What is the final concentration of the solution produced when The solution contained What is the molarity of the solution? An experiment in a general chemistry laboratory calls for a 2.

How many mL of The US Environmental Protection Agency EPA places limits on the quantities of toxic substances that may be discharged into the sewer system. Limits have been established for a variety of substances, including hexavalent chromium , which is limited to 0. If an industry is discharging hexavalent chromium as potassium dichromate K 2 Cr 2 O 7 , what is the maximum permissible molarity of that substance?

Paul Flowers University of North Carolina - Pembroke , Klaus Theopold University of Delaware and Richard Langley Stephen F. Austin State University with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.

Work on a jigsaw puzzle — Puzzles can be done on your own, or as a social activity. Putting together a puzzle requires concentration and spatial awareness, activating multiple parts of the brain and improving short-term memory.

Play a musical instrument — Research has shown that learning to play an instrument can improve neuroplasticity and help improve your memory. Playing music engages multiple regions of the brain, providing numerous benefits. Challenge yourself, no matter your age! Trying new hobbies is a great mental exercise to sharpen your brain.

You also may find a new activity that brings more joy to your life. Meditate — The practice of meditation has been around for thousands of years as a tool for reducing stress, clearing your mind, promoting relaxation, and improving focus. Meditation is a powerful tool that can boost your brain anytime, anywhere.

Play brain games — Chess, crossword puzzles, and sudoku all fall under this category. Brain games are an easy and fun way to improve concentration and strengthen memory.

The best part is that they only take a few minutes to play and offer a nice break during the day. Read a book with a book club — Reading a book offers many benefits, including stimulating different areas of your brain to process and analyze information. When you participate in a reading group , your brain will need to remember information for later recall.

This information recall is highly beneficial to protecting short-term memory. Book clubs also can provide a fun and supportive social network. Practice healthy habits You guessed it, those healthy habits that affect so many areas of your life are also tied to a healthy brain. Exercise — Moving your body increases blood flow to the brain, which can improve your ability to think critically, clearly, and creatively.

Additionally, physical activity is a known way to reduce stress and anxiousness. Research has shown creativity and problem-solving to be negatively affected by stress. Using exercise to combat stress can improve your ability to find solutions with a clear mind. By exercising regularly, your overall physical, emotional, and brain health may be positively impacted.

Healthy Diet — Dr. Daniel Amen teaches that one of the secrets to a healthy brain is to focus on detoxification in your diet. This includes avoiding alcohol, drinking plenty of water, and consuming detoxifying vegetables. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution.

Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4. Which type of bias involves becoming fixated on a single trait of a problem? Which type of bias do you recognize in your own decision making processes?

anchoring bias: faulty heuristic in which you fixate on a single aspect of a problem to find a solution. availability heuristic: faulty heuristic in which you make a decision based on information readily available to you.

confirmation bias: faulty heuristic in which you focus on information that confirms your beliefs. functional fixedness: inability to see an object as useful for any other use other than the one for which it was intended.

representative bias: faulty heuristic in which you stereotype someone or something without a valid basis for your judgment. trial and error: problem-solving strategy in which multiple solutions are attempted until the correct one is found.

working backwards: heuristic in which you begin to solve a problem by focusing on the end result. Skip to content Learning Objectives By the end of this section, you will be able to: Describe problem solving strategies Define algorithm and heuristic Explain some common roadblocks to effective problem solving.

Additional Problem Solving Strategies : Abstraction — refers to solving the problem within a model of the situation before applying it to reality.

Analogy — is using a solution that solves a similar problem. Brainstorming — refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.

Divide and conquer — breaking down large complex problems into smaller more manageable problems. Hypothesis testing — method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.

Lateral thinking — approaching problems indirectly and creatively by viewing the problem in a new and unusual light. Means-ends analysis — choosing and analyzing an action at a series of smaller steps to move closer to the goal. Method of focal objects — putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal.

Morphological analysis — analyzing the outputs of and interactions of many pieces that together make up a whole system. Proof — trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem.

Reduction — adapting the problem to be as similar problems where a solution exists. Research — using existing knowledge or solutions to similar problems to solve the problem.

Root cause analysis — trying to identify the cause of the problem. Missionary-Cannibal Problem Three missionaries and three cannibals are on one side of a river and need to cross to the other side. How long did it take you to solve this sudoku puzzle? You can see the answer at the end of this section.

Connect all nine dots with four connecting straight lines without lifting your pencil from the paper: Did you figure it out? The answer is at the end of this section. What steps did you take to solve this puzzle? You can read the solution at the end of this section. An example of trying to overcome functional fixedness in Apollo 13 :.

Exercises Review Questions: 1. an algorithm b. a heuristic c. a mental set d. trial and error 2. divide and conquer b. means-end analysis c.

analogy d. experiment 3. trial and error 4. anchoring bias b. confirmation bias c. representative bias d. availability bias 5. Which type of bias involves relying on a false stereotype to make a decision? availability bias 6. social adjustment b. student load payment options c. emotional learning d.

insight learning 7. functional fixedness b. working memory d. insight learning Critical Thinking Questions: 1. What is functional fixedness and how can overcoming it help you solve problems? How does an algorithm save you time and energy when solving a problem?

Personal Application Question: 1. Glossary: algorithm anchoring bias availability heuristic confirmation bias functional fixedness heuristic hindsight bias mental set problem-solving strategy representative bias trial and error working backwards.

Answers to Exercises Review Questions: 1.

If the solution has a density of 0. Copper I iodide CuI is often added to table salt as a dietary source of iodine. How many moles of CuI are contained in 1. What are the mole fractions of H 3 PO 4 and water in a solution of What are the mole fractions of HNO 3 and water in a concentrated solution of nitric acid What is the difference between a 1 M solution and a 1 m solution?

In a 1 M solution, the mole is contained in exactly 1 L of solution. In a 1 m solution, the mole is contained in exactly 1 kg of solvent. What is the molality of phosphoric acid, H 3 PO 4 , in a solution of What is the molality of nitric acid in a concentrated solution of nitric acid Calculate the molality of the solution.

Paul Flowers University of North Carolina - Pembroke , Klaus Theopold University of Delaware and Richard Langley Stephen F. Austin State University with contributing authors. Founded in to deepen the understanding of the intersection of well-being, purpose, and performance.

EN - US. For Business. Conditions related to concentration. Despite your best efforts, things are not progressing.

You need to focus on the task in front of you. But you just can't concentrate. The inability to concentrate on the task at hand is one of the maladies of our time--everyone wants to know how to focus better, how to concentrate. Yet, the benefits of improving concentration and focus make it an issue worth addressing.

Concentration means control of attention. It is the ability to focus the mind on one subject, object, or thought, and at the same time exclude from the mind every other unrelated thought, ideas, feelings, and sensations.

That last part is the tricky part for most of us. To concentrate is to exclude, or not pay attention to, every other unrelated thought, idea, feeling, or sensation.

Our daily routine is dominated by switching in and out of our mobile phones and computer. We get a constant influx of messages from WhatsApp, email, Telegram, and the half-dozen other apps that are somehow critical to our job.

We constantly search for information to help solve our daily problems or get our work done. Frequent distractions affect productivity. It takes longer to finish a task. It affects memory. This is a common question for many. And often, the answer can be found in your daily activities and some areas you can control.

These can include:. These are just a few examples of reasons you may not be able to concentrate. And they largely fall under five primary categories or factors. We are bombarded by a constant flow of information, whether new or old, during the process of doing something.

Researchers have found that our brains are so primed for this distraction that just seeing our smartphone impairs our ability to concentrate. We constantly assess whether the information is useful, sufficient, or meaningless. The sheer quantity coming in muddles our assessment of whether we actually need more information to make decisions.

Scientists have found that lack of sleep can lead to lower alertness , slower thought processes, and reduced concentration. You will have more difficulty focusing your attention and may become confused. As a result, your ability to perform tasks especially relating to reasoning or logic can be seriously affected.

Chronically poor sleep further affects your concentration and memory. Allison T. Siebern from the Stanford University Sleep Medicine Centre notes that if you cannot concentrate on what is at hand, it is unlikely to make it to either your short- or long-term memory. Have you ever noticed how vigorous exercise leaves you feeling more relaxed and energetic throughout the day?

You may feel tightness in your neck, shoulder, and chest and such persistent, low-level discomfort can affect your concentration. What we eat contributes to how we feel , including our mental sharpness and clarity, throughout the day. Low-fat diets can ruin focus because the brain needs certain essential fatty acids.

Other restrictive diets may negatively affect concentration by not providing the nutrients the brain needs or by creating hunger, cravings, or feeling of unwellness in the body that are themselves distracting. Depending on what you are doing, the environment can affect your focus. Obviously, a noise level that is too loud is a problem, but many people also have difficulty concentrating when it is too quiet.

A favorite song quickly has you singing along, happily distracted, while less distinct instrumentals might keep you attuned to the task.

Lighting that is too bright or too dim can affect your vision. A room that is too hot or too cold creates discomfort. Depending on the cause, you may have to temporarily accept that your concentration is low and learn a few tricks to reduce the impact or accept the dips as they come.

If you need help with concentration and think your difficulties go beyond the list above, consult with a professional. Now you know why you need help with concentration.

What can help you to focus better? Eliminate distractions. How do we focus better if we are always bombarded with information? Make a practice blocking time in your schedule to do a specific task or activity.

During this time, request that you be left alone or go to a place where others are unlikely to disturb you: a library, a coffee shop, a private room.

Close social media and other apps, silence notifications, and k eep your phone hidden from sight in a bag or backpack.

As described in HBR, researchers found that cognitive capacity was significantly better when the phone was out of sight , not just turned off. Keep Your primary focus is to complete what you need to do. Shutting off both internal and external disturbances can help you to concentrate.

Reduce multitasking. Attempting to perform multiple activities at the same time makes us feel productive. And lower productivity can lead to burnout. Examples of multitasking include listening to a podcast while responding to an email or talking to someone over the phone while writing your report.

Such multitasking not only hampers your ability to focus but compromises your work quality. Practice mindfulness and meditation. Meditating or practicing mindfulness activities can strengthen well-being and mental fitness and improve focus.

During the meditation process, our brain becomes calmer and our whole body becomes more relaxed. We focus on our breath during the process so that we will not be distracted by our minds. With practice, we can learn to use our breath to bring our attention back to a particular task so that it can be done well even if we get interrupted.

Get more sleep. Many factors affect your sleep. One of the most common is reading from an electronic device like a computer, phone, or tablet or watching your favorite movie or TV show on an LED TV just before bedtime. Research has shown that such devices emit light towards the blue end of the spectrum.

Such light will stimulate your eye retina and prevent the secretion of melatonin that promotes sleep anticipation in the brain. Use a filter or "blue light" glasses to minimize such blue light or avoid all electronic devices before bed. Other ways to improve sleep include avoiding exercise late in the day, staying hydrated throughout the day, using journaling or breathing exercises to quiet the mind, and creating a predictable bedtime routine and schedule.

Choose to focus on the moment. It might feel counterintuitive when you feel unable to concentrate, but remember that you choose where you focus. It's tough to concentrate when your mind is always in the past and worrying about the future. Acknowledge the impact, what you felt, and what you learned from it, then let it go.

Similarly, acknowledge your concerns about the future, consider how you are experiencing that anxiety in your body, then choose to let it go. We want to train our mental resources to focus on the details of what matters at the moment.

Our minds go in the direction we choose to focus. Take a short break. This also might seem counterintuitive, but when you focus on something for a long time, your focus may begin to die down. You may feel more and more difficulty devoting your attention to the task.

Researchers have found that our brains tend to ignore sources of constant stimulation. Taking very small breaks by refocusing your attention elsewhere can dramatically improve mental concentration after that. The next time you are working on a project, take a break when you begin to feel stuck.

Move around, talk to someone, or even switch to a different type of task. You will come back with a more focused mind to keep your performance high. Connect with nature. Research has found that even having plants in office spaces can help increase concentration and productivity, as well as workplace satisfaction and better air quality.

Finding time to take a walk in the park or appreciating the plants or flowers in your garden can boost your concentration and help you feel refreshed. Train your brain. Scientific research is starting to amass evidence on the ability of brain training activities to enhance cognitive abilities, including concentration, in adults.

Such brain training games for concentration can also help you develop your working and short-term memory, as well as your processing and problem-solving skills. Examples of such games include jigsaw puzzles, sudoku, chess, and brain-stimulating video games.

Start your day with simple exercise and get your body moving. According to the May issue of the Harvard Men's Health Watch, regular exercise releases chemicals key for memory, concentration, and mental sharpness. Other research found that exercise can boost the brain's dopamine, norepinephrine, and serotonin levels and all these will affect focus and attention.

Individuals who do some form of exercise or sports perform better on cognitive tasks when compared with those who have poor physical health. Physical movement helps relax the muscles and relieve tension in the body.

Since the body and mind are so closely linked, when your body feels better so, too, will your mind. Listen to music. Music has been shown to have therapeutic effects on our brains.

Light music may help you to concentrate better, but some music may distract you. Experts generally agree that classical music and nature sounds, such as water flowing, are good choices for concentration while music with lyrics and human voices may be distracting.

In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.

Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage suggesting that while collecting data for what would later be his book The Mentality of Apes on Tenerife in the Canary Islands between and , Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands.

While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole.

Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as insight , the sudden perception of useful or proper relations. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach.

In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain.

As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight.

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills.

Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below see figure is a 4×4 grid.

To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column.

Time yourself as you solve this puzzle and compare your time with a classmate. Here is another popular type of puzzle figure below that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:.

Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime Cyclopedia of Puzzles, n. Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? One doorway that has always been open in the past is now locked.

The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway.

A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft.

An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended.

For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals.

The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness.

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation.

Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis.

In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision.

These biases are summarized in the table below. Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above?

Here are the answers. Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution.

Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4. Which type of bias involves becoming fixated on a single trait of a problem? Which type of bias do you recognize in your own decision making processes?

anchoring bias: faulty heuristic in which you fixate on a single aspect of a problem to find a solution. availability heuristic: faulty heuristic in which you make a decision based on information readily available to you.

confirmation bias: faulty heuristic in which you focus on information that confirms your beliefs. functional fixedness: inability to see an object as useful for any other use other than the one for which it was intended. representative bias: faulty heuristic in which you stereotype someone or something without a valid basis for your judgment.

trial and error: problem-solving strategy in which multiple solutions are attempted until the correct one is found. working backwards: heuristic in which you begin to solve a problem by focusing on the end result.

Skip to content Learning Objectives By the end of this section, you will be able to: Describe problem solving strategies Define algorithm and heuristic Explain some common roadblocks to effective problem solving.

Additional Problem Solving Strategies : Abstraction — refers to solving the problem within a model of the situation before applying it to reality. Analogy — is using a solution that solves a similar problem. Brainstorming — refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.

Divide and conquer — breaking down large complex problems into smaller more manageable problems. Hypothesis testing — method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.

Lateral thinking — approaching problems indirectly and creatively by viewing the problem in a new and unusual light. Means-ends analysis — choosing and analyzing an action at a series of smaller steps to move closer to the goal.

Method of focal objects — putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal. Morphological analysis — analyzing the outputs of and interactions of many pieces that together make up a whole system.

Proof — trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem. Reduction — adapting the problem to be as similar problems where a solution exists.

Research — using existing knowledge or solutions to similar problems to solve the problem. Root cause analysis — trying to identify the cause of the problem. Missionary-Cannibal Problem Three missionaries and three cannibals are on one side of a river and need to cross to the other side.

How long did it take you to solve this sudoku puzzle? You can see the answer at the end of this section. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper: Did you figure it out?

The answer is at the end of this section. What steps did you take to solve this puzzle? You can read the solution at the end of this section. An example of trying to overcome functional fixedness in Apollo 13 :.

Exercises Review Questions: 1. an algorithm b. a heuristic c. a mental set d. trial and error 2. Results showed that when they listened to music while working out, participants more than doubled their scores on verbal fluency tests in contrast to when they worked out in silence.

Working out problems by sorting your thoughts on paper and then viewing them more objectively is easier than having all your thoughts stuck in your head and will provide better problem solving strategies.

The powerful combination of body awareness, breathing, and meditation that is required during yoga practice has been shown to significantly raise cognitive test scores. Other results from a University of Illinois study include shorter reaction times, more accuracy, and increased attention.

The Cheerios Effect is the name physicists have given to the event that happens when the last few cheerios in a bowl always cling to each other.

The cause of this occurrence is surface tension. The takeaway is that when it comes to experiencing tension while trying to solve a problem, cling to those around you.

Draw connections. Work together to get the job done. Mind Maps , a visual snapshot of a problem and its possible solutions, can help focus the mind, stimulate the brain, increase the capacity for creative thinking, and generate more ideas for solutions.

Make a Mind Map by drawing your problem as the central idea. Next, make a separate Mind Map of all possible solutions to the central problem. Make a final branch with the most suitable solution for the main problem.

What is psychological distance? This happens because thinking more abstractly helps us form unexpected connections between seemingly unrelated concepts, thus allowing our minds to increase its problem solving capacity. When in action, our brains are quickly multitasking between moving, anticipating, strategizing, reacting, and performing.

Doing all these things at once requires an enormous amount of brain activity. This can be related to our working world when we plan, reason, monitor our actions and problem solve all at once. To learn more about how to develop your problem-solving and decision making capabilities or to receive training on applied strategic thinking skills , contact CMOE today!

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Home Blog How to Improve Problem Solving Skills [10 Ways]. How to Improve Problem Solving Skills [10 Ways]. Problem Solving. What Are Problem Solving Skills? But there are also a few universal problem solving skills we all need: Defining the Problem: Deeply understanding a problem through research , leading to better solutions.

Brainstorming: Creating a myriad of new solutions quickly. In group brainstorms, allow everyone to state ideas.