometimes accompanied by an affective experience.
Methods to real-world problem solving
1. Participation (outpouring voice) approach
This approach is especially based on the creativity. Every students have special creativeness
in any particular area or field. Students can produce some inspired view, idea and resources
to overcome the real-world problem. Example; student of class 3 in Britain has suggested
school teacher to give home assignment regarding on the plastic road. Parent of the student
discussed with scientists and they tested plastic to make road raw material.
2. Project based learning approach
We can start either with a challenging problem or question and then tie it to our standards,
or we can start with our standards and connect them to a real-world challenge.
This approach is more foundational to project-based learning, for many reasons, including
student engagement, student voice, relevance and authenticity. But beyond that, we also do
it because this is where jobs are. Jobs are created and grown as we work to address the real
problems facing our world and peoples. Our students are ready to tackle the problems
facing our world. They have a voice. They have the tools and resources. And they are not
afraid to collaborate and form new communities poised for the problem-solving work that
needs to be done.
Students can carry them to collaborate, and use new technologies and form new
professional networks in order to address our current and future challenges. Let’s be
honest, our best hope of improving the status of our planet’s many issues truly lie with our
youth.
3. Problem solving approach

There are a number of current and ongoing real-world challenges that we currently face and
probably will for a long time. “problem-solving” in this context, as it implies that we can fix,
cure or eradicate a problem or challenge, but by going after our problems with new
solutions, we can certainly move progress forward. And in that movement, there is magic.
There is innovation. There is change. There is our collective human mission: how can we
creatively collaborate, critically think and communicate in ways that make our world a
better place to live.
Project work
Reality: We all use mathematics in every day. Mathematics is the universal language.
Mathematics helps for playing a game, listening to music, mankind and creation.
Mathematics tunes the creativity of students and turn their dreams into reality.

Math helps building things: Ask any contractor or construction worker--they'll tell you just
how important math is when it comes to build anything.

To create something of lasting value out of raw materials requires creativity, the right set of
tools, and a broad range of mathematics. Figuring the total amount of concrete needed for
a slab; accurately measuring lengths, widths, and angles; and estimating project costs are
just a few of the many cases in which math is necessary for real-life home improvement
projects.

Business investment

A businessman, Mr. Thapa, as presented the problem regarding the investment in new
business. He is planning to operate book shop in city.
The described case of Mr. Thapa, a book shop owner, we came to learn that, he is
facing problem on future planning and judging the profitability of the business
operation. To solve the problem, he mainly needs mathematical application in his
job and financial analysis. As, we know he is not well-educated, he does not know
mathematical application in judging profitability of business. He lacks knowledge about his
business’s selling targets against the cost of the products to be sold. For this, he needs break
even analysis. Using the analysis, he will be acknowledged of the point of selling where
the cost and revenue will be equal and after that sale, any additional sale will make
profit. This analysis will help him to set more reliable target of sales. He will also be
able to extend future purchase and sale.
Before break even analysis Mr. Thapa needs to calculate his cost of goods perfectly.
An important part of cost and expenditure is the yearly depreciation of the furniture
and the equipment used in the business. As Mr. Thapa lacks education he has little
knowledge on use of mathematics in valuation of depreciation. To find depreciated value
easily and correctly, arithmetic progression (AP) is applied in the solution of the case. It
relives a businessman from just assuming depreciation without proper knowledge.
The use of log in calculation eases the complicated tasks in business accounting. The
presentation of logarithm in calculating compound interest of loan reveals its utility. These
described terms are presented in the solution of the case of Mr. Thapa on application of
mathematics in business.
To students: Prepare a project work based on math helps building things.

Teacher Tip: Consider incorporating a small building project in the classroom--like a simple

Math is in the Grocery Store

Grocery shopping needs a broad range of math knowledge from multiplication to estimation
and percentages.

Each time customers calculate the price per unit, weigh produce, figure percentage
discounts, and estimate the final price.

To students: Prepare a project work based on math is in the Grocery Store.

Teacher Tip: Encourage students to play math challenges at the grocery store with or
without their family. They can estimate the total cost prior to checkout. Encourage students
to incorporate coupons, sales, and adjusted pricing for bulk items. The little bargain
shoppers will thank later when they’re saving money on their own groceries.

Teacher Tip: Teacher could also organise a field trip to the grocery store with the help of a
few parents working with smaller student groups making lists and pricing out items ahead of
time, that class can then use to cook with these items.

Math Makes Cooking Fun

Cooking and baking are sciences all their own and can be some of the most rewarding ways
of introducing children to mathematics.

Recipes are really just mathematical algorithms or self-contained, step-by-step sets of

Working in the kitchen requires a wide range of mathematical knowledge, including but not
limited to:

 measuring ingredients to follow a recipe

 multiplying, dividing fractions to account for more or less than a single batch

 converting a recipe from Celsius to Fahrenheit

 converting a recipe from metric (mL) to other standard units (teaspoon, tablespoon,
cups)

 calculating cooking time per each item and adjusting accordingly

 understanding ratios and proportions, particularly in baking (ex. the recipe calls for 1
egg and 2 cups of flour, then the ratio of eggs to flour is 1:2).

If conversions are necessary. Celsius or the metric system, and students can find doing
the math a fun part of the cooking experience.

Conversion method:

Celsius to Fahrenheit Conversion

Ex. The recipe calls for the oven to be set at 230°C, but yours is labelled by
Fahrenheit. To convert from Celsius to Fahrenheit in this recipe, follow the
following formula:

Formula: °C x 9/5 + 32 = °F

230 x 9/5 + 32 = °F

396 + 32 = 446°F

Metric to US Standard Unit Conversion

1 legal cup = 240 mL

1 tablespoon = 14.79 mL

1 teaspoon = 4.92 mL

1 fluid ounce = 29.57 mL

Teacher Tip: Organise baking food item in canteen with matric measure.

Questions

1. What is mathematics of real-world problem?

2. Prepare note based on real-world problem with mathematical example.

3. Prepare project work regarding new student admission in your school with mathematical
base to highlight the real-world problem.

Project work

Participate at least one project work according to the guideline of your teacher and present it
practically in your class. The field may be shopping mall, cinema hall, fun park, picnic, school
canteen, school administration activities etc.
Questions

1. What do you know about real world problem?

2. Why the society is facing various problems? Do you have any suggestion to overcome the social
problem?

3. What are the general area of problems in the globe? How international agencies are solving
them?

4. What are the basic approaches to problem solving?

5. How mathematics helps to solve the global problems?

Project Work

Prepare problem you have faced in your college. The problems may arise in college peers, teachers,
administration, canteen, transportation, computer and other labs. Prepare problems and suggest to
solve them.