Category: Critical thinking

The ability to think critically and solve problems is useful in many areas of work and study. These skills can be taught and learned separately, although critical thinking is often useful in problem solving. Thinking critically means considering things objectively, including the pros and cons or problems and benefits of a topic or situation. Thinking critically enables you to take a balanced look at a topic which is useful for essays but also for making decisions in real life. Problem solving skills are useful in many situations such as, working out math equations, working out the best route to get somewhere or deciding how many people you need to hire to finish a project.

Determine the facts. To think critically, you must be objective and that means differentiating between what you assume, or what you think you know, and what is factual. You may need to perform some research to ascertain more detail. This could involve spending time at the library, searching online or talking to colleagues or people from other organizations. Gathering data and establishing the facts is key to being able to critically think about something and solve related problems.

Assess your data. Think of resources you can use to determine more facts and consider the value of those resources. Are they biased? Are they based on someone's interpretation of the facts? Are they only relevant to one country or culture? Are they historical? Interrogating your data sources will help you interpret that data effectively and critically.

Balance your perspective. If time allows, using a wide variety of data sources will help you balance your perspective and help you to think about a topic openly and without prejudice. If you are on a tight deadline and you think your research may not give a full picture of the topic, bear this in mind when you assess the data you have.

Practice your critical thinking. You don't have to wait for an essay to be assigned to you at college, you can employ critical thinking in all kinds of situations. If you've just watched a movie that made you laugh, think about why it made you laugh. If you believe in God, think about the reasons why you believe in God and consider what other perspectives there may be and why they came about. You don't always have to do lots of research, unless you really are studying for a college assignment or work. Thinking critically can become a habit you use everyday in all kinds of situations. Once you have mastered thinking critically it will help you solve problems.

Think logically. Logic is often the key to problem solving. For example, if a company employs five people but they have too much work, then the logical solution is to hire more staff. Working out how many people to employ and how many people the company can afford to employ are further, related problems that will also have one or more logical solutions. Thinking critically can help you to work out logical solutions and solve problems.

Research your problem. Make sure you know exactly what needs to be achieved and if there are any timescales, budgets or other similar issues involved. Then you'll be able to logically think through possible solutions until you've solved your problem.

Make it a habit. Completing sudoku games, crosswords and jigsaw puzzles are more than just ways to pass the time. They are all exercises in problem solving that you can use every day to make problem solving a habit. Puzzles like these are easy to solve because you understand the rules. If you're presented with a puzzle or problem you don't understand then it's time to use critical thinking.

Critical Thinking and Problem solving

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Numerous decisions are taken every day. People choose when to get up on a certain morning. what clothing to wear. and whether to read a particular book. Most of the decisions made throughout the day are relatively trivial or inconsequential. It probably does not matter too much if it is decided to sleep an extra 15 minutes on a certain morning or if a blue shirt is

selected rather than a green one. However. some of the decisions can carry substantial consequences. Choosing to get an undergraduate or graduate degree. deciding on a new job or career. or selecting one vendor out of many candidates to be the long-term supplier of a company of a necessary resource are important decisions that are likely to have a significant and meaningful impact. Learning understanding. and applying critical thinking and problem-solving skills can improve the quality of the decisions that mean the most to us. The research also explores some fields where critical thinking proves a pathfinder in finding the correct solution to a problem

Critical Thinking and Problem Solving

Critical thinking and problem solving have been identified as essential skills for college students. Problem solving is defined as a step-by step process of defining the problem. searching for information. The goal of problem solving is to find and implement a solution. usually to a well defined and well- structured problem. Critical thinking is a broader term describing reasoning in an open-ended manner. with an unlimited number of solutions. The critical thinking process involves constructing the situation and supporting the reasoning behind a solution. Traditionally. critical thinking and problem solving have been associated with different fields. critical thinking is rooted in the behavioral science. whereas problem solving is associated with the math and science disciplines. Although a distinction is made between the two concepts. in real life situations the terms critical thinking and problem solving are often used interchangeably. In addition. assessment tests frequently overlap or measure both skills. Problem solving is defined as understanding the problem. being able to obtain background knowledge. generating possible solutions. identifying and evaluating the process. and exhibiting problem-solving dispositions

It is easy to fall into routine ways of thinking instead of being creative. The accompanying display lists some common barriers to creative thinking

A major block to creativity is groupthink (going along with the majority opinion while personally having another viewpoint. Nurses or the employees of the company. who engage in groupthink generally. wish to avoid interpersonal conflict. It takes intellectual courage to think something new and different from one 's peers. and then act on those thoughts. Independent thinking is a hallmark of persons who think critically and creatively

Critical Thinking and Problem Solving

Critical thinking includes problem solving and decision making processes. People use problem solving in their daily lives. With the problem-solving method. problems are identified. information is gathered. a specific.

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Promoting critical thinking and problem solving in mathematics education is crucial in the development of successful students. Critical thinking and problem solving go hand in hand. In order for students to learn mathematics through problem solving, they must also learn how to think critically. Critical thinking has not been at the forefront of teaching strategies in schools. Teachers need to see the importance and the need to begin promoting these key strategies. Critical thinking is such an important aspect for

Becoming a critical Thinker

The process of critical thinking possess many definitions although may be self explained as a highly.

children to learn in school. Many adults today have no idea on how to think critically. This is very sad because thinking critically can broaden your mind and give you such a feeling of intelligence and self-confidence. It used to be that teachers just taught material and gave the answers without any explanation of how the answer can to be. The reason they never gave an explanation was because they were never taught to think critically or even if they

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were, teaching critical thinking is a lot harder than just giving students the answer. We, as future teachers, need to take our job seriously and not always try to find the easy way out when it comes to teaching material. We need to realize the importance of critical thinking and not put it on the back burner. Another reason that many adults today do not think critically is that many educators have believed that only certain students are capable of

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thinking critically. Critical thinking strategies are usually only taught to the “advanced” ;students or the college prep students. Those students with lower grades and in vocational programs are not expected to use these strategies and therefore they are not introduced to them. This is very upsetting because everyone needs to learn these strategies. Critical thinking strategies are not only for the intelligent in an academic setting. These strategies can be used in everyday life. They can be used for finances,

Crisis Management

THE CUBAN MISSILE CRISIS - A Model of Crisis Management? A Biblical proverb says, "…by wise guidance, and in the abundance of counselors, there is victory." 1 It.

relationships, and even in life choices. People lacking these critical thinking strategies can be very impulsive and make a lot of choices that end up hurting them in many ways. I read an article by Thomas Sowell called Justice and Injustice. I really enjoyed this article because he emphasized how children on welfare have only about half as many words directed at them as children of working-class families and less than one-third as many words as children whose parents are

Crisis Management

THE CUBAN MISSILE CRISIS - A Model of Crisis Management? A Biblical proverb says, "…by wise guidance, and in the abundance of counselors, there is victory." 1 It is.

professionals. He also noted how painful this is because scientists have found that the physical development of the brain is affected by how much interaction young children receive. This then links critical thinking with social and economic status. If educators continue to show higher expectations for more “well-off” ;students and lower expectations for others than we will never be able to help a child off welfare or give every child the chance and ability to succeed. Another article I read

Career

The decision to choose a new career was extremely important to me. The function of a career is not just to provide a means to.

was entitled Intolerance is a

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*3.2 Skills in Problem Solving*

Basic mathematical skills such as solving equations and inequalities are necessary for mathematical problem solving. Formulating a problem can be very demanding but simplifying and solving the equation obtained, for example, is necessary to answer the question in the problem. Students who cannot manipulate algebraic expressions will definitely have difficulties in problem solving.

Our students, at UGRU, have difficulties in reading with understanding and extracting the information from the text of the problem. This skill has to be taught explicitly to our students. It is the first step in problem solving and students cannot make any progress if the problem is not understood.

*3.3 Thinking and Reasoning in Problem Solving*

Critical thinking is needed in all steps of problem solving. Students do not look back critically at the solution of a problem once it is solved. They tend to accept whatever answer they have obtained. Critical thinking is needed when extracting information from the text of the problem, formulating and solving the problem and analyzing the solution obtained. I now give an example of a problem that may be used to give opportunities to students to think critically.

Problem 6: Two boats on opposite banks of a river start moving towards each other. They first pass each other 1400 meters from one bank. They each continue to the opposite bank, immediately turn around and start back to the other bank. When they pass each other a second time, they are 600 meters from the other bank. We assume that each boat travels at a constant speed all along the journey. Is it possible to find the width of the river using the given information?

Students are guided to make a diagram and write the equations to formulate the problem.(see solution in appendix A)

Let t = 0 be the time when the two boats start moving. Let S1 and S2 be the constant speeds of the two boats and t1 the time when they first pass each other and t2 the time when they pass each other for the second time. Let X the width of the river.

Fig. 4: Diagram including unknowns in problem 6.

Because there are five unknowns and only four equations in the above system of equations. students are tempted to say that it is not possible to find the width X of the river. This particular problem can be used to generate activities where students will have to think in order to come up with a correct answer to the question in the problem. Enough time should be given to students to discuss such a challenging problem. They should be allowed to work in groups and if students cannot finish the work in class, they should be allowed to continue solving the problem as a homework assignment. Students will not benefit if the solution is given to them without giving them enough time to investigate this type of problems. Learning will take place through the time and efforts spent on finding a solution even if they have difficulties finding one. These types of problems involve a lot of thinking both to understand the problem and to come up with a solution and they are necessary if we want our students to develop their thinking skills to the highest level possible and become genuine problem solvers.

It is not difficult to design problems that can activate students thinking. One has to avoid problems with one obvious solution. Note that the question in problem 6 does not say �find the width of the river" but �is it possible to find the width of the river using the given information?". A question of the type �find the width of the river" already assumes that it is possible to find the width X. However questions of the second type are more demanding and therefore suitable to develop thinking skills.

Open ended problems, usually with many valid answers, can also be used as tools to generate activities where students have to think in order to come with answers. Useful discussions can be generated in order to compare all valid answers generated by students. I now give an example of an open ended problem.

*Problem 7:* Create a set of data points that satisfies the following conditions:

� The set includes 8 data values.

� The range of the data set is 20.

� The median is equal to the mean.

Show that your data set satisfies the conditions.

Logical reasoning is fundamental to success in mathematics in general and problem solving in particular. Inductive reasoning uses easy to understand cases to identify patterns and it can also be used to establish relationships between mathematical objects. Deductive reasoning uses mathematical definitions, axioms, rules and theorems to draw conclusions. Deductive reasoning is fundamental to critical thinking. Geometry problems may be used as tools to develop deductive reasoning [14]. I believe that both must be used and explicitly discussed with students.

This problem can be solved using ratios because the ratio of the weight of bricks to the number of bricks will be a constant proportion.

This is an excellent question because ratios and proportion can be applied to many routine problems encountered in everyday life. Ratios allow you to compute unit prices, projected cost, projected weight and volume, quantity of cooking ingredients, and solve many other common problems.

I am going to spend a little more space on the preliminary explanation because ratios are so useful.

For example, when shopping for the best value of a particular item, ratios will allow you to compare unit prices between items sold in different quantities.

Suppose you are shopping for a particular kind of breakfast cereal. If you are comparing the prices for boxes with different quantities (say, a 48 oz versus 35 oz box), ratios will allow you to compute prices per ounce.

Suppose you are shopping for small bundles of firewood. If you need to compare the prices for different quantities (say. 75 ft³ versus 1.5 ft³), ratios will allow you to compute prices per ft³.

A direct proportion between two variables means that one variable is a constant multiple of the other variable.

The terms “proportional relationship”, “direct variation” and “direct proportion” all mean the same thing. The terms are interchangeable.

The equation for a “proportional relationship” ALWAYS looks like this:

k is a constant. It is called the “constant of variation”.

__I’m going to rearrange that equation__ so it looks like this:

In other words, a direct proportion means that *DIVIDING the value of ONE VARIABLE BY THE value of the OTHER variable is a CONSTANT value* (*k, the constant of variation* ). (I’ll apply this idea to your problem shortly).

*For example*. if you have a job and are paid by the hour, your pay is proportional to the number of hours you work.

The more hours you work, the higher your pay.

The fewer hours you work, the lower the pay.

However, your total pay divided by the total number of hours you work is a constant value.

If your rate of pay is $25 per hour and you work 10 hours, you will earn $250.

$250 ÷ 10 hours = $25 per hour

If your rate of pay is $25 per hour and you work 1000 hours, you will earn $25,000.

$25,000 ÷ 1000 hours = $25 per hour

Pay divided by hours always EQUALS the same number, the CONSTANT of variation. In this example the constant of variation is 25. The constant of variation (25) will not change, regardless of the number of hours you work.

The *equation for computing the weight of one brick* in your problem statement is the same equation discussed in the preceding paragraphs. It will look like this:

*(weight of bricks) = k * (number of bricks)*

You need to calculate k, the constant of variation. That is the answer to your question.

The constant of variation brick is:

(weight of brick) / (number of bricks) = k

Since the problem statement presents ¾ of a brick with a weight of ¾ pound:

(¾ pounds) / (¾ of a brick) = k

(¾ pounds) / (¾ of a brick) = 1

k = 1

The *final equation* is:

(weight of bricks) = k * (number of bricks)

(weight of bricks) = 1 * (number of bricks)

For the sake of simplicity, let w = “weight in pounds” and n = “number of bricks”:

w = 1 * n

when n = 1

w = 1 * n

w = 1 * 1

w = 1

*1 brick weighs 1 pound*

Here you will find everything your child need to improve your child’s math skills. There are no formulas and definitions, your child will not memorize. There is an opportunity for your child *to think, reason, and argue* to convince his opinion.

Do not force your child with correct answers. He has his own logic, and you have no other way to get to know it patiently and kindly to support his version.

FUNtastic math worksheets focus on the development of *critical thinking, cognitive skills, reasoning, and problem solving*. as well as lead your child to *analyze and evaluate the results and become detail-oriented* .

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*Chapter Two: Characterizing Critical Thinking*

I begin the theoretical part of this chapter by examining the meanings of 'critical' and 'thinking'. After a systematic review of various definitions of 'critical thinking', I serve up the definition that will underpin the remainder of the handbook. I close by supplying an organized list of skills that figure into the process of critical thinking. In the applications part to follow, I offer teaching points and instructional tips related to an understanding of critical thinking and its attendant skills, along with an annotated bibliography of various books that concern critical thinking and critical thinking pedagogy.

*Introduce and use the technical terms.*Critical thinking, like most subjects, has its own technical terminology. Don’t shy away from using it in the classroom. It serves a number of valuable purposes. First, terms like "argument", "conclusion", and "valid" are introduced to mark distinct conceptual boundaries that you must respect if you are to do a competent job of assessing pieces of reasoning. Second, they fit together into a coherent fabric that should be delivered as one complete bolt and not as a collection of random swatches. Finally, when you use the terminology, you signal to the students that you are talking about critical thinking again. The more they hear these terms, the more ingrained the concepts become, and the more likely it is that they will emerge from your classroom with skills that can be taken and used in other classes.

*Work on the big picture.*Students need to learn the value of critical thinking first hand. Most have done it from time to time, but they likely have not done it systematically or put much thought into when they should do it. Put students in positions to determine where critical thinking is necessary. Work on assessing problems and asking questions. Here are some ideas for how this might be done:

- Have students come to class with two or three questions about the readings. If the reading is one that contains reasoning and a conclusion—this could be a fictional piece, of course—then have them identify the conclusion and ask questions about the reasons offered for that conclusion. Have them submit the questions, evaluate them, and return them.

- Have the students develop their own definitions, in a 10 minute free write before this discussion. Ask them to muse on the meaning of the term and work toward expressing what they understand by it. In discussion after this exercise, work with what they have developed by asking for illustration and defense. Be sure to do this in light of the meanings of the specific terms. (This is perhaps best done in classes where critical thinking as a topic is part of the stated content of the course, e.g. Core Discovery courses.)

*III. Annotated Bibliography of Readings Available at the UI Library or via ILL*

What follows is a bibliography of various books on critical thinking. A good many of these are located in the library, but some are only available via ILL. (The ILL books are marked as such.) The materials are listed alphabetically by author's name.

*Learning Through Problem Solving*. Daniel Apple, et al. (Eds.). This book contains*many*examples and problems in mathematics that could be used for teaching a variety of critical thinking skills. (Or, alternatively, it could teach problem solving skills that will come in handy as a part of the suite of critical thinking skills you might want your students to acquire.) It is pitched mainly at college instructors, but still worth a look if you teach math.

43 page) pamphlet on the nature of critical thinking. It includes three parts: "What Is Critical Thinking?", "Efforts to Improve Students' Thinking Skills", and "Improving Students' Critical Thinking Skills: Some Exercises". There are 20 pages or so of exercises. It's worth a look.

26 page) pamphlet that is mainly theoretical, but aimed at someone who will be taking on the challenge of teaching critical thinking. After the introduction, which includes a historical perspective, the parts are: "The Various Kinds of Thinking", "Influences on Thinking and Learning", and "The Teaching of Thinking".

50 pages) that is primarily theoretical. The parts are: "Higher Order Skills: A Working Definition and a Historical Perspective", "The Nature of Thinking and Learning: Going Beyond the Routine", "General Reasoning: Improving Intelligence", "Thinking in the Curriculum", "Cultivating the Disposition to Higher Order Thinking", and then a summary.